Testing and controlling for horizontal pleiotropy with the probabilistic Mendelian randomization in transcriptome-wide association studies

Integrating association results from both genome-wide association studies (GWASs) and expression quantitative trait locus (eQTL) mapping studies has the potential to shed light on the molecular mechanisms underlying disease etiology. Several statistical methods have been recently developed to integrate GWASs with eQTL studies in the form of transcriptome-wide association studies (TWASs). These existing methods can all be viewed as a form of two sample Mendelian randomization (MR) analysis, which has been widely applied in various GWASs for inferring the causal relationship among complex traits. Unfortunately, most existing TWAS and MR methods make an unrealistic modeling assumption and assume that instrumental variables do not exhibit horizontal pleiotropic effects. However, horizontal pleiotropic effects have been recently discovered to be wide spread across complex traits, and, as we will show here, are also wide spread across gene expression traits. Therefore, not allowing for horizontal pleiotropic effects can be overly restrictive, and, as we will be show here, can lead to a substantial inflation of test statistics and subsequently false discoveries in TWAS applications. Here, we present a probabilistic MR method, which we refer to as PMR-Egger, for testing and controlling for horizontal pleiotropic effects in TWAS applications. PMR-Egger relies on an MR likelihood framework that unifies many existing TWAS and MR methods, accommodates multiple correlated instruments, tests the causal effect of gene on trait in the presence of horizontal pleiotropy, and, with a newly developed parameter expansion version of the expectation maximization algorithm, is scalable to hundreds of thousands of individuals. With extensive simulations, we show that PMR-Egger provides calibrated type I error control for causal effect testing in the presence of horizontal pleiotropic effects, is reasonably robust for various types of horizontal pleiotropic effect mis-specifications, is more powerful than existing MR approaches, and, as a by-product, can directly test for horizontal pleiotropy. We illustrate the benefits of PMR-Egger in applications to 39 diseases and complex traits obtained from three GWASs including the UK Biobank. In these applications, we show how PMR-Egger can lead to new biological discoveries through integrative analysis.