The gsmr R-package implements the GSMR (Generalised Summary-data-based Mendelian Randomisation) method to test for putative causal association between a risk factor and a disease using summary-level data from genome-wide association studies (GWAS) (Zhu et al. 2018 Nat. Commun.). The R package is developed by Zhihong Zhu, Zhili Zheng, Futao Zhang and Jian Yang at Institute for Molecular Bioscience, the University of Queensland. Bug reports or questions: [email protected].
Note: The GSMR method has also been implemented in the GCTA software (GCTA-GSMR)
Zhu, Z. et al. (2018) Causal associations between risk factors and common diseases inferred from GWAS summary data. Nat. Commun. 9, 224 (https://www.nature.com/articles/s41467-017-02317-2).
Note: We included a new HEIDI-outlier method (as part of the GSMR analysis) in gsmr v1.0.7. However, the new HEIDI-outlier method is currently under development and subject to changes during the method development. From the GSMR R package (>= version 1.0.8), we changed the default back to the original HEIDI-outlier method described in Zhu et al. (2018 Nature Communications) and added a temporary flag ('gsmr2_beta') to test the new method. The command to use this flag can be found in the tutorial below. The new HEIDI-outlier method in gsmr (>= version 1.0.8) has been tested by extensive simulations and real data analyses. We will make a formal release in our next GSMR paper.
Sample data are available in test_data.zip. This document has been integrated in the gsmr R-package, we can check it by the standard command “?function_name” in R.
The gsmr requires R >= 2.15, you can install it in R by:
# gsmr requires the R-package(s)
install.packages(c('survey'));
# install gsmr
install.packages("http://cnsgenomics.com/software/gsmr/static/gsmr_1.0.9.tar.gz",repos=NULL,type="source")
V1.0.9 (gmr_1.0.9.tar.gz PDF, 18 Jun. 2019): Change the flag 'gsmr_beta' to 'gsmr2_beta'.
V1.0.8 (gmr_1.0.8.tar.gz PDF, 21 Jan. 2019): Added a flag 'gsmr_beta' to use a testing version of the HEIDI-outlier method.
V1.0.7 (gmr_1.0.7.tar.gz PDF, 9 Oct. 2018): Added a multi-SNP-based HEIDI-outlier test in the HEIDI-outlier analysis.
V1.0.6 (gmr_1.0.6.tar.gz PDF, 23 Jan. 2018): Added a function to remove SNPs in high LD.
V1.0.5 (gmr_1.0.5.tar.gz PDF, 13 Dec. 2017): Improved the approximation of the sampling covariance matrix.
V1.0.4 (gsmr_1.0.4.tar.gz PDF, 6 Nov. 2017): Added the bi-directional GSMR analysis. The HEIDI-outlier analysis has been integrated in the GSMR analysis by default.
V1.0.3 (gsmr_1.0.3.tar.gz PDF, 12 Oct. 2017): Added more example data.
Removed the initial versions (8 Nov 2016).
The GSMR analysis only requires summary-level data from GWAS. Here is an example, where the risk factor (x) is LDL cholesterol (LDL-c) and the disease (y) is coronary artery disease (CAD). GWAS summary data for both LDL-c and CAD are available in the public domain (Global Lipids Genetics Consortium et al. 2013, Nature Genetics; Nikpay, M. et al. 2015, Nature Genetics).
library("gsmr")
## Loading required package: markdown
data("gsmr")
head(gsmr_data)
## SNP a1 a2 a1_freq bzx bzx_se bzx_pval bzx_n bzy
## 1 rs10903129 A G 0.45001947 -0.0328 0.0037 3.030e-17 169920.0 0.008038
## 2 rs12748152 T C 0.08087758 0.0499 0.0066 3.209e-12 172987.5 0.013671
## 3 rs11206508 A G 0.14396988 0.0434 0.0055 2.256e-14 172239.0 0.030222
## 4 rs11206510 C T 0.19128911 -0.0831 0.0050 2.380e-53 172812.0 -0.074519
## 5 rs10788994 T C 0.18395430 0.0687 0.0049 8.867e-41 172941.9 0.038267
## 6 rs529787 G C 0.19713099 -0.0553 0.0052 8.746e-24 161969.0 0.001707
## bzy_se bzy_pval bzy_n
## 1 0.0092442 0.3845651000 184305
## 2 0.0185515 0.4611690000 184305
## 3 0.0141781 0.0330400000 184305
## 4 0.0133438 0.0000000234 184305
## 5 0.0118752 0.0012711000 184305
## 6 0.0135491 0.8997431000 184305
dim(gsmr_data)
## [1] 188 12
This is the input format for the GSMR analysis. In this data set, there are 188 near-independent SNPs associated with LDL-c at a genome-wide significance level (i.e. p < 5e-8).
# Save the genetic variants and effect alleles in a text file using R
write.table(gsmr_data[,c(1,2)], "gsmr_example_snps.allele", col.names=F, row.names=F, quote=F)
# Extract the genotype data from a GWAS dataset using GCTA
gcta64 --bfile gsmr_example --extract gsmr_example_snps.allele --update-ref-allele gsmr_example_snps.allele --recode --out gsmr_example
\textcolor{red}{Note: the two steps above guarantee that the LD correlations are calculated based on the effect alleles of the SNPs.}
Note: the two steps above guarantee that the LD correlations are calculated based on the effect alleles for the SNP effects.
# Estimate LD correlation matrix using R
snp_coeff_id = scan("gsmr_example.xmat.gz", what="", nlines=1)
snp_coeff = read.table("gsmr_example.xmat.gz", header=F, skip=2)
# Match the SNP genotype data with the summary data
snp_id = Reduce(intersect, list(gsmr_data$SNP, snp_coeff_id))
gsmr_data = gsmr_data[match(snp_id, gsmr_data$SNP),]
snp_order = match(snp_id, snp_coeff_id)
snp_coeff_id = snp_coeff_id[snp_order]
snp_coeff = snp_coeff[, snp_order]
# Calculate the LD correlation matrix
ldrho = cor(snp_coeff)
# Check the size of the correlation matrix and double-check if the order of the SNPs in the LD correlation matrix is consistent with that in the GWAS summary data
colnames(ldrho) = rownames(ldrho) = snp_coeff_id
dim(ldrho)
## [1] 188 188
# Show the first 5 rows and columns of the matrix
ldrho[1:5,1:5]
## rs10903129 rs12748152 rs11206508 rs11206510 rs10788994
## rs10903129 1.000000000 -0.0045378845 0.008066621 -0.01372112 -0.0234447102
## rs12748152 -0.004537884 1.0000000000 -0.006687181 0.00445927 0.0003629201
## rs11206508 0.008066621 -0.0066871806 1.000000000 -0.21125757 0.0512593434
## rs11206510 -0.013721120 0.0044592696 -0.211257567 1.00000000 -0.1842706205
## rs10788994 -0.023444710 0.0003629201 0.051259343 -0.18427062 1.0000000000
\textcolor{red}{Note: all the analyses implemented in this R-package only require the summary data and the LD correlation matrix (“ldrho”) listed above.}
Note: all the analyses implemented in this R-package only require the summary data (e.g. “gsmr_data”) and the LD correlation matrix (e.g. “ldrho”) listed above.
This is an optional process. If the risk factor was not standardised in GWAS, the effect sizes can be scaled using the method below. Note that this process requires allele frequencies, z-statistics and sample size. After scaling, bzx is interpreted as the per-allele effect of a SNP on the exposure in standard deviation units.
snpfreq = gsmr_data$a1_freq # allele frequencies of the SNPs
bzx = gsmr_data$bzx # effects of the instruments on risk factor
bzx_se = gsmr_data$bzx_se # standard errors of bzx
bzx_n = gsmr_data$bzx_n # GWAS sample size for the risk factor
std_zx = std_effect(snpfreq, bzx, bzx_se, bzx_n) # perform standardisation
gsmr_data$std_bzx = std_zx$b # standardized bzx
gsmr_data$std_bzx_se = std_zx$se # standardized bzx_se
head(gsmr_data)
## SNP a1 a2 a1_freq bzx bzx_se bzx_pval bzx_n bzy
## 1 rs10903129 A G 0.45001947 -0.0328 0.0037 3.030e-17 169920.0 0.008038
## 2 rs12748152 T C 0.08087758 0.0499 0.0066 3.209e-12 172987.5 0.013671
## 3 rs11206508 A G 0.14396988 0.0434 0.0055 2.256e-14 172239.0 0.030222
## 4 rs11206510 C T 0.19128911 -0.0831 0.0050 2.380e-53 172812.0 -0.074519
## 5 rs10788994 T C 0.18395430 0.0687 0.0049 8.867e-41 172941.9 0.038267
## 6 rs529787 G C 0.19713099 -0.0553 0.0052 8.746e-24 161969.0 0.001707
## bzy_se bzy_pval bzy_n std_bzx std_bzx_se
## 1 0.0092442 0.3845651000 184305 -0.03055942 0.003447252
## 2 0.0185515 0.4611690000 184305 0.04713698 0.006234550
## 3 0.0141781 0.0330400000 184305 0.03829018 0.004852442
## 4 0.0133438 0.0000000234 184305 -0.07181919 0.004321251
## 5 0.0118752 0.0012711000 184305 0.06149455 0.004386074
## 6 0.0135491 0.8997431000 184305 -0.04695042 0.004414868
This is the main analysis of this R-package. It uses SNPs associated with the risk factor (e.g. at p < 5e-8) as the instruments to test for putative causal effect of the risk factor on the disease. The analysis involves a step that uses the HEIDI-outlier approach to remove SNPs that have effects on both the risk factor and the disease because of pleiotropy.
bzx = gsmr_data$std_bzx # SNP effects on the risk factor
bzx_se = gsmr_data$std_bzx_se # standard errors of bzx
bzx_pval = gsmr_data$bzx_pval # p-values for bzx
bzy = gsmr_data$bzy # SNP effects on the disease
bzy_se = gsmr_data$bzy_se # standard errors of bzy
bzy_pval = gsmr_data$bzy_pval # p-values for bzy
n_ref = 7703 # Sample size of the reference sample
gwas_thresh = 5e-8 # GWAS threshold to select SNPs as the instruments for the GSMR analysis
single_snp_heidi_thresh = 0.01 # p-value threshold for single-SNP-based HEIDI-outlier analysis
multi_snp_heidi_thresh = 0.01 # p-value threshold for multi-SNP-based HEIDI-outlier analysis
nsnps_thresh = 10 # the minimum number of instruments required for the GSMR analysis
heidi_outlier_flag = T # flag for HEIDI-outlier analysis
ld_r2_thresh = 0.05 # LD r2 threshold to remove SNPs in high LD
ld_fdr_thresh = 0.05 # FDR threshold to remove the chance correlations between the SNP instruments
gsmr2_beta = 0 # 0 - the original HEIDI-outlier method; 1 - the new HEIDI-outlier method that is currently under development
gsmr_results = gsmr(bzx, bzx_se, bzx_pval, bzy, bzy_se, bzy_pval, ldrho, snp_coeff_id, n_ref, heidi_outlier_flag, gwas_thresh, single_snp_heidi_thresh, multi_snp_heidi_thresh, nsnps_thresh, ld_r2_thresh, ld_fdr_thresh, gsmr2_beta) # GSMR analysis
filtered_index=gsmr_results$used_index
cat("The estimated effect of the exposure on outcome: ",gsmr_results$bxy)
## The estimated effect of the exposure on outcome: 0.4234802
cat("Standard error of bxy: ",gsmr_results$bxy_se)
## Standard error of bxy: 0.02221671
cat("P-value for bxy: ", gsmr_results$bxy_pval)
## P-value for bxy: 5.290993e-81
cat("Indexes of the SNPs used in the GSMR analysis: ", gsmr_results$used_index[1:5], "...")
## Indexes of the SNPs used in the GSMR analysis: 1 2 3 5 6 ...
cat("Number of SNPs with missing estimates in the summary data: ", length(gsmr_results$na_snps))
## Number of SNPs with missing estimates in the summary data: 0
cat("Number of non-significant SNPs: ", length(gsmr_results$weak_snps))
## Number of non-significant SNPs: 39
cat("Number of SNPs in high LD ( LD rsq >", ld_r2_thresh, "): ", length(gsmr_results$linkage_snps))
## Number of SNPs in high LD ( LD rsq > 0.05 ): 5
cat("Number of pleiotropic outliers: ", length(gsmr_results$pleio_snps))
## Number of pleiotropic outliers: 9
The script below runs bi-directional GSMR analyses, i.e. a forward-GSMR analysis as described above and a reverse-GSMR analysis that uses SNPs associated with the disease (e.g. at p < 5e-8) as the instruments to test for putative causal effect of the disease on risk factor.
gsmr_results = bi_gsmr(bzx, bzx_se, bzx_pval, bzy, bzy_se, bzy_pval, ldrho, snp_coeff_id, n_ref, heidi_outlier_flag, gwas_thresh, single_snp_heidi_thresh, multi_snp_heidi_thresh, nsnps_thresh, ld_r2_thresh, ld_fdr_thresh, gsmr2_beta) # GSMR analysis
cat("Effect of risk factor on disease: ",gsmr_results$forward_bxy)
## Effect of risk factor on disease: 0.4234802
cat("Standard error of bxy in the forward-GSMR analysis: ",gsmr_results$forward_bxy_se)
## Standard error of bxy in the forward-GSMR analysis: 0.02221671
cat("P-value of bxy in the forward-GSMR analysis: ", gsmr_results$forward_bxy_pval)
## P-value of bxy in the forward-GSMR analysis: 5.290993e-81
cat("Effect of disease on risk factor: ",gsmr_results$reverse_bxy)
## Effect of disease on risk factor: -0.02640003
cat("Standard error of bxy in the reverse-GSMR analysis: ",gsmr_results$reverse_bxy_se)
## Standard error of bxy in the reverse-GSMR analysis: 0.009642801
cat("P-value of bxy in the reverse-GSMR analysis: ", gsmr_results$reverse_bxy_pval)
## P-value of bxy in the reverse-GSMR analysis: 0.006185232
effect_col = colors()[75]
vals = c(bzx[filtered_index]-bzx_se[filtered_index], bzx[filtered_index]+bzx_se[filtered_index])
xmin = min(vals); xmax = max(vals)
vals = c(bzy[filtered_index]-bzy_se[filtered_index], bzy[filtered_index]+bzy_se[filtered_index])
ymin = min(vals); ymax = max(vals)
par(mar=c(5,5,4,2))
plot(bzx[filtered_index], bzy[filtered_index], pch=20, cex=0.8, bty="n", cex.axis=1.1, cex.lab=1.2,
col=effect_col, xlim=c(xmin, xmax), ylim=c(ymin, ymax),
xlab=expression(LDL~cholesterol~(italic(b[zx]))),
ylab=expression(Coronary~artery~disease~(italic(b[zy]))))
abline(0, gsmr_results$forward_bxy, lwd=1.5, lty=2, col="dim grey")
nsnps = length(bzx[filtered_index])
for( i in 1:nsnps ) {
# x axis
xstart = bzx[filtered_index [i]] - bzx_se[filtered_index[i]]; xend = bzx[filtered_index[i]] + bzx_se[filtered_index[i]]
ystart = bzy[filtered_index[i]]; yend = bzy[filtered_index[i]]
segments(xstart, ystart, xend, yend, lwd=1.5, col=effect_col)
# y axis
xstart = bzx[filtered_index[i]]; xend = bzx[filtered_index[i]]
ystart = bzy[filtered_index[i]] - bzy_se[filtered_index[i]]; yend = bzy[filtered_index[i]] + bzy_se[filtered_index[i]]
segments(xstart, ystart, xend, yend, lwd=1.5, col=effect_col)
}