Title: | Diet Mendelian Randomization |
---|---|
Description: | Encodes several methods for performing Mendelian randomization analyses with summarized data. Similar to the 'MendelianRandomization' package, but with fewer bells and whistles, and less frequent updates. As described in Yavorska (2017) <doi:10.1093/ije/dyx034> and Broadbent (2020) <doi:10.12688/wellcomeopenres.16374.2>. |
Authors: | Stephen Burgess [aut, cre] , Olena Yavorska [aut], James Staley [ctb] , Fernando Hartwig [ctb] , Jim Broadbent [ctb] , Christopher Foley [ctb] , Andrew Grant [ctb], Amy Mason [ctb] , Ting Ye [ctb] , Haoran Xue [ctb] , Zhaotong Lin [ctb] , Siqi Xu [ctb], Ashish Patel [ctb] , Hyunseung Kang [ctb], Sheng Wang [ctb], Ville Karhunen [ctb] |
Maintainer: | Stephen Burgess <[email protected]> |
License: | GPL-2 | GPL-3 |
Version: | 0.2.0 |
Built: | 2024-11-08 04:59:11 UTC |
Source: | https://github.com/cran/MRZero |
Two sets of example data are included in the package: one illustrating uncorrelated variants, and the other correlated variants. These are the data on correlated variants.
calcium calciumse fastgluc fastglucse calc.rho
calcium calciumse fastgluc fastglucse calc.rho
An object of class numeric
of length 6.
An object of class numeric
of length 6.
An object of class numeric
of length 6.
An object of class numeric
of length 6.
An object of class matrix
(inherits from array
) with 6 rows and 6 columns.
The variables calcium
, and fastgluc
are the genetic associations with calcium and fasting glucose for 6 genetic variants reported by Burgess et al (2015). The respective standard errors of the associations are given as calciumse
and fastglucse
. The matrix of correlations between the genetic variants is given as calc.rho
.
These data can be used to test out the various functions in the package.
Stephen Burgess, Robert A Scott, Nic J Timpson, George Davey Smith, Simon G Thompson. Using published data in Mendelian randomization: a blueprint for efficient identification of causal risk factors. Eur J Epidemiol 2015; 30(7):543-552. doi: 10.1007/s10654-015-0011-z.
An object containing the confidence intervals produced using the conditional likelihood ratio method (CLR) and other identification-robust methods.
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
ARlower
The lower bounds of the causal estimate based on inverting Anderson and Rubin's test.
ARupper
The upper bounds of the causal estimate based on inverting Anderson and Rubin's test.
Klower
The lower bounds of the causal estimate based on inverting Kleibergen's test.
Kupper
The upper bounds of the causal estimate based on inverting Kleibergen's test.
CLRlower
The lower bounds of the causal estimate based on inverting Moreira's conditional likelihood ratio test.
CLRupper
The upper bounds of the causal estimate based on inverting Moreira's conditional likelihood ratio test.
CIMin
The smallest value used in the search to find the confidence interval.
CIMax
The largest value used in the search to find the confidence interval.
CIStep
The step size used in the search to find the confidence interval.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Internal function of mr_cML. Estimate theta, b vector, r vector with constrained maximum likelihood.
cML_estimate( b_exp, b_out, se_exp, se_out, K, initial_theta = 0, initial_mu = rep(0, length(b_exp)), maxit = 100 )
cML_estimate( b_exp, b_out, se_exp, se_out, K, initial_theta = 0, initial_mu = rep(0, length(b_exp)), maxit = 100 )
b_exp |
Vector of estimated effects for exposure. |
b_out |
Vector or estimated effects for outcome. |
se_exp |
Vector of standard errors for exposure. |
se_out |
Vector of standard errors for outcome. |
K |
Constraint parameter, number of invalid IVs. |
initial_theta |
Starting point for theta. |
initial_mu |
Starting point for mu. |
maxit |
Maximum number of iteration. |
A list contains: theta is the estimate causal effect, b_vec is the estimated vector of b, r_vec is the estimated vector of r.
cML_estimate(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, K = 5)
cML_estimate(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, K = 5)
Internal function of mr_cML. Get estimated theta, se of estimated theta and negative log-likelihood, using multiple random starting points.
cML_estimate_random( b_exp, b_out, se_exp, se_out, K, random_start = 0, maxit = 100 )
cML_estimate_random( b_exp, b_out, se_exp, se_out, K, random_start = 0, maxit = 100 )
b_exp |
Vector of estimated effects for exposure. |
b_out |
Vector or estimated effects for outcome. |
se_exp |
Vector of standard errors for exposure. |
se_out |
Vector of standard errors for outcome. |
K |
Constraint parameter, number of invalid IVs. |
random_start |
Number of random starting points, default is 0. |
maxit |
Maximum number of iteration. |
A list contains: theta is the estimate causal effect, se is standard error of estimated theta, l is negative log-likelihood, r_est is estimated r vector.
cML_estimate_random(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, K = 5)
cML_estimate_random(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, K = 5)
Internal function of mr_cML. Get the standard error of estimated theta from constrained maximum likelihood.
cML_SdTheta(b_exp, b_out, se_exp, se_out, theta, b_vec, r_vec)
cML_SdTheta(b_exp, b_out, se_exp, se_out, theta, b_vec, r_vec)
b_exp |
Vector of estimated effects for exposure. |
b_out |
Vector or estimated effects for outcome. |
se_exp |
Vector of standard errors for exposure. |
se_out |
Vector of standard errors for outcome. |
theta |
Estimated theta from cML. |
b_vec |
Estimated vector of b from cML. |
r_vec |
Estimated vector of r from cML. |
Standard error of theta.
# First get estimates: MLE_result = cML_estimate(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, K = 5) # Calculate standard error: cML_SdTheta(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, theta = MLE_result$theta, b_vec = MLE_result$b_vec, r_vec = MLE_result$r_vec)
# First get estimates: MLE_result = cML_estimate(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, K = 5) # Calculate standard error: cML_SdTheta(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse, se_out = chdloddsse, theta = MLE_result$theta, b_vec = MLE_result$b_vec, r_vec = MLE_result$r_vec)
An object containing the estimate produced using the debiased inverse-variance weighted (dIVW) method as well as various statistics.
Over.dispersion
Should the method consider overdispersion (balanced horizontal pleiotropy)? Default is TRUE.
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Estimate
The causal point estimate from the median-based method.
StdError
The standard error associated with Estimate
(obtained from bootstrapping).
CILower
The lower bound of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bound of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate from the Wald method.
SNPs
The number of SNPs that used in the calculation.
Condition
A measure defined as (average F-statistic -1)*sqrt(# snps) that needs to be large for reliable asymptotic approximation based on the dIVW estimator. It is recommended to be greater than 20.
An object containing the estimate produced using the MR-Egger method as well as various statistics.
The MR-Egger model uses a random-effects model; a fixed-effect model does not make sense as pleiotropy leads to heterogeneity between the causal estimates targeted by the genetic variants. The (multiplicative) random-effects model allows over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1).
Model
Model always takes the value random
, as only random-effects analyses are permitted.
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
Robust
Whether robust regression was used in the regression model relating the genetic associations with the outcome and those with the exposure.
Penalized
Whether weights in the regression model were penalized for variants with heterogeneous causal estimates.
Estimate
The causal point estimate from the MR-Egger method.
StdError.Est
The standard error associated with Estimate
.
Pvalue.Est
P-value associated with the causal estimate from the Wald method.
CILower.Est
The lower bound of the confidence interval for Estimate
based on StdError.Est
.
CIUpper.Est
The upper bound of the confidence interval for Estimate
based on StdError.Est
.
Intercept
The intercept estimate from the MR-Egger method. Under the InSIDE assumption, the intercept represents the average pleiotropic effect (average direct effect on the outcome) of a genetic variant. If the intercept differs from zero, this is evidence that the genetic variants are not all valid instruments; specifically, there is directional pleiotropy.
StdError.Int
The standard error associated with Intercept
.
Pvalue.Int
P-value associated with the intercept from the Wald method.
CILower.Int
The lower bound of the confidence interval for Intercept
based on StdError.Int
.
CIUpper.Int
The upper bound of the confidence interval for Estimate
based on StdError.Int
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
SNPs
The number of SNPs that were used in the calculation.
Causal.pval
P-value associated with the causal estimate.
Pleio.pval
P-value associated with the intercept (p-value for the MR-Egger intercept test of directional pleiotropy).
RSE
The estimated residual standard error from the regression model.
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that the MR-Egger regression model describes the associations with the outcome with no excess heterogeneity.
I.sq
A measure of heterogeneity between the genetic associations with the exposure (see Bowden IJE 2016: "Assessing the suitability of summary data for Mendelian randomization analyses using MR-Egger regression: The role of the I2 statistic."). Low values of I.sq
relate both to large differences in precision between MR-Egger and IVW estimates, and to more weak instrument bias (in a two-sample setting, this is attenuation of MR-Egger estimate towards the null).
An object containing the estimate produced using the inverse-variance weighted (IVW) method as well as various statistics.
Model
The model used for estimation: random-effects ("random"
) or fixed-effect ("fixed"
). The default option ("default"
) is to use a fixed-effect model when there are three or fewer genetic variants, and a random-effects model when there are four or more. The (multiplicative) random-effects model allows for heterogeneity between the causal estimates targeted by the genetic variants by allowing over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1, as in a fixed-effect analysis).
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
Robust
Whether robust regression was used in the regression model relating the genetic associations with the outcome and those with the exposure.
Penalized
Whether weights in the regression model were penalized for variants with heterogeneous causal estimates.
Estimate
The causal point estimate from the inverse-variance weighted method.
StdError
The standard error associated with Estimate
.
CILower
The lower bound of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bound of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate.
SNPs
The number of SNPs that were used in the calculation.
RSE
The estimated residual standard error from the regression model.
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.
Fstat
An approximation of the first-stage F statistic for all variants based on the summarized data.
Two sets of example data are included in the package: one illustrating uncorrelated variants, and the other correlated variants. These are the data on uncorrelated variants.
The variables ldlc
, hdlc
, trig
, and chdlodds
are the genetic associations with (respectively) LDL-cholesterol, HDL-cholesterol, triglycerides, and coronary heart disease (CHD) risk for 28 genetic variants reported by Waterworth et al (2010). The respective standard errors of the associations are given as ldlcse
, hdlcse
, trigse
, and chdloddsse
.
These data can be used to test out the various functions in the package.
ldlc hdlc hdlcse ldlcse trig trigse chdlodds chdloddsse lipid_effect lipid_other lipid_eaf
ldlc hdlc hdlcse ldlcse trig trigse chdlodds chdloddsse lipid_effect lipid_other lipid_eaf
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class numeric
of length 28.
An object of class character
of length 28.
An object of class character
of length 28.
An object of class numeric
of length 28.
Dawn Waterworth, Sally Ricketts, ..., Manj Sandhu: Genetic variants influencing circulating lipid levels and risk of coronary artery disease. Arterioscler Thromb Vasc Biol 2010; 30:2264-227. doi: 10.1161/atvbaha.109.201020.
An object containing the estimate produced using the maximum-likelihood method as well as various statistics.
Model
The model used for estimation: fixed-effect ("fixed"
) or random-effects ("random"
).
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
Psi
The correlations between genetic associations with the exposure and with the outcome.
Estimate
The causal point estimate from the inverse-variance weighted method.
StdError
The standard error associated with Estimate
.
CILower
The lower bound of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bound of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate.
SNPs
The number of SNPs that were used in the calculation.
RSE
The estimated residual standard error from the regression model.
Heter.Stat
Heterogeneity statistic (likelihood ratio statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.
The function mr_allmethods
implements Mendelian randomization analyses using summarized data to calculate estimates (as well as standard
errors and confidence interval limits) for all the methods included in the package (or alternatively for the group of methods chosen).
mr_allmethods(object, method = "all", ...) ## S4 method for signature 'MRInput' mr_allmethods(object, method = "all", ...)
mr_allmethods(object, method = "all", ...) ## S4 method for signature 'MRInput' mr_allmethods(object, method = "all", ...)
object |
An |
method |
Which estimation method should be included in the calculation. By default, all estimates are computed ( |
... |
Additional arguments to be passed to other methods. |
See mr_median
, mr_egger
, and mr_ivw
for details of how each of the methods is implemented.
An object of type MRAll
with the following slots :
Data |
The MRInput object used to calculate the various values. |
Values |
A data.frame containing the various estimates. |
Method |
The choice of methods estimated (default is |
See mr_median
, mr_egger
, and mr_ivw
.
mr_allmethods(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), method="main", iterations = 100) # iterations is set to 100 to reduce runtime for the mr_median method, # at least 10000 iterations are recommended in practice
mr_allmethods(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), method="main", iterations = 100) # iterations is set to 100 to reduce runtime for the mr_median method, # at least 10000 iterations are recommended in practice
The mr_clr
function calculates confidence intervals based on inverting the conditional likelihood ratio and other identification-robust tests.
mr_clr(object, nx, ny, alpha = 0.05, CIMin = -10, CIMax = 10, CIStep = 0.01) ## S4 method for signature 'MRInput' mr_clr(object, nx, ny, alpha = 0.05, CIMin = -10, CIMax = 10, CIStep = 0.01)
mr_clr(object, nx, ny, alpha = 0.05, CIMin = -10, CIMax = 10, CIStep = 0.01) ## S4 method for signature 'MRInput' mr_clr(object, nx, ny, alpha = 0.05, CIMin = -10, CIMax = 10, CIStep = 0.01)
object |
An |
nx |
The sample size used to compute genetic associations with the exposure. |
ny |
The sample size used to compute genetic associations with the outcome. |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
CIMin |
The smallest value to use in the search to find the confidence interval (default is -10). |
CIMax |
The largest value to use in the search to find the confidence interval (default is +10). |
CIStep |
The step size to use in the search to find the confidence interval (default is 0.01). Using a lower value (such as 0.001) will give more precise confidence intervals, but increase run time. |
In weak instrument settings, usual inference based on point estimates and standard errors may not be accurate. This method calculates confidence intervals based on inverting identification-robust tests proposed in Wang and Kang (2021, Biometrics) that provide valid inferences regardless of instrument strength.
This includes conditional likelihood ratio (CLR), Kleibergen (K), and Anderson and Rubin (AR) tests.
Evidence from the econometrics literature suggests that CLR inference is the best option in terms of power under a wide range of settings.
Please note that these methods do not provide point estimates, only confidence intervals. While most examples provide a confidence interval that is a single range of values, in some cases the confidence interval may comprise multiple ranges of values. In other cases, a valid confidence interval may not exist.
The output from the function is an CLR
object containing:
Exposure |
A character string with the name given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Correlation |
The matrix of genetic correlations. |
ARlower |
The lower bounds of the causal estimate based on inverting Anderson and Rubin's test. |
ARupper |
The upper bounds of the causal estimate based on inverting Anderson and Rubin's test. |
Klower |
The lower bounds of the causal estimate based on inverting Kleibergen's test. |
Kupper |
The upper bounds of the causal estimate based on inverting Kleibergen's test. |
CLRlower |
The lower bounds of the causal estimate based on inverting Moreira's conditional likelihood ratio test. |
CLRupper |
The upper bounds of the causal estimate based on inverting Moreira's conditional likelihood ratio test. |
CIMin |
The smallest value used in the search to find the confidence interval. |
CIMax |
The largest value used in the search to find the confidence interval. |
CIStep |
The step size used in the search to find the confidence interval. |
Alpha |
The significance level used when calculating the confidence intervals. |
Description of the CLR method: "Weak-instrument robust tests in two-sample summary-data Mendelian randomization", S. Wang and H. Kang, Biometrics, 2021.
mr_clr(mr_input(bx = calcium, bxse = calciumse, by = fastgluc, byse = fastglucse, correl = calc.rho), nx=6351, ny=133010)
mr_clr(mr_input(bx = calcium, bxse = calciumse, by = fastgluc, byse = fastglucse, correl = calc.rho), nx=6351, ny=133010)
Constrained maximum likelihood (cML) based Mendelian Randomization method robust to both correlated and uncorrelated pleiotropy.
mr_cML( object, MA = TRUE, DP = TRUE, K_vec = 0:(length(object@betaX) - 2), random_start = 0, num_pert = 200, random_start_pert = 0, maxit = 100, random_seed = 314, n, Alpha = 0.05 ) ## S4 method for signature 'MRInput' mr_cML( object, MA = TRUE, DP = TRUE, K_vec = 0:(length(object@betaX) - 2), random_start = 0, num_pert = 200, random_start_pert = 0, maxit = 100, random_seed = 314, n, Alpha = 0.05 )
mr_cML( object, MA = TRUE, DP = TRUE, K_vec = 0:(length(object@betaX) - 2), random_start = 0, num_pert = 200, random_start_pert = 0, maxit = 100, random_seed = 314, n, Alpha = 0.05 ) ## S4 method for signature 'MRInput' mr_cML( object, MA = TRUE, DP = TRUE, K_vec = 0:(length(object@betaX) - 2), random_start = 0, num_pert = 200, random_start_pert = 0, maxit = 100, random_seed = 314, n, Alpha = 0.05 )
object |
An |
MA |
Whether model average is applied or not. Default is TRUE. |
DP |
Whether data perturbation is applied or not. Default is TRUE. |
K_vec |
Set of candidate K's, the constraint parameter representing number of invalid IVs. Default is from 0 to (#IV - 2). |
random_start |
Number of random starting points for cML, default is 0. |
num_pert |
Number of perturbation when DP is TRUE, default is 200. |
random_start_pert |
Number of random start points for cML with data perturbation, default is 0. |
maxit |
Maximum number of iterations for each optimization. Default is 100. |
random_seed |
Random seed, default is 314. When |
n |
Sample size. When sample sizes of GWAS for exposure and outcome are different, and/or when sample sizes of different SNPs are different, the smallest sample size is recommended to get conservative result and avoid type-I error. See reference for more discussions. |
Alpha |
Significance level for the confidence interval for estimate, default is 0.05. |
The MRcML method selects invalid IVs with correlated
and/or uncorrelated peliotropic effects using constrained maximum
likelihood. cML-BIC
gives results of the selected model with
original data, while cML-MA-BIC
averages over all candidate models.
cML-BIC-DP
and cML-MA-BIC-DP
are the versions with
data-perturbation to account for selection uncertainty when
many invalid IVs have weak pleiotropic effects.
When DP is performed, two goodness-of-fit (GOF) tests are developed to check whether the model-based and DP- based variance estimates converge to the same estimate. Small p-values of GOF tests indicate selection uncertainty is not ignorable, and results from DP is more reliable. See reference for more details.
As the constrained maximum likelihood function is non-convex, multiple random starting points could be used to find a global minimum. For some starting points the algorithm may not converge and a warning message will be prompted, typically this will not affect the results.
The output from the function is an MRcML
object containing:
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Estimate |
Estimate of theta. |
StdError |
Standard error of estimate. |
Pvalue |
p-value of estimate. |
BIC_invalid |
Set of selected invalid IVs if cML-BIC is performed, i.e. without MA or DP. |
GOF1_p |
p-value of the first goodness-of-fit test. |
GOF2_p |
p-value of the second goodness-of-fit test. |
SNPs |
The number of SNPs that were used in the calculation. |
Alpha |
Significance level for the confidence interval for estimate, default is 0.05. |
CILower |
Lower bound of the confidence interval for estimate. |
CIUpper |
Upper bound of the confidence interval for estimate. |
MA |
Indicator of whether model average is applied. |
DP |
Indicator of whether data perturbation is applied. |
Xue, H., Shen, X., & Pan, W. (2021). Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects. The American Journal of Human Genetics, 108(7), 1251-1269.
# Perform cML-MA-BIC-DP: mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), num_pert=5, MA = TRUE, DP = TRUE, n = 17723) # num_pert is set to 5 to reduce computational time # the default value of 200 is recommended in practice # Perform cML-BIC-DP: mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), MA = TRUE, DP = FALSE,, n = 17723)
# Perform cML-MA-BIC-DP: mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), num_pert=5, MA = TRUE, DP = TRUE, n = 17723) # num_pert is set to 5 to reduce computational time # the default value of 200 is recommended in practice # Perform cML-BIC-DP: mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), MA = TRUE, DP = FALSE,, n = 17723)
Contamination mixture method for robust and efficient estimation under the 'plurality valid' assumption.
mr_conmix(object, psi = 0, CIMin = NA, CIMax = NA, CIStep = 0.01, alpha = 0.05) ## S4 method for signature 'MRInput' mr_conmix(object, psi = 0, CIMin = NA, CIMax = NA, CIStep = 0.01, alpha = 0.05)
mr_conmix(object, psi = 0, CIMin = NA, CIMax = NA, CIStep = 0.01, alpha = 0.05) ## S4 method for signature 'MRInput' mr_conmix(object, psi = 0, CIMin = NA, CIMax = NA, CIStep = 0.01, alpha = 0.05)
object |
An |
psi |
The value of the standard deviation of the distribution of invalid estimands (default value is 0, corresponding to 1.5 times the standard deviation of the ratio estimates). |
CIMin |
The smallest value to use in the search to find the confidence interval. The default value is NA, which means that the method uses the smallest value of the lower bound of the 95% confidence interval for the variant-specific ratio estimates as the smallest value. |
CIMax |
The largest value to use in the search to find the confidence interval. The default value is NA, which means that the method uses the greatest value of the upper bound of the 95% confidence interval for the variant-specific ratio estimates as the largest value. |
CIStep |
The step size to use in the search to find the confidence interval (default is 0.01). The confidence interval is determined by a grid search algorithm. Using the default settings, we calculate the likelihood at all values from -1 to +1 increasing in units of 0.01. If this range is too large or the step size is too small, then the method will take a long time to run. |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
The contamination mixture method is implemented by constructing a likelihood function based on the variant-specific causal estimates. If a genetic variant is a valid instrument, then its causal estimate will be normally distributed about the true value of the causal effect. If a genetic variant is not a valid instrument, then its causal estimate will be normally distributed about some other value. We assume that the values estimated by invalid instruments are normally distributed about zero with a large standard deviation. This enables a likelihood function to be specified that is a product of two-component mixture distributions, with one mixture distribution for each variant. The computational time for maximizing this likelihood directly is exponential in the number of genetic variants. We use a profile likelihood approach to reduce the computational complexity to be linear in the number of variants.
We consider different values of the causal effect in turn. For each value, we calculate the contribution to the likelihood for each genetic variant as a valid instrument and as an invalid instrument. If the contribution to the likelihood as a valid instrument is greater, then we take the variant's contribution as a valid instrument; if less, then its contribution is taken as an invalid instrument. This gives us the configuration of valid and invalid instruments that maximizes the likelihood for the given value of the causal effect. This is a profile likelihood, a one-dimensional function of the causal effect. The point estimate is then taken as the value of the causal effect that maximizes the profile likelihood.
Confidence intervals are evaluated by calculating the log-likelihood function, and finding all points within a given vertical distance of the maximum of the log-likelihood function (which is the causal estimate). As such, if the log-likelihood function is multimodal, then the confidence interval may include multiple disjoint ranges. This may indicate the presence of multiple causal mechanisms by which the exposure may influence the outcome with different magnitudes of causal effect. As the confidence interval is determined by a grid search, care must be taken when chosing the minimum (CIMin
) and maximum (CIMax
) values in the search, as well as the step size (CIStep
). The default values will not be suitable for all applications.
The output from the function is an MRConMix
object containing:
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Psi |
The value of the standard deviation parameter. |
Estimate |
The value of the causal estimate. |
CIRange |
The range of values in the confidence interval based on a grid search between the minimum and maximum values for the causal effect provided. |
CILower |
The lower limit of the confidence interval. If the confidence interval contains multiple ranges, then lower limits of all ranges will be reported. |
CIUpper |
The upper limit of the confidence interval. If the confidence interval contains multiple ranges, then upper limits of all ranges will be reported. |
CIMin |
The smallest value used in the search to find the confidence interval. |
CIMax |
The largest value used in the search to find the confidence interval. |
CIStep |
The step size used in the search to find the confidence interval. |
Pvalue |
The p-value associated with the estimate calculated using the likelihood function and a chi-squared distribution. |
Valid |
The numbers of genetic variants that were considered valid instruments at the causal estimate. |
ValidSNPs |
The names of genetic variants that were considered valid instruments at the causal estimate. |
Alpha |
The significance level used when calculating the confidence intervals. |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
Stephen Burgess, Christopher N Foley, Elias Allara, Joanna Howson. A robust and efficient method for Mendelian randomization with hundreds of genetic variants: unravelling mechanisms linking HDL-cholesterol and coronary heart disease. Nat Comms 2020. doi: 10.1038/s41467-019-14156-4.
mr_conmix(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), psi = 3, CIMin = -1, CIMax = 5, CIStep = 0.01)
mr_conmix(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), psi = 3, CIMin = -1, CIMax = 5, CIStep = 0.01)
The mr_divw
function implements the debiased inverse-variance weighted method.
mr_divw(object, over.dispersion = TRUE, alpha = 0.05, diagnostics = FALSE) ## S4 method for signature 'MRInput' mr_divw(object, over.dispersion = TRUE, alpha = 0.05, diagnostics = FALSE)
mr_divw(object, over.dispersion = TRUE, alpha = 0.05, diagnostics = FALSE) ## S4 method for signature 'MRInput' mr_divw(object, over.dispersion = TRUE, alpha = 0.05, diagnostics = FALSE)
object |
An |
over.dispersion |
Should the method consider overdispersion (balanced horizontal pleiotropy)? Default is TRUE. |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05. |
diagnostics |
Should the function returns the q-q plot for assumption diagnosis. Default is FALSE. |
The debiased inverse-variance weighted method (dIVW) removes the weak instrument bias of the IVW method and is more robust under many weak instruments.
The output from the function is a DIVW
object containing:
Over.dispersion |
|
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Estimate |
The value of the causal estimate. |
StdError |
Standard error of the causal estimate calculated using bootstrapping. |
CILower |
The lower bound for the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper |
The upper bound for the causal estimate based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-value associated with the estimate (calculated using |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
Condition |
A measure (average F-statistic -1)*sqrt(# snps) that needs to be large for reliable asymptotic approximation based on the dIVW estimator. It is recommended to be greater than 20. |
Ting Ye, Jun Shao, Hyunseung Kang (2021). Debiased Inverse-Variance Weighted Estimator in Two-Sample Summary-Data Mendelian Randomization. The Annals of Statistics, 49(4), 2079-2100. Also available at https://arxiv.org/abs/1911.09802.
mr_divw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
mr_divw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
The mr_egger
function implements the MR-Egger method introduced by Bowden et al (2015).
This method provides: 1) a test of the for directional pleiotropy (the MR-Egger intercept test), 2) a test for a causal effect, and 3) an estimate of the causal effect. If the intercept term differs from zero, then the genetic variants are not all valid instrumental variables and the standard (inverse-variance weighted) estimate is biased. If the InSIDE (Instrument Strength Independent of Direct Effect) assumption holds, then the MR-Egger slope parameter provides a test for a causal effect, and a consistent estimate of the causal effect even if the intercept differs from zero.
mr_egger( object, robust = FALSE, penalized = FALSE, correl = FALSE, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_egger( object, robust = FALSE, penalized = FALSE, correl = FALSE, distribution = "normal", alpha = 0.05, ... )
mr_egger( object, robust = FALSE, penalized = FALSE, correl = FALSE, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_egger( object, robust = FALSE, penalized = FALSE, correl = FALSE, distribution = "normal", alpha = 0.05, ... )
object |
An |
robust |
Indicates whether robust regression using the |
penalized |
Indicates whether a penalty should be applied to the weights to downweight the contribution of genetic variants with outlying ratio estimates to the analysis. |
correl |
If the genetic variants are correlated, then this correlation can be accounted for. The matrix of correlations between must be provided: the elements of this matrix are the correlations between the individual variants (diagonal elements are 1). If a correlation is specified, then the values of |
distribution |
The type of distribution used to calculate the confidence intervals, can be |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the regression method. |
The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factor, with weights being the inverse-variances of the associations with the outcome. The intercept is estimated (in contrast with the inverse-variance weighted method, where the intercept is set to zero).
As part of the analysis, the genetic variants are orientated so that all of the associations with the risk factor are positive (and signs of associations with the outcome are changed to keep the orientation consistent if required). Re-orientation of the genetic variants is performed automatically as part of the function.
The MR-Egger model uses a random-effects model ("random"
); a fixed-effect model does not make sense as pleiotropy leads to heterogeneity between the causal estimates targeted by the genetic variants. The (multiplicative) random-effects model allows over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1).
The output of the function is an Egger
object containing:
Model |
A character string giving the type of model used ( |
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Correlation |
The matrix of genetic correlations. |
Robust |
|
Penalized |
|
Estimate |
The value of the causal estimate (slope coefficient). |
StdError.Est |
Standard error of the causal estimate. |
Pvalue.Est |
The p-value associated with the estimate (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
CILower.Est |
The lower bound of the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper.Est |
The upper bound of the causal estimate based on the estimated standard error and the significance level provided. |
Intercept |
The value of the intercept estimate. |
StdError.Int |
Standard error of the intercept estimate. |
Pvalue.Int |
The p-value associated with the intercept. |
CILower.Int |
The lower bound of the intercept based on the estimated standard error and the significance level provided. |
CIUpper.Int |
The upper bound of the intercept based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals (same as |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
Causal.pval |
The p-value for the MR-Egger causal estimate. |
Pleio.pval |
The p-value for the MR-Egger intercept test (a low p-value suggests either directional pleiotropy or failure of the InSIDE assumption, and indicates that the IVW estimate is biased). |
RSE |
The estimated residual standard error from the regression model. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that the regression model (including an intercept) fits the regression model with no additional variability. Rejection of the null hypothesis is expected if genetic variants are pleiotropic, and doesn't mean that the MR-Egger analysis or the InSIDE assumption is invalid. |
I.sq |
A measure of heterogeneity between the genetic associations with the exposure (see Bowden IJE 2016). Low values of |
Jack Bowden, George Davey Smith, Stephen Burgess. Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression. International Journal of Epidemiology 2015; 44:512–525. doi: 10.1093/ije/dyv080.
Confidence intervals, and robust and penalized weights: Stephen Burgess, Jack Bowden, Frank Dudbridge, Simon G Thompson. Robust instrumental variable methods using multiple candidate instruments with application to Mendelian randomization. arXiv 2016; 1606.03729.
I-squared statistic: Jack Bowden and others. Assessing the suitability of summary data for Mendelian randomization analyses using MR-Egger regression: The role of the I2 statistic. Int J Epidemiol 2016 (to appear).
mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse)) mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), robust = TRUE) mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), penalized = TRUE) mr_egger(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho)) ## correlated variants
mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse)) mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), robust = TRUE) mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), penalized = TRUE) mr_egger(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho)) ## correlated variants
The mr_forest
function draws a forest plot of causal estimates. The default option plots the variant-specific causal estimates (by/bx
) and the estimate from the mr_ivw
function using default settings (assuming variants are uncorrelated, random-effects for 4+ variants). Options allow users to plot estimates from a variety of different methods.
mr_forest( object, alpha = 0.05, snp_estimates = TRUE, methods = "ivw", ordered = FALSE ) ## S4 method for signature 'MRInput' mr_forest( object, alpha = 0.05, snp_estimates = TRUE, methods = "ivw", ordered = FALSE )
mr_forest( object, alpha = 0.05, snp_estimates = TRUE, methods = "ivw", ordered = FALSE ) ## S4 method for signature 'MRInput' mr_forest( object, alpha = 0.05, snp_estimates = TRUE, methods = "ivw", ordered = FALSE )
object |
An |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05, corresponding to 95% confidence intervals. |
snp_estimates |
Whether to plot the variant-specific estimates. Defaults to |
methods |
Takes a string of computation methods used to calculate estimates. Defaults to |
ordered |
Determines by whether to arrange the variant-specific estimates in ascending order. Defaults to |
As the function produces a ggplot
object, graphical parameters can be changed by adding commands from the ggplot2
package.
mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), alpha = 0.01, ordered = TRUE) mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), methods = c("ivw", "wmedian", "egger"), snp_estimates = FALSE) forest = mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse)) # how to change x-axis limits # library(ggplot2) # forest2 = forest + coord_cartesian(xlim=c(-5,5)) # forest2
mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), alpha = 0.01, ordered = TRUE) mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), methods = c("ivw", "wmedian", "egger"), snp_estimates = FALSE) forest = mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse)) # how to change x-axis limits # library(ggplot2) # forest2 = forest + coord_cartesian(xlim=c(-5,5)) # forest2
The mr_funnel
function draws a funnel plot of variant-specific causal estimates. Estimates (by/bx
) are plotted against the precision of the estimates (abs(bx)/byse
). Precision is the reciprocal of standard error. A vertical dashed line is plotted at the estimate from the mr_ivw
function.
mr_funnel(object, CI = TRUE) ## S4 method for signature 'MRInput' mr_funnel(object, CI = TRUE)
mr_funnel(object, CI = TRUE) ## S4 method for signature 'MRInput' mr_funnel(object, CI = TRUE)
object |
An |
CI |
A |
As the function produces a ggplot
object, graphical parameters can be changed by adding commands from the ggplot2
package.
mr_funnel(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
mr_funnel(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
The mr_input
function is required for inputting and formatting data for use in any of the estimation functions provided in this package. The MRInput
class outputted by the function can also be viewed graphically using the mr_plot
function.
mr_input( bx = 0, bxse = 0, by = 0, byse = 0, correlation = matrix(), exposure = "exposure", outcome = "outcome", snps = "snp", effect_allele = NA, other_allele = NA, eaf = NA )
mr_input( bx = 0, bxse = 0, by = 0, byse = 0, correlation = matrix(), exposure = "exposure", outcome = "outcome", snps = "snp", effect_allele = NA, other_allele = NA, eaf = NA )
bx |
A numeric vector of beta-coefficient values for genetic associations with the first variable (often referred to as the exposure, risk factor, or modifiable phenotype). |
bxse |
The standard errors associated with the beta-coefficients |
by |
A numeric vector of beta-coefficient values for genetic associations with the second variable (often referred to as the outcome). For a disease outcome, the beta coefficients are log odds estimates from logistic regression analyses. |
byse |
The standard errors associated with the beta-coefficients in |
correlation |
The matrix of correlations between genetic variants. If this variable is not provided, then we assume that genetic variants are uncorrelated. |
exposure |
The name of the exposure variable. |
outcome |
The name of the outcome variable. |
snps |
The names of the genetic variants (SNPs) included in the analysis. The inputs |
effect_allele |
The name of the effect allele for each SNP. The beta-coefficients are the associations with the exposure and outcome per additional copy of the effect allele. |
other_allele |
The name of the non-effect allele. |
eaf |
The expected allele frequencies (numeric). The slots |
The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors.
If the four variables are not all the same length, then an error message will be reported. The analyses will still try to run, but the output may be misleading. However, in some analyses (for example, the standard IVW and MR-Egger methods), the values of bxse
are not used in the analysis, and can therefore safely be omitted (provided that the other variables are correctly labelled).
An MRInput object containing:
betaX |
The genetic associations with the exposure. |
betaXse |
The corresponding standard errors. |
betaY |
The genetic associations with the outcome. |
betaYse |
The corresponding standard errors. |
correlation |
The matrix of genetic correlations. |
exposure |
A character string giving the name given to the exposure. |
outcome |
A character string giving the name given to the outcome. |
snps |
A vector of character strings with the names of the genetic variants. |
effect_allele |
A vector of character strings with the names of the effect alleles. |
other_allele |
A vector of character strings with the names of the non-effect alleles. |
eaf |
A numeric vector with the effect allele frequencies. |
extract.pheno.csv()
for a description of how an MRInput
object can be extracted from PhenoScanner (http://www.phenoscanner.medschl.cam.ac.uk/).
The mr_ivw
function implements the inverse-variance method, informally known as the "Toby Johnson" method. With a single
genetic variant, this is simply the ratio method.
mr_ivw( object, model = "default", robust = FALSE, penalized = FALSE, weights = "simple", psi = 0, correl = FALSE, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_ivw( object, model = "default", robust = FALSE, penalized = FALSE, weights = "simple", psi = 0, correl = FALSE, distribution = "normal", alpha = 0.05, ... )
mr_ivw( object, model = "default", robust = FALSE, penalized = FALSE, weights = "simple", psi = 0, correl = FALSE, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_ivw( object, model = "default", robust = FALSE, penalized = FALSE, weights = "simple", psi = 0, correl = FALSE, distribution = "normal", alpha = 0.05, ... )
object |
An |
model |
What type of model should be used: |
robust |
Indicates whether robust regression using the |
penalized |
Indicates whether a penalty should be applied to the weights to downweight the contribution of genetic variants with outlying ratio estimates to the analysis. |
weights |
Which weights to use in the weighted regression. If |
psi |
The correlation between the genetic associations with the exposure and the association with the outcome for each variant resulting from sample overlap. The default value is |
correl |
If the genetic variants are correlated, then this correlation can be accounted for. The matrix of correlations between must be provided in the |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the regression method. |
With multiple uncorrelated genetic variants, this estimate can be thought of as: 1) the inverse-variance weighted combination of the ratio estimates from a meta-analysis; 2) the ratio estimate from combining the genetic variants into a weighted score and then using this score as an instrumental variable (the same estimate is obtained from the two-stage least squares method using individual-level data); 3) the coefficient from weighted linear regression of the associations with the outcome on the associations with the risk factor fixing the intercept to zero and using the inverse-variance weights.
Here, we implement the method using weighted linear regression. If the variants are correlated, the method is implemented using generalized weighted linear regression; this is hard coded using matrix algebra.
The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factor, with the intercept set to zero and weights being the inverse-variances of the associations with the outcome.
With a single genetic variant, the estimate is the ratio of coefficients betaY/betaX and the standard error is the first term of the delta method approximation betaYse/betaX.
The output from the function is an IVW
object containing:
Model |
A character string giving the type of model used ( |
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Correlation |
The matrix of genetic correlations. |
Robust |
|
Penalized |
|
Estimate |
The value of the causal estimate. |
StdError |
Standard error of the causal estimate. |
CILower |
The lower bound of the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper |
The upper bound of the causal estimate based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-value associated with the estimate (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RSE |
The estimated residual standard error from the regression model. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic. |
Fstat |
An approximation of the first-stage F statistic for all variants based on the summarized data. |
Original implementation: The International Consortium for Blood Pressure Genome-Wide Association Studies. Genetic variants in novel pathways influence blood pressure and cardiovascular disease risk. Nature 2011; 478:103-109. doi: 10.1038/nature10405.
Detailed description of method: Stephen Burgess, Adam S Butterworth, Simon G Thompson. Mendelian randomization analysis with multiple genetic variants using summarized data. Genetic Epidemiology 2013; 37:658-665. doi: 10.1002/gepi.21758.
Robust and penalized weights: Stephen Burgess, Jack Bowden, Frank Dudbridge, Simon G Thompson. Robust instrumental variable methods using multiple candidate instruments with application to Mendelian randomization. arXiv 2016; 1606.03729.
Heterogeneity test: Fabiola del Greco, Cosetta Minelli, Nuala A Sheehan, John R Thompson. Detecting pleiotropy in Mendelian randomisation studies with summary data and a continuous outcome. Stat Med 2015; 34(21):2926-2940. doi: 10.1002/sim.6522.
Simple versus delta weights (first-order versus second-order): Stephen Burgess, Jack Bowden. Integrating summarized data from multiple genetic variants in Mendelian randomization: bias and coverage properties of inverse-variance weighted methods. arXiv:1512.04486.
mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse)) mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), robust = TRUE) mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), penalized = TRUE) mr_ivw(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho)) ## correlated variants
mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse)) mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), robust = TRUE) mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), penalized = TRUE) mr_ivw(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho)) ## correlated variants
The mr_lasso
function performs the MR-Lasso method, which applies lasso-type penalization to the direct effects of genetic variants on the outcome.
The causal estimate is described as a post-lasso estimate, and is obtained by performing the IVW method using only those genetic variants that are identified as valid by the lasso procedure.
mr_lasso(object, distribution = "normal", alpha = 0.05, lambda = numeric(0)) ## S4 method for signature 'MRInput' mr_lasso(object, distribution = "normal", alpha = 0.05, lambda = numeric(0))
mr_lasso(object, distribution = "normal", alpha = 0.05, lambda = numeric(0)) ## S4 method for signature 'MRInput' mr_lasso(object, distribution = "normal", alpha = 0.05, lambda = numeric(0))
object |
An |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05. |
lambda |
The value of the tuning parameter used by the lasso procedure which controls the level of sparsity. If not specified, the tuning parameter will be calculated by the heterogeneity stopping rule. |
MR-Lasso extends the IVW model to include an intercept term for each genetic variant. These intercept terms represent associations between the genetic variants and the outcome which bypass the risk factor. The causal effect estimates are estimated by weighted linear regression where the intercept terms are subject to lasso-type penalization. The lasso penalization will tend to shrink the intercept terms corresponding to the valid instruments to zero.
The lasso penalty relies on a tuning parameter which controls the level of sparsity. The default is to use a heterogeneity stopping rule, but a fixed value may be specified.
As part of the analysis, the genetic variants are orientated so that all of the associations with the risk factor are positive (and signs of associations with the outcome are changed to keep the orientation consistent if required). Re-orientation of the genetic variants is performed automatically as part of the function.
The MR-Lasso method is performed in two steps. First, a regularized regression model is fitted, and some genetic variants are identified as valid instruments. Second, the causal effect is estimated using standard IVW with only the valid genetic variants. The post-lasso method will be performed as long as at least two genetic variants are identified as valid instruments. The default heterogeneity stopping rule will always return at least two genetic variants as valid instruments. The main estimate given by the method is the post-lasso estimate. However, parameter estimates from the regularized regression model used to identify invalid variants are also provided for completeness.
If a substantial proportion of genetic variants are removed from the analysis, the MR-Lasso method may give a false impression of confidence in the causal estimate due to homogeneity of the variant-specific causal estimates amongst the remaining variants. However, it is not reasonable to claim that there is strong evidence for a causal effect after a large number of variants with heterogeneous estimates have been removed from the analysis.
The output from the function is an MRLasso
object containing:
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Estimate |
The causal estimate from the MR-Lasso method. This is the post-lasso estimate. |
StdError |
The standard error of the causal estimate from the MR-Lasso method. |
CILower |
The lower bound of the confidence interval for the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper |
The upper bound of the confidence interval for the causal estimate based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-value associated with the causal estimate using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RegEstimate |
The estimate from the regularized regression model used in the MR-Lasso method. |
RegIntercept |
The intercept estimates from the regularized regression model used in the MR-Lasso method. |
Valid |
The number of genetic variants that have been identified as valid instruments. |
ValidSNPs |
The names of genetic variants that have been identified as valid instruments. |
Lambda |
The value of the tuning parameter used to compute |
Jessica MB Rees, Angela M Wood, Frank Dudbridge, Stephen Burgess. Robust methods in Mendelian randomization via penalization of heterogeneous causal estimates. PLoS ONE 2019; 14(9):e0222362
mr_lasso(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
mr_lasso(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
The mr_loo
function draws a forest plot of causal estimates from the mr_ivw
function using default settings (assuming variants are uncorrelated, random-effects for 4+ variants) omitting each variant in turn. So the estimate labelled snp_1
includes all variants except the labelled variant, and so on. The mr_ivw
estimate including all variants ("IVW estimate") is also provided for reference.
mr_loo(object, alpha = 0.05) ## S4 method for signature 'MRInput' mr_loo(object, alpha = 0.05)
mr_loo(object, alpha = 0.05) ## S4 method for signature 'MRInput' mr_loo(object, alpha = 0.05)
object |
An |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05, corresponding to 95% confidence intervals. |
As the function produces a ggplot
object, graphical parameters can be changed by adding commands from the ggplot2
package.
mr_loo(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), alpha = 0.01)
mr_loo(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), alpha = 0.01)
The mr_maxlik
function implements the maximum-likelihood method introduced by Burgess et al (2013).
mr_maxlik( object, model = "default", correl = FALSE, psi = 0, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_maxlik( object, model = "default", correl = FALSE, psi = 0, distribution = "normal", alpha = 0.05, ... )
mr_maxlik( object, model = "default", correl = FALSE, psi = 0, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_maxlik( object, model = "default", correl = FALSE, psi = 0, distribution = "normal", alpha = 0.05, ... )
object |
An |
model |
What type of model should be used: |
correl |
If the genetic variants are correlated, then this correlation can be accounted for. The matrix of correlations between must be provided in the |
psi |
The correlation between the association with the exposure and the association with the outcome for each variant resulting from sample overlap. |
distribution |
The type of distribution used to calculate the confidence intervals, can be |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the optimization method. |
A likelihood function is defined by assuming that the summarized data for each genetic variant are normally distributed. A bivariate normal distribution is assumed for the associations of each genetic variant with the exposure and with the outcome. The mean of the association with the outcome is taken as the mean association with the exposure multiplied by the causal effect parameter.
Thus, if there are K
genetic variants, then K+1
parameters are estimated by the method: one for each gene–exposure association, plus the causal parameter. If the number of genetic variants is large, then maximization of this function may be an issue. If the maximum likelihood estimate substantially differs from the inverse-variance weighted estimate, this may indicate that convergence has not occurred in the optimization algorithm.
The variance-covariance matrices for the bivariate normal distributions are obtained from the standard error estimates provided. The correlation psi
between genetic associations with the exposure and with the outcome due to sample overlap can be specified; its default value is zero.
Two features why this method may be preferred over the inverse-variance weighted method are the incorporation in the model of uncertainty in the genetic associations with the exposure, and of correlation between the genetic association estimates with exposure and outcome for each variant. The method is implemented both for uncorrelated and correlated genetic variants. It can also be used for a single genetic variant.
The original version of the maximum-likelihood method assumed that all genetic variants identify the same causal estimate; a fixed-effect model. The causal estimate may be overly precise if the fixed-effect model is incorrect and there is substantial heterogeneity in the causal estimates from the different variants. The random-effects analysis implemented here is an ad hoc solution to the problem of heterogeneity, but one that should result in reasonable confidence intervals that incorporate this heterogeneity.
The output from the function is an MaxLik
object containing:
Model |
A character string giving the type of model used ( |
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Correlation |
The matrix of genetic correlations. |
Psi |
The correlation between genetic associations with the exposure and with the outcome. |
Estimate |
The value of the causal estimate. |
StdError |
Standard error of the causal estimate. |
CILower |
The lower bound of the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper |
The upper bound of the causal estimate based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-value associated with the estimate (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RSE |
The estimated residual standard error from the regression model (always equal to 1, as a fixed-effect model is required. |
Heter.Stat |
Heterogeneity statistic (likelihood ratio statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic. |
Stephen Burgess, Adam S Butterworth, Simon G Thompson. Mendelian randomization analysis with multiple genetic variants using summarized data. Genetic Epidemiology 2013; 37:658-665. doi: 10.1002/gepi.21758.
mr_maxlik(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10], by = chdlodds[1:10], byse = chdloddsse[1:10])) mr_maxlik(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10], by = chdlodds[1:10], byse = chdloddsse[1:10]), psi=0.2) mr_maxlik(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho)) ## correlated variants
mr_maxlik(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10], by = chdlodds[1:10], byse = chdloddsse[1:10])) mr_maxlik(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10], by = chdlodds[1:10], byse = chdloddsse[1:10]), psi=0.2) mr_maxlik(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho)) ## correlated variants
The mr_mbe
function implements the mode-based method introduced by Hartwig, Bowden and Davey Smith (2017).
mr_mbe( object, weighting = "weighted", stderror = "simple", phi = 1, seed = 314159265, iterations = 10000, distribution = "normal", alpha = 0.05 ) ## S4 method for signature 'MRInput' mr_mbe( object, weighting = "weighted", stderror = "delta", phi = 1, seed = 314159265, iterations = 10000, distribution = "normal", alpha = 0.05 )
mr_mbe( object, weighting = "weighted", stderror = "simple", phi = 1, seed = 314159265, iterations = 10000, distribution = "normal", alpha = 0.05 ) ## S4 method for signature 'MRInput' mr_mbe( object, weighting = "weighted", stderror = "delta", phi = 1, seed = 314159265, iterations = 10000, distribution = "normal", alpha = 0.05 )
object |
An |
weighting |
Whether the analysis should be |
stderror |
Whether standard error estimates should be i) |
phi |
The choice of bandwidth in the kernel-smoothly density method. A value of 1 (the default value) represents the bandwidth value selected by the modified Silverman's bandwidth rule, as recommended by Hartwig et al. A value of 0.5 represents half that value, and so on. |
seed |
The random seed to use when generating the bootstrap samples used to calculate the confidence intervals (for reproducibility). The default value is 314159265. If set to |
iterations |
Number of iterations to use in the bootstrap procedure. |
distribution |
The type of distribution used to calculate the confidence intervals, can be |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
The mode-based estimation (MBE) method takes the variant-specific ratio estimates from each genetic variant in turn, and calculates the modal estimate. This is implemented by constructing a kernel-smoothed density out of the ratio estimates, and taking the maximum value as the modal estimate. The standard error is calculated by a bootstrap procedure, and confidence intervals based on the estimate having a normal distribution.
The method should give consistent estimates as the sample size increases if a plurality (or weighted plurality) of the genetic variants are valid instruments. This means that the largest group of variants with the same causal estimate in the asymptotic limit are the valid instruments.
The output from the function is an MRMBE
object containing:
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Weighting |
A character string |
StdErr |
A character string |
Phi |
The value of the bandwidth factor. |
Estimate |
The value of the causal estimate. |
StdError |
Standard error of the causal estimate. |
CILower |
The lower bound of the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper |
The upper bound of the causal estimate based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-value associated with the estimate (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
Fernando Pires Hartwig, George Davey Smith, Jack Bowden. Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption. International Journal of Epidemiology 2017; 46(6): 1985-1998. doi: 10.1093/ije/dyx102.
mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), iterations=100) mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), phi=0.5, iterations=100) mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting="weighted", stderror="delta", iterations=100) # iterations set to 100 to reduce computational time, # more iterations are recommended in practice
mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), iterations=100) mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), phi=0.5, iterations=100) mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting="weighted", stderror="delta", iterations=100) # iterations set to 100 to reduce computational time, # more iterations are recommended in practice
The mr_median
function implements the weighted median (default) or simple median method introduced by Bowden et al (2016) to calculate
the median of the ratio instrumental variable estimates evaluated using each genetic variant individually.
mr_median( object, weighting = "weighted", distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 ) ## S4 method for signature 'MRInput' mr_median( object, weighting = "weighted", distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 )
mr_median( object, weighting = "weighted", distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 ) ## S4 method for signature 'MRInput' mr_median( object, weighting = "weighted", distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 )
object |
An |
weighting |
The type of weighting applied. The default option is to calculate the weighted median ( |
distribution |
The type of distribution to use to calculate the 95% confidence intervals, can be |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05. |
iterations |
The number of bootstrap samples to generate when calculating the estimated standard error. The default value is 10000. |
seed |
The random seed to use when generating the bootstrap samples (for reproducibility). The default value is 314159265. If set to |
The median-based methods have greater robustness to individual genetic variants with strongly outlying causal estimates compared with the inverse-variance weighted and MR-Egger methods. Formally, the simple median method gives a consistent estimate of the causal effect when at least 50% of the genetic variants are valid instrumental variables (for the weighted median method, when 50% of the weight comes from valid instrumental variables).
When the weighting is "simple"
, the estimate is obtained by calculating the ratio causal estimates
from each genetic variants theta = betaY/betaX, and finding the median estimate.
When the weighting is "weighted"
, the estimate is obtained by:
Calculating the ratio causal estimates and ordering the genetic variants according to the magnitude of their estimates, i.e.
Calculate normalized inverse-variance weights for each genetic variant , as:
Find k such that
and
Calculate the weighted median estimate by extrapolation as:
The simple median estimate is the same as the weighted median estimate when all the weights are equal. Standard errors for both the simple and weighted median methods are calculated through bootstrapping.
When the weighting is "penalized"
, the weighted method is used, but the contribution of genetic variants with outlying (heterogeneous) ratio estimates to the analysis is downweighted.
The output from the function is a WeightedMedian
object containing:
Type |
The type of weights used: |
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Estimate |
The value of the causal estimate. |
StdError |
Standard error of the causal estimate calculated using bootstrapping. |
CILower |
The lower bound for the causal estimate based on the estimated bootstrapped standard error and the significance level provided. |
CIUpper |
The upper bound for the causal estimate based on the estimated bootstrapped standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-value associated with the estimate (calculated using |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
Jack Bowden, George Davey Smith, Philip C Haycock, Stephen Burgess. Consistent estimation in Mendelian randomization with some invalid instruments using a weighted median estimator. Genetic Epidemiology 2016; 40(4):304-314. doi: 10.1002/gepi.21965.
mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting = "weighted", iterations = 100) # iterations is set to 100 to reduce runtime for the mr_median method, # 10000 iterations are recommended in practice mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting = "simple", iterations = 100) mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting = "penalized", iterations = 100)
mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting = "weighted", iterations = 100) # iterations is set to 100 to reduce runtime for the mr_median method, # 10000 iterations are recommended in practice mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting = "simple", iterations = 100) mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), weighting = "penalized", iterations = 100)
The mr_mvegger
function performs multivariable Mendelian randomization via the MR-Egger method. This is implemented by multivariable weighted linear regression.
mr_mvegger( object, orientate = 1, correl = FALSE, distribution = "normal", alpha = 0.05 ) ## S4 method for signature 'MRMVInput' mr_mvegger( object, orientate = 1, correl = FALSE, distribution = "normal", alpha = 0.05 )
mr_mvegger( object, orientate = 1, correl = FALSE, distribution = "normal", alpha = 0.05 ) ## S4 method for signature 'MRMVInput' mr_mvegger( object, orientate = 1, correl = FALSE, distribution = "normal", alpha = 0.05 )
object |
An |
orientate |
The risk factor that genetic associations are orientated to. The univariable and multivariable versions of MR-Egger are both sensitive to the choice of parameterization of the genetic associations - which allele the associations are orientated with respect to (in other words, which allele is the effect allele). For univariable MR-Egger, this is resolved by setting the genetic associations with the exposure all to be positive. In multivariable MR-Egger, we have to choose which of the exposures to orientate the genetic associations to. The default option is |
correl |
If the genetic variants are correlated, then this correlation can be accounted for. The matrix of correlations between must be provided in the |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
Multivariable MR-Egger is an extension of the MR-Egger method to deal with genetic variants that are associated with multiple risk factors.
We implement the method using multivariable weighted linear regression. If the variants are correlated, the method is implemented using generalized weighted linear regression; this is hard coded using matrix algebra.
The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factors, with the intercept estimated and weights being the inverse-variances of the associations with the outcome.
The output from the function is an MVEgger
object containing:
Model |
A character string giving the type of model used ( |
Orientate |
The number corresponding to the risk factor that the genetic associations are orientated to. |
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Correlation |
The matrix of genetic correlations. |
Estimate |
A vector of the causal estimates (slope coefficient). |
StdError.Est |
Standard errors of the causal estimates. |
Pvalue.Est |
The p-values associated with the estimates using a normal or t-distribution (as specified in |
CILower.Est |
The lower bound of the causal estimates based on the estimated standard error and the significance level provided. |
CIUpper.Est |
The upper bound of the causal estimates based on the estimated standard error and the significance level provided. |
Intercept |
The value of the intercept estimate. |
StdError.Int |
Standard error of the intercept estimate. |
Pvalue.Int |
The p-value associated with the intercept. |
CILower.Int |
The lower bound of the intercept based on the estimated standard error and the significance level provided. |
CIUpper.Int |
The upper bound of the intercept based on the estimated standard error and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RSE |
The estimated residual standard error from the regression model. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic. |
Jessica Rees, Angela Wood, Stephen Burgess. Extending the MR-Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy. Statistics in Medicine 2017; 36(29): 4705-4718. doi: 10.1002/sim.7492.
mr_mvegger(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse), orientate = 1)
mr_mvegger(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse), orientate = 1)
The mr_mvgmm
function performs multivariable Mendelian randomization via the generalized method of moments method.
mr_mvgmm(object, nx, ny, cor.x = NULL, robust = TRUE, alpha = 0.05, ...) ## S4 method for signature 'MRMVInput' mr_mvgmm(object, nx, ny, cor.x = NULL, robust = TRUE, alpha = 0.05, ...)
mr_mvgmm(object, nx, ny, cor.x = NULL, robust = TRUE, alpha = 0.05, ...) ## S4 method for signature 'MRMVInput' mr_mvgmm(object, nx, ny, cor.x = NULL, robust = TRUE, alpha = 0.05, ...)
object |
An |
nx |
Vector of sample sizes used to compute genetic associations with the exposure (one for each exposure). |
ny |
The sample size used to compute genetic associations with the outcome. |
cor.x |
Correlation matrix for exposures. Default is to assume the exposures are uncorrelated. |
robust |
Indicates whether overdispersion heterogeneity is accounted for in the model. Default is TRUE. |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the optimization routines to calculate GMM estimates and overdispersion parameter. |
Robust inference in two-sample multivariable Mendelian randomization using the generalized method of moments. The method accounts for overdispersion heterogeneity in genetic variant-outcome associations.
The output from the function is an MVGMM
object containing:
Robust |
|
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Correlation |
The matrix of genetic correlations if supplied. If not supplied, then an identity matrix will be returned. |
ExpCorrelation |
|
CondFstat |
A vector of conditional F-statistics (one for each exposure). |
Estimate |
A vector of causal estimates. |
StdError |
A vector of standard errors of the causal estimates. |
CILower |
The lower bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
CIUpper |
The upper bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
Overdispersion |
The estimate of the overdispersion parameter. If this is negative, then a value of zero is used in the method. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal distribution. |
Alpha |
The significance level used when calculating the confidence intervals. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model only): the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more genetic variants may be pleiotropic. |
Description of the generalized method of moments: Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, pp.1029-1054.
mr_mvgmm(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse), nx=rep(17723,3), ny=17723)
mr_mvgmm(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse), nx=rep(17723,3), ny=17723)
The mr_mvinput
function is required for inputting and formatting data for use in the multivariable Mendelian randomization functions provided in this package.
mr_mvinput( bx = matrix(), bxse = matrix(), by = 0, byse = 0, correlation = matrix(), exposure = "exposure", outcome = "outcome", snps = "snp", effect_allele = NA, other_allele = NA, eaf = NA )
mr_mvinput( bx = matrix(), bxse = matrix(), by = 0, byse = 0, correlation = matrix(), exposure = "exposure", outcome = "outcome", snps = "snp", effect_allele = NA, other_allele = NA, eaf = NA )
bx |
A matrix of beta-coefficient values for genetic associations with the risk factor variables. These should be arranged so that column 1 are the beta-coefficients for risk factor 1, and row 1 are the beta-coefficients for genetic variant 1. |
bxse |
The matrix of standard errors associated with the beta-coefficients |
by |
A numeric vector of beta-coefficient values for genetic associations with the second variable (often referred to as the outcome). For a disease outcome, the beta coefficients are log odds estimates from logistic regression analyses. |
byse |
The vector standard errors associated with the beta-coefficients in |
correlation |
The matrix of correlations between genetic variants. If this variable is not provided, then we assume that genetic variants are uncorrelated. |
exposure |
The names of the exposure variables. |
outcome |
The name of the outcome variable. |
snps |
The names of the genetic variants (SNPs) included in the analysis. The inputs |
effect_allele |
The name of the effect allele for each SNP. The beta-coefficients are the associations with the exposure and outcome per additional copy of the effect allele. |
other_allele |
The name of the non-effect allele. |
eaf |
The expected allele frequencies (numeric). The slots |
The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors.
If the variables are not all the same length, then an error message will be reported. The analyses will still try to run, but the output may be misleading. However, in some analyses (for example, the standard IVW and MR-Egger methods), the values of bxse
are not used in the analysis, and can therefore safely be omitted (provided that the other variables are correctly labelled).
An MRMVInput object containing:
betaX |
The genetic associations with the exposures. |
betaXse |
The corresponding standard errors. |
betaY |
The genetic associations with the outcome. |
betaYse |
The corresponding standard errors. |
correlation |
The matrix of genetic correlations. |
exposure |
Character strings with the names given to the exposures. |
outcome |
A character string giving the name given to the outcome. |
snps |
A vector of character strings with the names of the genetic variants. |
effect_allele |
A vector of character strings with the names of the effect alleles. |
other_allele |
A vector of character strings with the names of the non-effect alleles. |
eaf |
A numeric vector with the effect allele frequencies. |
The mr_mvivw
function performs multivariable Mendelian randomization via the inverse-variance method. This is implemented by multivariable weighted linear regression.
mr_mvivw( object, model = "default", robust = FALSE, correl = FALSE, correl.x = NULL, nx = NA, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRMVInput' mr_mvivw( object, model = "default", robust = FALSE, correl = FALSE, correl.x = NULL, nx = NA, distribution = "normal", alpha = 0.05, ... )
mr_mvivw( object, model = "default", robust = FALSE, correl = FALSE, correl.x = NULL, nx = NA, distribution = "normal", alpha = 0.05, ... ) ## S4 method for signature 'MRMVInput' mr_mvivw( object, model = "default", robust = FALSE, correl = FALSE, correl.x = NULL, nx = NA, distribution = "normal", alpha = 0.05, ... )
object |
An |
model |
What type of model should be used: |
robust |
Indicates whether robust regression using the |
correl |
If the genetic variants are correlated, then this correlation can be accounted for. The matrix of correlations between must be provided in the |
correl.x |
Correlation matrix for exposures (Optional). Default is to assume the exposures are uncorrelated. This is only used in the computation of conditional F-statistics. |
nx |
Either a single value, or a vector of sample sizes for the genetic associations with the exposures (one for each exposure, and assumed equal for all variants). If a single value is provided, it is assumed this is the sample size for all exposures. This is optional, and it is only used in the calculation of conditional F statistics. If not supplied, then conditional F statistics are not reported. |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the regression method. |
Multivariable Mendelian randomization is an extension of Mendelian randomization to deal with genetic variants that are associated with multiple risk factors. Two scenarios are envisioned for its use: 1) risk factors that are biologically related, such as lipid fractions; and 2) risk factors where there is potentially a network of causal effects (mediation) from one risk factor to another. In both cases, under the extended assumptions of multivariable Mendelian randomization, coefficients represent the direct causal effects of each risk factor in turn with the other risk factors being fixed.
We implement the method using multivariable weighted linear regression. If the variants are correlated, the method is implemented using generalized weighted linear regression; this is hard coded using matrix algebra.
The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factors, with the intercept set to zero and weights being the inverse-variances of the associations with the outcome.
The output from the function is an MVIVW
object containing:
Model |
A character string giving the type of model used ( |
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Robust |
|
Correlation |
The matrix of genetic correlations. |
Estimate |
A vector of causal estimates. |
StdError |
A vector of standard errors of the causal estimates. |
CILower |
The lower bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
CIUpper |
The upper bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RSE |
The estimated residual standard error from the regression model. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic. |
CondFstat |
Conditional F statistics: An approximation of the first-stage conditional F statistics for all variants based on the summarized data. This represents the instrument strength for each exposure conditional on other exposures in the model. This is only reported if the sample sizes for the genetic associations with the exposures are provided. |
Description of approach: Stephen Burgess, Simon G Thompson. Multivariable Mendelian Randomization: the use of pleiotropic genetic variants to estimate causal effects. American Journal of Epidemiology 2015; 181(4):251-260. doi: 10.1093/aje/kwu283.
Description of inverse-variance weighted method: Stephen Burgess, Frank Dudbridge, Simon G Thompson. Re: "Multivariable Mendelian randomization: the use of pleiotropic genetic variants to estimate causal effects." American Journal of Epidemiology 2015; 181(4):290-291. doi: 10.1093/aje/kwv017.
Use for mediation analysis: Stephen Burgess, Deborah J Thompson, Jessica MB Rees, Felix R Day, John R Perry, Ken K Ong. Dissecting causal pathways using Mendelian randomization with summarized genetic data: Application to age at menarche and risk of breast cancer. Genetics 2017; 207(2):481-487. doi: 10.1534/genetics.117.300191.
Calculation of conditional F statistics: Ashish Patel, Dipender Gill, Dmitry Shungin, Christos Mantzoros, Lotte Bjerre Knudsen, Jack Bowden, Stephen Burgess. Robust use of phenotypic heterogeneity at drug target genes for mechanistic insights: application of multivariable Mendelian randomization to GLP1R gene region. Pre-print.
mr_mvivw(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse))
mr_mvivw(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse))
The mr_mvivwme
function performs multivariable Mendelian randomization via the inverse-variance method with measurement error.
mr_mvivwme( object, model = "default", correl = FALSE, correl.x = NULL, distribution = "normal", alpha = 0.05, max_iter = 100, no_ini = 1, seed = 20201201, ... ) ## S4 method for signature 'MRMVInput' mr_mvivwme( object, model = "default", correl = FALSE, correl.x = NULL, distribution = "normal", alpha = 0.05, max_iter = 100, no_ini = 1, seed = 20201201, ... )
mr_mvivwme( object, model = "default", correl = FALSE, correl.x = NULL, distribution = "normal", alpha = 0.05, max_iter = 100, no_ini = 1, seed = 20201201, ... ) ## S4 method for signature 'MRMVInput' mr_mvivwme( object, model = "default", correl = FALSE, correl.x = NULL, distribution = "normal", alpha = 0.05, max_iter = 100, no_ini = 1, seed = 20201201, ... )
object |
An |
model |
What type of model should be used: |
correl |
If the genetic variants are correlated, then this correlation can be accounted for. |
correl.x |
Correlation matrix for exposures. Default is to assume the exposures are uncorrelated. |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
max_iter |
The maximum number of iterations in the optimisation procedure. |
no_ini |
The number of initial values for the optimisation procedure. |
seed |
The random seed to use for the optimisation procedure. The default value is 20201201. If set to |
... |
Additional arguments to be passed to the regression method. |
The extension of multivariable Mendelian randomization to account for measurement error in the genetic associations with the exposure traits.
The output from the function is an MVIVWME
object containing:
Model |
A character string giving the type of model used ( |
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Estimate |
A vector of causal estimates. |
StdError |
A vector of standard errors of the causal estimates. |
CILower |
The lower bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
CIUpper |
The upper bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
Correlation |
The matrix of genetic correlations. |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RSE |
The estimated residual standard error from the regression model. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic. |
Zhu, Jiazheng, Stephen Burgess, and Andrew J. Grant. Bias in Multivariable Mendelian Randomization Studies Due to Measurement Error on Exposures, 2022. https://doi.org/10.48550/arXiv.2203.08668.
mr_mvivwme(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse))
mr_mvivwme(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse))
The mr_mvlasso
function performs the multivariable MR-Lasso method, which applies lasso-type penalization to the direct effects of genetic variants on the outcome.
The causal estimates are described as post-lasso estimates, and are obtained by performing the multivariable IVW method using only those genetic variants that are identified as valid by the lasso procedure.
mr_mvlasso( object, orientate = 1, distribution = "normal", alpha = 0.05, lambda = numeric(0) ) ## S4 method for signature 'MRMVInput' mr_mvlasso( object, orientate = 1, distribution = "normal", alpha = 0.05, lambda = numeric(0) )
mr_mvlasso( object, orientate = 1, distribution = "normal", alpha = 0.05, lambda = numeric(0) ) ## S4 method for signature 'MRMVInput' mr_mvlasso( object, orientate = 1, distribution = "normal", alpha = 0.05, lambda = numeric(0) )
object |
An |
orientate |
The risk factor that genetic associations are orientated to. The default option is |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05. |
lambda |
The value of the tuning parameter used by the lasso procedure which controls the level of sparsity. If not specified, the tuning parameter will be calculated by the heterogeneity stopping rule. |
Multivariable MR-Lasso extends the multivariable IVW model to include an intercept term for each genetic variant. These intercept terms represent associations between the genetic variants and the outcome which bypass the risk factors. The regularized regression model is estimated by multivariable weighted linear regression where the intercept terms are subject to lasso-type penalization. The lasso penalization will tend to shrink the intercept terms corresponding to the valid instruments to zero.
The lasso penalty relies on a tuning parameter which controls the level of sparsity. The default is to use a heterogeneity stopping rule, but a fixed value may be specified.
As part of the analysis, the genetic variants are orientated so that all of the associations with one of the risk factors are positive (the first risk factor is used by default). Re-orientation of the genetic variants is performed automatically as part of the function.
The MR-Lasso method is performed in two steps. First, a regularized regression model is fitted, and some genetic variants are identified as valid instruments. Second, causal effects are estimated using standard multivariable IVW with only the valid genetic variants. The post-lasso method will be performed as long as the number of genetic variants identified as valid instruments is greater than the number of risk factors. The default heterogeneity stopping rule will always return more genetic variants as valid instruments than risk factors for identification. The main estimates given by the method are the post-lasso estimates. However, parameter estimates from the regularized regression model used to identify invalid variants are also provided for completeness.
If a substantial proportion of genetic variants are removed from the analysis, the multivariable MR-Lasso method may give a false impression of confidence in the causal estimate due to homogeneity of the variant-specific causal estimates amongst the remaining variants. However, it is not reasonable to claim that there is strong evidence for a causal effect after a large number of variants with heterogeneous estimates have been removed from the analysis.
The output from the function is an MVLasso
object containing:
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Estimate |
A vector of causal estimates from the multivariable MR-Lasso method. These are the post-lasso estimates. |
StdError |
A vector of standard errors of the causal estimates from the multivariable MR-Lasso method. |
CILower |
The lower bounds of the confidence intervals for the causal estimates based on the estimated standard errors and the significance level provided. |
CIUpper |
The upper bounds of the confidence intervals for the causal estimates based on the estimated standard errors and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-values associated with the (post-lasso) causal estimates using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
RegEstimate |
The estimates from the regularized regression model used in the multivariable MR-Lasso method. |
RegIntercept |
The intercept estimates estimates from the regularized regression model used in the multivariable MR-Lasso method. |
Valid |
The number of genetic variants that have been identified as valid instruments. |
ValidSNPs |
The names of genetic variants that have been identified as valid instruments. |
Lambda |
The value of the tuning parameter used to compute |
Andrew J Grant, Stephen Burgess. Pleiotropy robust methods for multivariable Mendelian randomization. arXiv 2020; 2008.11997
mr_mvlasso(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse))
mr_mvlasso(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse))
The mr_mvmedian
function performs multivariable Mendelian randomization via the median method. This is implemented by multivariable weighted quantile regression, with the quantile set to 0.5 (the median).
mr_mvmedian( object, distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 ) ## S4 method for signature 'MRMVInput' mr_mvmedian( object, distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 )
mr_mvmedian( object, distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 ) ## S4 method for signature 'MRMVInput' mr_mvmedian( object, distribution = "normal", alpha = 0.05, iterations = 10000, seed = 314159265 )
object |
An |
distribution |
The type of distribution used to calculate the confidence intervals. Options are |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05. |
iterations |
The number of bootstrap samples to generate when calculating the estimated standard error. The default value is 10000. |
seed |
The random seed to use when generating the bootstrap samples (for reproducibility). The default value is 314159265. If set to |
The multivariable median method is similar to the univariable weighted median method, except that it is implemented using quantile regression. The regression model is multivariable and weighted by the inverse of the variances of the variant-specific estimates. Confidence intervals are calculated by parametric bootstrap to estimate the standard error of the estimates, and then using quantiles of a normal or t-distribution (depending on the value of distribution
).
The output from the function is an MVMedian
object containing:
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Estimate |
A vector of causal estimates. |
StdError |
A vector of standard errors of the causal estimates. |
CILower |
The lower bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
CIUpper |
The upper bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
Alpha |
The significance level used when calculating the confidence intervals. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal or t-distribution (as specified in |
SNPs |
The number of genetic variants (SNPs) included in the analysis. |
mr_mvmedian(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse), iterations = 100) # iterations is set to 100 to reduce runtime for the mr_mvmedian method, # 10000 iterations are recommended in practice
mr_mvmedian(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse), iterations = 100) # iterations is set to 100 to reduce runtime for the mr_mvmedian method, # 10000 iterations are recommended in practice
The mr_mvpcgmm
function performs multivariable Mendelian randomization via the principal components generalized method of moments method.
mr_mvpcgmm( object, nx, ny, cor.x = NULL, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... ) ## S4 method for signature 'MRMVInput' mr_mvpcgmm( object, nx, ny, cor.x = NULL, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... )
mr_mvpcgmm( object, nx, ny, cor.x = NULL, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... ) ## S4 method for signature 'MRMVInput' mr_mvpcgmm( object, nx, ny, cor.x = NULL, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... )
object |
An |
nx |
Vector of sample sizes used to compute genetic associations with the exposure (one for each exposure). |
ny |
The sample size used to compute genetic associations with the outcome. |
cor.x |
Correlation matrix for exposures. Default is to assume the exposures are uncorrelated. |
r |
The number of genetic principal components to be used to instrument the exposures. Default chooses |
thres |
The threshold value of variation in the sample weighted genetic correlation matrix explained by the genetic principal components. The default value is 0.99, indicating that 99% of variation is explained by the principal components. Note that if |
robust |
Indicates whether overdispersion heterogeneity is accounted for in the model. Default is TRUE. |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the optimization routines to calculate GMM estimates and overdispersion parameter. |
When a Mendelian randomization analysis is performed using correlated genetic variants from a single gene region, there is a tradeoff between using too few variants (and compromising on power) and using too many variants (in which case, estimates can be highly sensitive to small variation in the correlation matrix). This method performs dimension reduction on a weighted version of the genetic correlation matrix to form principal components based on the genetic variants, which are then used as instruments. It is recommended not to include very highly correlated variants in this method (say, r^2 > 0.95
), but the method should cope well with variants correlated below this level.
This function runs a multivariable version of the PC-GMM method, which can be used when there are distinct exposures associated with variants at a single gene region. Phenotypic heterogeneity (that is, the genetic associations with the exposures are not collinear) at genomic loci encoding drug targets can be exploited by multivariable Mendelian randomization to provide insight on the pathways by which pharmacological interventions may affect disease risk.
This method provides two-sample multivariable Mendelian randomization estimates and associated confidence intervals that account for overdispersion heterogeneity in dimension-reduced genetic associations (when robust = TRUE
).
The output from the function is an MVPCGMM
object containing:
Robust |
|
Exposure |
A character vector with the names given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Correlation |
The matrix of genetic correlations. |
ExpCorrelation |
|
CondFstat |
A vector of conditional F-statistics (one for each exposure). |
Estimate |
A vector of causal estimates. |
StdError |
A vector of standard errors of the causal estimates. |
CILower |
The lower bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
CIUpper |
The upper bounds of the causal estimates based on the estimated standard errors and the significance level provided. |
Overdispersion |
The estimate of the overdispersion parameter. |
PCs |
The number of genetic principal components used to instrument the exposures. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal distribution. |
Alpha |
The significance level used when calculating the confidence intervals. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model only): the null hypothesis is that all genetic principal components estimate the same causal parameter; rejection of the null is an indication that one or more principal components may be pleiotropic. |
Description of multivariable Mendelian randomization: Stephen Burgess, Simon G Thompson. Multivariable Mendelian Randomization: the use of pleiotropic genetic variants to estimate causal effects. American Journal of Epidemiology 2015; 181(4):251-260. doi: 10.1093/aje/kwu283.
Description of the PC-GMM method: "Robust use of phenotypic heterogeneity at drug target genes for mechanistic insights: application of cis-multivariable Mendelian randomization to GLP1R gene region" (Preprint).
mr_mvpcgmm(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse, correlation = diag(length(ldlc))), nx=rep(17723,3), ny=17723) # Note this example does not use variants from a single gene region, and is provided # to demonstrate that the code works, rather than to illustrate a recommended use case.
mr_mvpcgmm(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse), by = chdlodds, byse = chdloddsse, correlation = diag(length(ldlc))), nx=rep(17723,3), ny=17723) # Note this example does not use variants from a single gene region, and is provided # to demonstrate that the code works, rather than to illustrate a recommended use case.
The mr_pcgmm
function performs multivariable Mendelian randomization via the principal components generalized method of moments method.
mr_pcgmm( object, nx, ny, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_pcgmm( object, nx, ny, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... )
mr_pcgmm( object, nx, ny, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... ) ## S4 method for signature 'MRInput' mr_pcgmm( object, nx, ny, r = NULL, thres = 0.99, robust = TRUE, alpha = 0.05, ... )
object |
An |
nx |
The sample size used to compute genetic associations with the exposure. |
ny |
The sample size used to compute genetic associations with the outcome. |
r |
The number of genetic principal components to be used to instrument the exposure. Default chooses |
thres |
The threshold value of variation in the sample weighted genetic correlation matrix explained by the genetic principal components. The default value is 0.99, indicating that 99% of variation is explained by the principal components. Note that if |
robust |
Indicates whether overdispersion heterogeneity is accounted for in the model. Default is TRUE. |
alpha |
The significance level used to calculate the confidence interval. The default value is 0.05. |
... |
Additional arguments to be passed to the optimization routines to calculate the GMM estimate and overdispersion parameter. |
When a Mendelian randomization analysis is performed using correlated genetic variants from a single gene region, there is a tradeoff between using too few variants (and compromising on power) and using too many variants (in which case, estimates can be highly sensitive to small variation in the correlation matrix). This method performs dimension reduction on a weighted version of the genetic correlation matrix to form principal components based on the genetic variants, which are then used as instruments. It is recommended not to include very highly correlated variants in this method (say, r^2 > 0.95
), but the method should cope well with variants correlated below this level.
This function runs a univariable version of the PC-GMM method, which can be used when there are a single exposure associated with variants at a given gene region.
This method provides two-sample univariable Mendelian randomization estimates and associated confidence intervals that account for overdispersion heterogeneity in dimension-reduced genetic associations (when robust = TRUE
).
The output from the function is an PCGMM
object containing:
Robust |
|
Exposure |
A character string with the name given to the exposure. |
Outcome |
A character string with the names given to the outcome. |
Correlation |
The matrix of genetic correlations. |
Estimate |
The causal estimate. |
StdError |
The standard error of the causal estimate. |
CILower |
The lower bound of the causal estimate based on the estimated standard error and the significance level provided. |
CIUpper |
The upper bound of the causal estimate based on the estimated standard error and the significance level provided. |
Fstat |
The first-stage F statistic for all genetic principal components used as instruments. |
Overdispersion |
The estimate of the overdispersion parameter. |
PCs |
The number of genetic principal components used to instrument the exposure. |
Pvalue |
The p-values associated with the estimates (calculated as Estimate/StdError as per Wald test) using a normal distribution. |
Alpha |
The significance level used when calculating the confidence intervals. |
Heter.Stat |
Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model only): the null hypothesis is that all genetic principal components estimate the same causal parameter; rejection of the null is an indication that one or more principal components may be pleiotropic. |
Description of the PC-GMM method: "Robust use of phenotypic heterogeneity at drug target genes for mechanistic insights: application of cis-multivariable Mendelian randomization to GLP1R gene region" (Preprint).
mr_pcgmm(mr_input(bx = calcium, bxse = calciumse, by = fastgluc, byse = fastglucse, correlation = calc.rho), nx=6351, ny=133010)
mr_pcgmm(mr_input(bx = calcium, bxse = calciumse, by = fastgluc, byse = fastglucse, correlation = calc.rho), nx=6351, ny=133010)
The mr_pivw
function implements the penalized inverse-variance weighted (pIVW) method.
mr_pivw( object, lambda = 1, over.dispersion = TRUE, delta = 0, sel.pval = NULL, Boot.Fieller = TRUE, alpha = 0.05 ) ## S4 method for signature 'MRInput' mr_pivw( object, lambda = 1, over.dispersion = TRUE, delta = 0, sel.pval = NULL, Boot.Fieller = TRUE, alpha = 0.05 )
mr_pivw( object, lambda = 1, over.dispersion = TRUE, delta = 0, sel.pval = NULL, Boot.Fieller = TRUE, alpha = 0.05 ) ## S4 method for signature 'MRInput' mr_pivw( object, lambda = 1, over.dispersion = TRUE, delta = 0, sel.pval = NULL, Boot.Fieller = TRUE, alpha = 0.05 )
object |
An |
lambda |
The penalty parameter in the pIVW estimator. It plays a role in the bias-variance trade-off of the estimator. It is recommended to choose |
over.dispersion |
Should the method consider overdispersion (balanced horizontal pleiotropy)? Default is TRUE. |
delta |
The z-score threshold for IV selection. |
sel.pval |
A numeric vector containing the P-values of the SNP effects on the exposure, which will be used for the IV selection. |
Boot.Fieller |
If |
alpha |
The significance level used to calculate the confidence intervals. The default value is 0.05. |
The penalized inverse-variance weighted (pIVW) estimator accounts for weak instruments and balanced horizontal pleiotropy simultaneously
in two-sample MR with summary statistics, i.e., an exposure sample (with IV-exposure effect Bx
and standard error Bxse
) and
an outcome sample (with IV-outcome effect By
and standard error Byse
).
The pIVW estimator also allows for IV selection in three-sample MR, where weak IVs are screened out using
an extra sample (with IV-exposure effect Bx*
and standard error Bxse*
) independent of the exposure sample and outcome sample.
Generally, the P-value for Bx*
can be computed by sel.pval=2*pnorm(abs(Bx*/Bxse*), lower.tail = FALSE)
,
Given sel.pval
and a z-score threshold delta
, the variants kept in the analysis will be those
with sel.pval<2*pnorm(delta,lower.tail = FALSE)
.
The mr_pivw
function outputs a measure Condition
that needs to be large for reliable asymptotic properties of the pIVW estimator.
We also refer to Condition
as effective sample size, which is a function of a measure of IV strength and the number of IVs.
When delta
is zero (i.e., no IV selection), Condition = (average F-statistic -1)*sqrt(# snps)
. When delta
is not zero
(i.e., IV selection is conducted), Condition = [(average F-statistic -1)*sqrt(# snps)]/c
,
where the numerator is computed using the selected variants, and the denominator c
involves the selection probabilities
of all variants (see more details in the paper). We suggest that Condition
should be greater than 5 for the pIVW estimator to achieve reliable asymptotic properties.
The output from the function is a PIVW
object containing:
Over.dispersion |
|
Boot.Fieller |
|
Lambda |
The penalty parameter in the pIVW estimator. |
Delta |
The z-score threshold for IV selection. |
Exposure |
A character string giving the name given to the exposure. |
Outcome |
A character string giving the name given to the outcome. |
Estimate |
The causal point estimate from the pIVW estimator. |
StdError |
The standard error associated with |
CILower |
The lower bound of the confidence interval for |
CIUpper |
The upper bound of the confidence interval for |
Alpha |
The significance level used in constructing the confidence interval. |
Pvalue |
P-value associated with the causal estimate from the pIVW estimator, which is derived from the bootstrapping Fieller method or normal distribution. |
Tau2 |
The variance of the balanced horizontal pleiotropy. |
SNPs |
The number of SNPs after IV selection. |
Condition |
The estimated effective sample size. It is recommended to be greater than 5 for the pIVW estimator to achieve reliable asymptotic properties. See 'Details'. |
Xu S., Wang P., Fung W.K. and Liu Z. (2022). A Novel Penalized Inverse-Variance Weighted Estimator for Mendelian Randomization with Applications to COVID-19 Outcomes. Biometrics. doi: 10.1111/biom.13732.
mr_pivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
mr_pivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
The function mr_plot
has three functionalities. It can generate a visual representation of MRInput
, MRMVInput
and MRAll
objects.
mr_plot( object, error = TRUE, line = "ivw", orientate = FALSE, interactive = TRUE, labels = FALSE ) ## S4 method for signature 'MRInput' mr_plot( object, error = TRUE, line = "ivw", orientate = FALSE, interactive = TRUE, labels = FALSE ) ## S4 method for signature 'MRAll' mr_plot(object) ## S4 method for signature 'MRMVInput' mr_plot( object, error = TRUE, line = TRUE, orientate = FALSE, interactive = TRUE, labels = FALSE )
mr_plot( object, error = TRUE, line = "ivw", orientate = FALSE, interactive = TRUE, labels = FALSE ) ## S4 method for signature 'MRInput' mr_plot( object, error = TRUE, line = "ivw", orientate = FALSE, interactive = TRUE, labels = FALSE ) ## S4 method for signature 'MRAll' mr_plot(object) ## S4 method for signature 'MRMVInput' mr_plot( object, error = TRUE, line = TRUE, orientate = FALSE, interactive = TRUE, labels = FALSE )
object |
An |
error |
When viewing an |
line |
When viewing an |
orientate |
When viewing an |
interactive |
When viewing an |
labels |
When viewing an |
The result is dependent on the type of object passed to mr_plot
.
When the object is an MRInput
object, the function uses either the plot
command (if interactive
is set to FALSE
) or plotly
syntax (if interactive
is set to TRUE
) to plot the association estimates against each other.
When the object is an MRMVInput
object, functionality is similar except that we plot the estimated associations with the outcome on the y-axis, and fitted values of the associations with the outcome from the inverse-variance weighted method on the x-axis.
If interactive
is set to FALSE
, then a static graph is produced. By setting labels
to TRUE
, the names of the genetic variants appear above the points. This produces a less visually appealing graph, but one where it is easier to identify the individual genetic variants.
If interactive
is set to TRUE
, then the plot is interactive and the user can hover over the various points to see the name of the associated genetic variant and its association estimates.
When the object is an MRAll
object, the function generates a ggplot
to compare the causal estimates proposed by different methods.
mr_plot(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), line="egger", orientate = TRUE) mr_plot(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), line="ivw", interactive=FALSE) # produces a static graph mr_plot(mr_allmethods(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), method="all", iterations = 50)) # iterations is set to 50 to reduce runtime for the mr_median method, # 10000 iterations are recommended in practice
mr_plot(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), line="egger", orientate = TRUE) mr_plot(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), line="ivw", interactive=FALSE) # produces a static graph mr_plot(mr_allmethods(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), method="all", iterations = 50)) # iterations is set to 50 to reduce runtime for the mr_median method, # 10000 iterations are recommended in practice
An object containing the estimates produced using the mr_allmethods
function.
Data
The mr_input
object that was used as an input to the mr_allmethods
function. This includes the original data, so that a call to mr_plot
can plot the original data and the various causal estimates.
Values
A data.frame object comprising estimates from the various methods called by the mr_allmethods
function. The first column gives the names of the methods, then the causal estimates, standard errors, 95% confidence intervals, and p-values.
Method
A string indicating whether all methods are implemented ("all"
, the default option), or just main methods ("main"
), or only a subset of methods ("ivw"
, "egger"
, or "median"
).
An object containing the results of MRcML.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Estimate
Estimate of theta.
StdError
Standard error of estimate.
Pvalue
p-value of estimate.
BIC_invalid
Set of selected invalid IVs if cML-BIC is performed, i.e. without MA or DP.
GOF1_p
p-value of the first goodness-of-fit test.
GOF2_p
p-value of the second goodness-of-fit test.
SNPs
The number of SNPs that were used in the calculation.
Alpha
Significance level for the confidence interval for estimate, default is 0.05.
CILower
Lower bound of the confidence interval for estimate.
CIUpper
Upper bound of the confidence interval for estimate.
MA
Indicator of whether model average is applied.
DP
Indicator of whether data perturbation is applied.
An object containing the estimate produced using the contamination mixture method as well as various statistics.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Psi
The value of the standard deviation of the distribution of invalid estimands (default is 1.5 times the standard deviation of the ratio estimates).
Estimate
The causal estimate from the contamination mixture method.
CIRange
The confidence interval for Estimate
based on a grid search.
CILower
The lower limit of the confidence interval. If the confidence interval contains multiple ranges, then lower limits of all ranges will be reported.
CIUpper
The upper limit of the confidence interval. If the confidence interval contains multiple ranges, then upper limits of all ranges will be reported.
CIMin
The smallest value used in the search to find the confidence interval.
CIMax
The largest value used in the search to find the confidence interval.
CIStep
The step size used in the search to find the confidence interval.
Pvalue
The p-value associated with the estimate calculated using the likelihood function and a chi-squared distribution.
Valid
The numbers of genetic variants that were considered valid instruments at the causal estimate.
ValidSNPs
The names of genetic variants that were considered valid instruments at the causal estimate.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
SNPs
The number of SNPs that were used in the calculation.
An object containing the estimate produced using the heterogeneity-penalized model-averaging mode-based estimation method as well as various statistics.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Prior
The value of the prior probability of a genetic variant being a valid instrument (default is 0.5).
Estimate
The causal estimate from the heterogeneity-penalized method.
CIRange
The confidence interval for Estimate
based on a grid search.
CILower
The lower limit of the confidence interval. If the confidence interval contains multiple ranges, then lower limits of all ranges will be reported.
CIUpper
The upper limit of the confidence interval. If the confidence interval contains multiple ranges, then upper limits of all ranges will be reported.
CIMin
The smallest value used in the search to find the confidence interval.
CIMax
The largest value used in the search to find the confidence interval.
CIStep
The step size used in the search to find the confidence interval.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
SNPs
The number of SNPs that were used in the calculation.
An object containing the four vectors of summary statistics required to calculate Mendelian randomization estimates.
The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors. Estimates can either be specified by the user, or extracted from the PhenoScanner tool.
betaX
A numeric vector of beta-coefficient values for genetic associations with the first variable (often referred to as the exposure, risk factor, or modifiable phenotype).
betaY
A numeric vector of beta-coefficient values for genetic associations with the second variable (often referred to as the outcome). For a disease outcome, the beta coefficients are log odds estimates from logistic regression analyses.
betaXse
The standard errors associated with the beta-coefficients in betaX
.
betaYse
The standard errors associated with the beta-coefficients in betaY
.
correlation
The matrix of correlations between genetic variants. If this variable is not provided, then we assume that genetic variants are uncorrelated.
exposure
The name of the exposure variable.
outcome
The name of the outcome variable.
snps
The names of the genetic variants (SNPs) included in the analysis. The slots exposure
, outcome
, and snps
are not required, but may be useful for keeping track of various MRInput
objects. They are also used by the mr_plot
function.
effect_allele
The name of the effect allele for each SNP. The beta-coefficients are the associations with the exposure and outcome per additional copy of the effect allele.
other_allele
The name of the non-effect allele.
eaf
The expected allele frequencies (numeric). The slots effect_allele
, other_allele
, and eaf
are neither required, nor currently used in the MendelianRandomization package. They are included for future compatibility with the MR-Base suite of functions.
extract.pheno.csv()
for a description of how the above values can be extracted from PhenoScanner http://www.phenoscanner.medschl.cam.ac.uk/.
An object containing the estimates produced using the MR-Lasso method as well as various statistics.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Estimate
The causal estimate from the MR-Lasso method.
StdError
The standard error associated with Estimate
.
CILower
The lower bounds of the confidence intervals for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence intervals for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate from the MR-Lasso method.
SNPs
The number of SNPs used in the calculation.
RegEstimate
The estimate from the regularized regression model used in the MR-Lasso method.
RegIntercept
The intercept estimates from the regularized regression model used in the MR-Lasso method. An intercept estimate of zero identifies the corresponding genetic variant as a valid instrument. Genetic variants with non-zero intercept estimates will be excluded from the post-lasso estimator.
Valid
The number of genetic variants that have been identified as valid instruments.
ValidSNPs
The names of genetic variants that have been identified as valid instruments.
Lambda
The value of the tuning parameter used to compute RegEstimate
(default is to calulate Lambda
using the heterogeneity stopping rule).
An object containing the estimate produced using the mode-based estimation method of Hartwig et al as well as various statistics.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Weighting
Whether the analysis was weighted
or unweighted
.
StdErr
Whether the simple
or delta
version of the standard errors were used.
Phi
The value of the bandwidth factor.
Estimate
The causal estimate from the mode-based estimation method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate.
SNPs
The number of SNPs that were used in the calculation.
An object containing the summary statistics required to calculate multivariable Mendelian randomization estimates.
The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors.
betaX
A matrix of beta-coefficient values for genetic associations with the risk factor variables. These should be arranged so that column 1 are the beta-coefficients for risk factor 1, and row 1 are the beta-coefficients for genetic variant 1.
betaY
A numeric vector of beta-coefficient values for genetic associations with the second variable (often referred to as the outcome). For a disease outcome, the beta coefficients are log odds estimates from logistic regression analyses.
betaXse
The matrix of standard errors associated with the beta-coefficients in betaX
.
betaYse
The vector of standard errors associated with the beta-coefficients in betaY
.
correlation
The matrix of correlations between genetic variants. If this variable is not provided, then we assume that genetic variants are uncorrelated.
exposure
The names of the exposure variables.
outcome
The name of the outcome variable.
snps
The names of the genetic variants (SNPs) included in the analysis. The slots exposure
, outcome
, and snps
are not required, but may be useful for keeping track of various MRInput
objects. They are also used by the mr_plot
function.
effect_allele
The name of the effect allele for each SNP. The beta-coefficients are the associations with the exposure and outcome per additional copy of the effect allele.
other_allele
The name of the non-effect allele.
eaf
The expected allele frequencies (numeric). The slots effect_allele
, other_allele
, and eaf
are neither required, nor currently used in the MendelianRandomization package. They are included for future compatibility with the MR-Base suite of functions.
An object containing the estimates produced using the multivariable MR-Egger method as well as various statistics.
Model
Model always takes the value random
, as only random-effects analyses are permitted.
Orientate
The number of the risk factor that genetic associations are orientated to. The default value is 1
, meaning that genetic associations with the first risk factor are set to be positive.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
Estimate
The causal estimates from the inverse-variance weighted method.
StdError.Est
The standard errors associated with Estimate
.
CILower.Est
The lower bounds of the confidence interval for Estimate
based on StdError
.
CIUpper.Est
The upper bounds of the confidence interval for Estimate
based on StdError
.
Pvalue.Est
P-value associated with the causal estimate.
Intercept
The intercept estimate from the MR-Egger method. Under the InSIDE assumption, the intercept represents the average pleiotropic effect (average direct effect on the outcome) of a genetic variant. If the intercept differs from zero, this is evidence that the genetic variants are not all valid instruments; specifically, there is directional pleiotropy.
StdError.Int
The standard error associated with Intercept
.
CILower.Int
The lower bound of the confidence interval for Intercept
based on StdError.Int
.
CIUpper.Int
The upper bound of the confidence interval for Estimate
based on StdError.Int
.
Pvalue.Int
P-value associated with the intercept.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
SNPs
The number of SNPs that were used in the calculation.
RSE
The estimated residual standard error from the regression model.
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.
An object containing the estimates produced using the multivariable generalized method of methods (GMM) method.
robust
Whether the robust model with overdispersion heterogeneity is estimated.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants if specified. If not specified, an identity matrix will be returned.
ExpCorrelation
Whether an exposure correlation matrix was specified.
CondFstat
The conditional F-statistic for each exposure.
Estimate
The causal estimates from the GMM method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence interval for Estimate
based on StdError
.
Overdispersion
The estimate of the overdispersion parameter for the robust model. If this is negative, then a value of zero is used in the method.
Pvalue
P-value associated with the causal estimates.
Alpha
The significance level used in constructing confidence intervals (default is 0.05).
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model): the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more genetic variants may be pleiotropic.
An object containing the estimates produced using the multivariable inverse-variance weighted (IVW) method as well as various statistics.
Model
The model used for estimation: random-effects ("random"
) or fixed-effect ("fixed"
). The default option ("default"
) is to use a fixed-effect model when there are three or fewer genetic variants, and a random-effects model when there are four or more. The (multiplicative) random-effects model allows for heterogeneity between the causal estimates targeted by the genetic variants by allowing over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1, as in a fixed-effect analysis).
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Robust
Whether robust regression was used in the regression model relating the genetic associations with the outcome and those with the exposure.
Correlation
The matrix of correlations between genetic variants.
Estimate
The causal estimates from the inverse-variance weighted method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate.
SNPs
The number of SNPs that were used in the calculation.
RSE
The estimated residual standard error from the regression model.
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.
CondFstat
Conditional F statistics: An approximation of the first-stage conditional F statistics for all variants based on the summarized data. This represents the instrument strength for each exposure conditional on other exposures in the model. This is only reported if the sample sizes for the genetic associations with the exposures are provided.
An object containing the estimates produced using the multivariable inverse-variance weighted (IVW) method with measurement error, as well as various statistics.
Model
The model used for estimation: random-effects ("random"
) or fixed-effect ("fixed"
). The default option ("default"
) is to use a fixed-effect model when there are three or fewer genetic variants, and a random-effects model when there are four or more. The (multiplicative) random-effects model allows for heterogeneity between the causal estimates targeted by the genetic variants by allowing over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1, as in a fixed-effect analysis).
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
Estimate
The causal estimates from the inverse-variance weighted method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate.
SNPs
The number of SNPs that were used in the calculation.
RSE
The estimated residual standard error from the regression model.
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.
An object containing the estimates produced using the multivariable MR-Lasso method as well as various statistics.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Orientate
The number of the risk factor that genetic associations are orientated to. The default value is 1
, meaning that genetic associations with the first risk factor are set to be positive.
Estimate
The causal estimates from the multivariable MR-Lasso method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence intervals for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence intervals for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-values associated with the causal estimates from the multivariable MR-Lasso method.
SNPs
The number of SNPs used in the calculation.
RegEstimate
The estimates from the regularized regression model used in the multivariable MR-Lasso method.
RegIntercept
The intercept estimates from the regularized regression model used in the multivariable MR-Lasso method. An intercept estimate of zero identifies the corresponding genetic variant as a valid instrument. Genetic variants with non-zero intercept estimates will be excluded from the MR-Lasso method, which is obtained as a post-lasso estimator.
Valid
The number of genetic variants that have been identified as valid instruments.
ValidSNPs
The names of genetic variants that have been identified as valid instruments.
Lambda
The value of the tuning parameter used to compute RegEstimate
(default is to calulate Lambda
using the heterogeneity stopping rule).
An object containing the estimates produced using the multivariable median method as well as various statistics.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Estimate
The causal estimates from the multivariable median method.
StdError
The standard errors associated with Estimate
(obtained from bootstrapping).
CILower
The lower bounds of the confidence intervals for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence intervals for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-values associated with the causal estimates from the Wald method.
SNPs
The number of SNPs that used in the calculation.
An object containing the results of MVMRcML.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Estimate
The causal estimates from the multivariable MRcML method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence intervals for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence intervals for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-values associated with the causal estimates from the multivariable MRcML method.
BIC_invalid
The index set of selected invalid IVs by MVMRcML-BIC.
K_hat
The number of selected invalid IVs by MVMRcML-BIC, or a vector for each data perturbation in MVMRcML-DP.
eff_DP_B
The number of data perturbations with successful convergence in MVMRcML-DP.
SNPs
The number of SNPs that were used in the calculation.
DP
Indicator of whether data perturbation is applied.
An object containing the estimates produced using the multivariable principal components generalized method of methods (PC-GMM) method as well as various statistics.
robust
Whether the robust model with overdispersion heterogeneity is estimated.
Exposure
The names of the exposure variables.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
ExpCorrelation
Whether an exposure correlation matrix was specified.
CondFstat
The conditional F-statistic for each exposure.
Estimate
The causal estimates from the PC-GMM method.
StdError
The standard errors associated with Estimate
.
CILower
The lower bounds of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bounds of the confidence interval for Estimate
based on StdError
.
Overdispersion
The estimate of the overdispersion parameter for the robust model.
PCs
The number of genetic principal components used to instrument the exposures.
Pvalue
P-value associated with the causal estimates.
Alpha
The significance level used in constructing confidence intervals (default is 0.05).
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model): the null hypothesis is that all principal components estimate the same causal parameter; rejection of the null is an indication that one or more principal components may be pleiotropic.
An object containing the estimates produced using the univariable principal components generalized method of methods (PC-GMM) method as well as various statistics.
robust
Whether the robust model with overdispersion heterogeneity is estimated.
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Correlation
The matrix of correlations between genetic variants.
Estimate
The causal estimate from the PC-GMM method.
StdError
The standard error associated with Estimate
.
CILower
The lower bound of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bound of the confidence interval for Estimate
based on StdError
.
Fstat
The first-stage F statistic for all genetic principal components used as instruments.
Overdispersion
The estimate of the overdispersion parameter for the robust model.
PCs
The number of genetic principal components used to instrument the exposure.
Pvalue
P-value associated with the causal estimate.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Heter.Stat
Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model): the null hypothesis is that all principal components estimate the same causal parameter; rejection of the null is an indication that one or more principal components may be pleiotropic.
An object containing the estimate produced using the penalized inverse-variance weighted (pIVW) method as well as various statistics.
Over.dispersion
Should the method consider overdispersion (balanced horizontal pleiotropy)? Default is TRUE.
Boot.Fieller
If Boot.Fieller=TRUE
, then the P-value and the confidence interval of the causal effect will be calculated based on the bootstrapping Fieller method. Otherwise, the P-value and the confidence interval of the causal effect will be calculated from the normal distribution. It is recommended to use the bootstrapping Fieller method when Condition
(the estimated effective sample size) is smaller than 10. By default, Boot.Fieller=TRUE
.
Lambda
The penalty parameter in the pIVW estimator. The penalty parameter plays a role in the bias-variance trade-off of the estimator. It is recommended to choose lambda=1
to achieve the smallest bias and valid inference. By default, lambda=1
.
Delta
The z-score threshold for IV selection. By default, delta=0
(i.e., no IV selection will be conducted).
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Estimate
The causal point estimate from the pIVW estimator.
StdError
The standard error associated with Estimate
.
CILower
The lower bound of the confidence interval for Estimate
, which is derived from the bootstrapping Fieller method or normal distribution. For the bootstrapping Fieller's interval, if it contains multiple ranges, then lower limits of all ranges will be reported.
CIUpper
The upper bound of the confidence interval for Estimate
, which is derived from the bootstrapping Fieller method or normal distribution. For the bootstrapping Fieller's interval, if it contains multiple ranges, then upper limits of all ranges will be reported.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate from the pIVW estimator.
Tau2
The variance of the balanced horizontal pleiotropy. Tau2
is calculated by using all IVs in the data before conducting the IV selection.
SNPs
The number of SNPs after IV selection.
Condition
The estimated effective sample size. It is recommended to be greater than 5 for the pIVW estimator to achieve reliable asymptotic properties.
An object containing the estimate produced using the median-based method as well as various statistics.
Type
The type of median that has been calculated, "simple"
, "weighted"
, or "penalized"
.
Exposure
The name of the exposure variable.
Outcome
The name of the outcome variable.
Estimate
The causal point estimate from the median-based method.
StdError
The standard error associated with Estimate
(obtained from bootstrapping).
CILower
The lower bound of the confidence interval for Estimate
based on StdError
.
CIUpper
The upper bound of the confidence interval for Estimate
based on StdError
.
Alpha
The significance level used in constructing the confidence interval (default is 0.05).
Pvalue
P-value associated with the causal estimate from the Wald method.
SNPs
The number of SNPs that used in the calculation.