Two-stage multivariate Mendelian randomization on multiple outcomes with mixed distributions.

In clinical research, it is important to study whether certain clinical factors or exposures have causal effects on clinical and patient-reported outcomes such as toxicities, quality of life, and self-reported symptoms, which can help improve patient care. Usually, such outcomes are recorded as multiple variables with different distributions. Mendelian randomization (MR) is a commonly used technique for causal inference with the help of genetic instrumental variables to deal with observed and unobserved confounders. Nevertheless, the current methodology of MR for multiple outcomes only focuses on one outcome at a time, meaning that it does not consider the correlation structure of multiple outcomes, which may lead to a loss of statistical power. In situations with multiple outcomes of interest, especially when there are mixed correlated outcomes with different distributions, it is much more desirable to jointly analyze them with a multivariate approach. Some multivariate methods have been proposed to model mixed outcomes; however, they do not incorporate instrumental variables and cannot handle unmeasured confounders. To overcome the above challenges, we propose a two-stage multivariate Mendelian randomization method (MRMO) that can perform multivariate analysis of mixed outcomes using genetic instrumental variables. We demonstrate that our proposed MRMO algorithm can gain power over the existing univariate MR method through simulation studies and a clinical application on a randomized Phase III clinical trial study on colorectal cancer patients.