A data-adaptive method for investigating effect heterogeneity with high-dimensional covariates in Mendelian randomization

Abstract

Mendelian randomization is a popular method for causal inference with observational data that uses genetic variants as instrumental variables. Similarly to a randomized trial, a standard Mendelian randomization analysis estimates the population-averaged effect of an exposure on an outcome. Dividing the population into subgroups can reveal effect heterogeneity to inform who would most benefit from intervention on the exposure. However, as covariates are measured post-”randomization”, naive stratification typically induces collider bias in stratum-specific estimates. We extend a previously proposed stratification method (the “doubly-ranked method”) to form strata based on a single covariate, and introduce a data-adaptive random forest method to calculate stratum-specific estimates that are robust to collider bias based on a high-dimensional covariate set. We also propose measures to assess heterogeneity between stratum-specific estimates (to understand whether estimates are more variable than expected due to chance alone) and variable importance (to identify the key drivers of effect heterogeneity). We show that the effect of body mass index (BMI) on lung function is heterogeneous, depending most strongly on hip circumference and weight. While for most individuals, the predicted effect of increasing BMI on lung function is negative, it is positive for some individuals and strongly negative for others.