Robust Mendelian randomization in the presence of residual population stratification, batch effects and horizontal pleiotropy.

Mendelian Randomization (MR) studies are threatened by population stratification, batch effects, and horizontal pleiotropy. Although a variety of methods have been proposed to mitigate those problems, residual biases may still remain, leading to highly statistically significant false positives in large databases. Here we describe a suite of sensitivity analysis tools that enables investigators to quantify the robustness of their findings against such validity threats. Specifically, we propose the routine reporting of sensitivity statistics that reveal the minimal strength of violations necessary to explain away the MR results. We further provide intuitive displays of the robustness of the MR estimate to any degree of violation, and formal bounds on the worst-case bias caused by violations multiple times stronger than observed variables. We demonstrate how these tools can aid researchers in distinguishing robust from fragile findings by examining the effect of body mass index on diastolic blood pressure and Townsend deprivation index.

Generalizing experimental results by leveraging knowledge of mechanisms.

We show how experimental results can be generalized across diverse populations by leveraging knowledge of local mechanisms that produce the outcome of interest, only some of which may differ in the target domain. We use structural causal models and a refined version of selection diagrams to represent such knowledge, and to decide whether it entails the invariance of probabilities of causation across populations, which then enables generalization. We further provide: (i) bounds for the target effect when some of these conditions are violated; (ii) new identification results for probabilities of causation and the transported causal effect when trials from multiple source domains are available; as well as (iii) a Bayesian approach for estimating the transported causal effect from finite samples. We illustrate these methods both with simulated data and with a real example that transports the effects of Vitamin A supplementation on childhood mortality across different regions.