Conditional inference in cis‐Mendelian randomization using weak genetic factors

Mendelian randomization (MR) is a widely used method to estimate the causal effect of an exposure on an outcome by using genetic variants as instrumental variables. MR analyses that use variants from only a single genetic region (cis‐MR) encoding the protein target of a drug are able to provide supporting evidence for drug target validation. This paper proposes methods for cis‐MR inference that use many correlated variants to make robust inferences even in situations, where those variants have only weak effects on the exposure. In particular, we exploit the highly structured nature of genetic correlations in single gene regions to reduce the dimension of genetic variants using factor analysis. These genetic factors are then used as instrumental variables to construct tests for the causal effect of interest. Since these factors may often be weakly associated with the exposure, size distortions of standard t‐tests can be severe. Therefore, we consider two approaches based on conditional testing. First, we extend results of commonly‐used identification‐robust tests for the setting where estimated factors are used as instruments. Second, we propose a test which appropriately adjusts for first‐stage screening of genetic factors based on their relevance. Our empirical results provide genetic evidence to validate cholesterol‐lowering drug targets aimed at preventing coronary heart disease.