Towards More Accurate Causal Inference with Instrumental Variables and Mendelian Randomisation Analyses

Abstract

Instrumental variable (IV) approach is a commonly used statistical approach to make causal inference in the presence of unmeasured confounding, and the use of genetic variants as instrumental variables in epidemiological studies is known as Mendelian Randomisation (MR). The conventional modelling assumption for using IVs is to assume a linear structural equation model between the exposure and the outcome. In recent years, there have been various developments in the literature that attempt to relax this strong linearity assumption and propose methods that estimate nonlinear causal effects using IVs. We review some of the important nonlinear IV methods, including approaches that nonparametrically generalise the usual 2SLS and GMM estimators using machine-learning algorithms. We also review stratified nonlinear MR, a widely used method for nonlinear causal effect estimation in MR that is based on dividing the population into strata with different average levels of the exposure and estimating average causal effect within each stratum. We present all the methods under a unified causal model and compare their performances through a simulation study. Stratified nonlinear MR aggregates stratum-specific estimates using a fractional polynomial regression, which is unable to capture nonlinear exposure-outcome relationships beyond fractional polynomials. We propose a nonparametric extension to stratified nonlinear MR, which we call nonparametric MR, that can characterise more complex nonlinear structural functions. The estimand of nonparametric MR, called quantile average causal effect (QACE), approximates the derivative of the true structural function. We firstly develop nonparametric MR with discrete IVs, and then extend this framework to situations where the instrument is continuous. We demonstrate through extensive simulation studies that nonparametric MR outperforms stratified nonlinear MR in a wide range of scenarios that cover various instrument-exposure relationships and different instrument strengths. We also illustrate our method using real data examples from UK Biobank. Selection bias is a common issue in statistical applications which biases IV analyses. Starting with linear IV models, we firstly show that adjusting for measured confounders can reduce but cannot eliminate selection bias, and then provide asymptotic guarantees for using inverse probability weighting (IPW) to eliminate selection bias. We argue that in finite samples, IPW may fail to account for selection bias under severe selection even when the selection model is fully known. We demonstrate our findings through simulation studies and real data examples from UK Biobank that cover different selection mechanisms. We further consider selection bias for stratified nonlinear MR and argue that, unlike bias for the standard MR estimate, bias for stratum-specific estimates cannot be corrected using IPW if the we can only stratify on the selected sample. We also illustrate this argument through a simulation study.