---
title: "Sensitivity Analyses in Triangulate"
output: 
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 2
    number_sections: true
vignette: >
  %\VignetteIndexEntry{Sensitivity Analyses in Triangulate}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(triangulate)
library(dplyr)
library(tibble)
library(ggplot2)
```

## Introduction

This article demonstrates how to conduct simple sensitivity analyses using the triangulate package. We will explore how changes in bias priors influence the resulting adjusted estimates, allowing us to assess how sensitive bias-adjusted results are to different assumptions.

We use a manually-created, simplified version of the CHD dataset, examining how different assumptions affect the pooled results.

## Create example dataset

We define a small synthetic dataset mimicking studies with moderate bias and indirectness.

```{r data}
# creates 4 made up study results with effect estimates (yi) and variances (vi)

example_data <- tibble(
  result_id = paste0("S", 1:4),
  study = paste("Study", 1:4),
  yi = c(-0.2, 0.25, -0.1, 0.15),
  vi = c(0.02, 0.03, 0.015, 0.025)
)
```

## Define Default Bias and Indirectness Priors

We apply "moderate" priors for all studies, similar to a base-case analysis.

```{r bias-indirect}
# assumptions about additive and proportional bias, each with some uncertainty

bias_priors <- example_data %>%
  mutate(
    domain = "all",
    j = "moderate",
    bias_m_add = 0.1,
    bias_v_add = 0.05,
    bias_m_prop = 0.1,
    bias_v_prop = 0.02,
    type = "RCT"  # or whatever design you want
  )

indirectness_priors <- tibble(
  result_id = example_data$result_id,
  domain = "all",
  j = "moderate",
  ind_m_add = 0.05,
  ind_v_add = 0.03,
  ind_m_prop = 0.05,
  ind_v_prop = 0.02
)
```

## Run bias adjustment

We use tri_prep_data() and tri_calculate_adjusted_estimates() to get bias-adjusted effect sizes.

```{r adjustment}
# this is where we combine the bias/indirectness priors with the study results and adjusts yi and vi to get new columns yi_adj and vi_adj for the adjusted estimate and varainces, respectively

base_prepped <- tri_prep_data(bias_priors, indirectness_priors)
base_adjusted <- tri_calculate_adjusted_estimates(base_prepped)

base_adjusted %>% 
  select(result_id, yi, yi_adj, vi, vi_adj)
```

## Stricter sensitivity scenario

We now increase the additive and proportional bias priors to simulate a more conservative scenario.

```{r scenario}
# represents a stricter assumption e.g if the bias was worse than originally thought. same process applied as before but with new priors

sensitive_bias <- bias_priors %>%
  mutate(
    bias_m_add = 0.2,
    bias_v_add = 0.08,
    bias_m_prop = 0.15,
    bias_v_prop = 0.04
)

sensitive_prepped <- tri_prep_data(sensitive_bias, indirectness_priors)
sensitive_adjusted <- tri_calculate_adjusted_estimates(sensitive_prepped)

sensitive_adjusted %>%
  select(result_id, yi, yi_adj, vi, vi_adj)
```

## Compare results

We plot the adjusted effect estimates under both scenarios.

```{r compare, fig.alt="Plot comparing estimates", fig.width=7}
# overlays the 2 scenarios to visually represent how the priors affect the estimated effect
comparison <- bind_rows(
  base_adjusted %>% mutate(scenario = "Base"),
  sensitive_adjusted %>% mutate(scenario = "Stricter Bias")
) %>%
  mutate(result_id = factor(result_id, levels = paste0("S", 1:4)))  # or use your preferred order

ggplot(comparison, aes(y = result_id, x = yi_adj, color = scenario)) +
  geom_point(position = position_dodge(0.4), size = 3) +
  geom_errorbarh(
    aes(xmin = yi_adj - sqrt(vi_adj), xmax = yi_adj + sqrt(vi_adj)),
    height = 0.2,
    position = position_dodge(0.4)
  ) +
  geom_vline(xintercept = 0, linetype = "dashed") +
  labs(
    title = "Adjusted Estimates: Base vs. Stricter Bias Priors",
    x = "Bias-Adjusted Effect",   # now horizontal axis
    y = "Study"                   # now vertical axis
  ) +
  theme_minimal()
```

## Conclusion

This vignette illustrates how small changes in prior assumptions can impact adjusted effect estimates. While triangulate doesn't yet include a built-in sensitivity function, this process can be easily scripted for exploring model robustness.

Note that the `echo = FALSE` parameter was added to the code chunk to prevent printing of the R code that generated the plot.