FreedomIntelligence Version Compatibility
Reference examples tested with: R stats (base), ggplot2 3.5+
Before using code patterns, verify installed versions match. If versions differ:
- R:
packageVersion('<pkg>')then?function_nameto verify parameters
If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.
Mediation Analysis
"Test whether gene expression mediates the effect of this variant on disease" → Decompose the total genetic effect into direct and indirect (mediated) paths through a molecular phenotype, estimating ACME, ADE, and proportion mediated with bootstrap confidence intervals.
- R:
mediation::mediate()for causal mediation analysis
Framework
Causal mediation decomposes the total effect of a treatment (genotype) on an outcome (phenotype) into:
- ACME (Average Causal Mediation Effect) - Indirect effect through the mediator
- ADE (Average Direct Effect) - Direct effect not through the mediator
- Total effect = ACME + ADE
- Proportion mediated = ACME / Total effect
Typical genomic applications:
- SNP -> gene expression (mediator) -> disease
- SNP -> DNA methylation (mediator) -> gene expression
- SNP -> protein levels (mediator) -> clinical outcome
Basic Mediation with the mediation Package
Goal: Decompose a genetic effect into direct and indirect (mediated) paths through a molecular phenotype.
Approach: Fit separate models for mediator and outcome, then run mediate() with bootstrap to estimate ACME (indirect), ADE (direct), and proportion mediated.
library(mediation)
# --- Step 1: Fit mediator model ---
# How does the treatment (genotype) affect the mediator (expression)?
mediator_model <- lm(expression ~ genotype + age + sex + pc1 + pc2, data = dat)
# --- Step 2: Fit outcome model ---
# How do treatment and mediator jointly affect the outcome?
# For binary outcome, use glm with family = binomial
outcome_model <- glm(
disease ~ genotype + expression + age + sex + pc1 + pc2,
data = dat, family = binomial
)
# --- Step 3: Run mediation analysis ---
# treat: name of treatment variable (genotype)
# mediator: name of mediator variable (expression)
# boot = TRUE: Use nonparametric bootstrap for CIs
# sims: Number of bootstrap simulations (1000 minimum for publication)
med_result <- mediate(
mediator_model, outcome_model,
treat = 'genotype', mediator = 'expression',
boot = TRUE, sims = 1000
)
summary(med_result)
# Key outputs:
# ACME: Indirect effect (through expression)
# ADE: Direct effect (not through expression)
# Total Effect: ACME + ADE
# Prop. Mediated: ACME / Total
Interpreting Results
# Extract key quantities
acme <- med_result$d0 # Indirect (mediated) effect
acme_ci <- med_result$d0.ci # 95% CI for ACME
ade <- med_result$z0 # Direct effect
total <- med_result$tau.coef # Total effect
prop_med <- med_result$n0 # Proportion mediated
cat('ACME (indirect):', round(acme, 4), '\n')
cat('ACME 95% CI:', round(acme_ci[1], 4), 'to', round(acme_ci[2], 4), '\n')
cat('ADE (direct):', round(ade, 4), '\n')
cat('Total effect:', round(total, 4), '\n')
cat('Proportion mediated:', round(prop_med, 3), '\n')
# Significant ACME (CI excludes 0): Evidence for mediation
# Proportion mediated > 0.2: Meaningful mediation
# Proportion mediated > 0.8: Mediator explains most of the effect
eQTL Mediation
Goal: Test whether gene expression mediates the effect of an eQTL on a disease outcome across multiple genes.
Approach: Wrap the mediation workflow in a function, loop over candidate genes, and adjust p-values for multiple testing.
library(mediation)
run_eqtl_mediation <- function(dat, snp_col, expr_col, outcome_col, covariates) {
covar_formula <- paste(covariates, collapse = ' + ')
med_formula <- as.formula(paste(expr_col, '~', snp_col, '+', covar_formula))
out_formula <- as.formula(paste(outcome_col, '~', snp_col, '+', expr_col, '+', covar_formula))
med_model <- lm(med_formula, data = dat)
if (length(unique(dat[[outcome_col]])) == 2) {
out_model <- glm(out_formula, data = dat, family = binomial)
} else {
out_model <- lm(out_formula, data = dat)
}
result <- mediate(
med_model, out_model,
treat = snp_col, mediator = expr_col,
boot = TRUE, sims = 1000
)
data.frame(
snp = snp_col, gene = expr_col,
acme = result$d0, acme_p = result$d0.p,
ade = result$z0, ade_p = result$z0.p,
total = result$tau.coef, total_p = result$tau.p,
prop_mediated = result$n0
)
}
# Example: test mediation for multiple genes
genes <- c('GENE_A', 'GENE_B', 'GENE_C')
covars <- c('age', 'sex', 'pc1', 'pc2', 'pc3')
mediation_results <- do.call(rbind, lapply(genes, function(g) {
run_eqtl_mediation(dat, 'rs12345', g, 'disease_status', covars)
}))
# Adjust for multiple testing
mediation_results$acme_fdr <- p.adjust(mediation_results$acme_p, method = 'BH')
Multi-Omics Mediation
Goal: Test cascading mediation chains across multiple molecular layers (e.g., SNP -> methylation -> expression -> disease).
Approach: Fit sequential models for each link in the chain and run separate mediation analyses for each mediator-outcome pair.
# Test mediation chains: SNP -> methylation -> expression -> disease
library(mediation)
# Step 1: SNP -> methylation
mod_meth <- lm(methylation ~ genotype + age + sex, data = dat)
# Step 2: methylation -> expression (controlling for genotype)
mod_expr <- lm(expression ~ methylation + genotype + age + sex, data = dat)
# Step 3: expression -> disease (controlling for methylation and genotype)
mod_disease <- glm(
disease ~ expression + methylation + genotype + age + sex,
data = dat, family = binomial
)
# Test methylation as mediator of SNP -> expression
med_meth_expr <- mediate(mod_meth, mod_expr, treat = 'genotype', mediator = 'methylation',
boot = TRUE, sims = 1000)
# Test expression as mediator of methylation -> disease
med_expr_disease <- mediate(mod_expr, mod_disease, treat = 'methylation', mediator = 'expression',
boot = TRUE, sims = 1000)
High-Dimensional Mediation (HDMA)
Goal: Test thousands of potential mediators simultaneously (e.g., all CpG sites) to identify which mediate a genetic effect.
Approach: Use HIMA's penalized regression to jointly select significant mediators from a high-dimensional mediator matrix and estimate their indirect effects.
# For testing many potential mediators simultaneously (e.g., all CpG sites)
# install.packages('HIMA')
library(HIMA)
# X: treatment (genotype), M: high-dimensional mediators, Y: outcome
# HIMA uses penalized regression to select significant mediators
result <- hima(
X = dat$genotype,
Y = dat$disease,
M = as.matrix(dat[, mediator_cols]),
COV.XM = as.matrix(dat[, covariate_cols]),
Y.family = 'binomial',
M.family = 'gaussian',
penalty = 'MCP' # Minimax concave penalty (default)
)
# Results: significant mediators with estimated indirect effects
significant_mediators <- result[result$BH.FDR < 0.05, ]
Assumptions and Diagnostics
# --- Sequential ignorability assumption ---
# 1. No unmeasured confounders between treatment and mediator
# 2. No unmeasured confounders between mediator and outcome
# 3. No unmeasured confounders between treatment and outcome
# This assumption is UNTESTABLE but can be probed with sensitivity analysis
# --- Sensitivity analysis ---
# Tests how robust results are to unmeasured confounding
sens <- medsens(med_result, rho.by = 0.1, effect.type = 'indirect', sims = 1000)
summary(sens)
# rho: Correlation between residuals of mediator and outcome models
# At what rho does ACME cross zero? (larger |rho| = more robust)
# rho at which ACME = 0 is called the sensitivity parameter
# |rho| > 0.3: Reasonably robust to unmeasured confounding
plot(sens)
Visualization
library(ggplot2)
plot_mediation_diagram <- function(acme, ade, total, prop_med) {
cat('Mediation Path Diagram:\n\n')
cat(' Genotype ---[a]---> Mediator ---[b]---> Outcome\n')
cat(' | ^\n')
cat(' +----------[c' (ADE)]----------------+\n')
cat('\n')
cat(' Indirect (a*b = ACME):', round(acme, 4), '\n')
cat(' Direct (c' = ADE):', round(ade, 4), '\n')
cat(' Total (c):', round(total, 4), '\n')
cat(' Proportion mediated:', round(prop_med, 3), '\n')
}
plot_mediation_results <- function(results_df) {
results_df$gene <- factor(results_df$gene, levels = results_df$gene[order(results_df$prop_mediated)])
ggplot(results_df, aes(x = gene, y = prop_mediated)) +
geom_col(fill = 'steelblue', alpha = 0.7) +
geom_hline(yintercept = 0.2, linetype = 'dashed', color = 'red', alpha = 0.5) +
coord_flip() +
labs(x = NULL, y = 'Proportion Mediated', title = 'Mediation by Gene Expression') +
theme_minimal()
}
Related Skills
- mendelian-randomization - Causal inference using genetic instruments
- colocalization-analysis - Test if signals share a causal variant
- population-genetics/association-testing - GWAS for treatment-outcome associations
- multi-omics-integration/mofa-integration - Multi-omics data for mediation chains