  Mediation analysis seeks to identify and quantify the paths by which an
exposure affects an outcome. Intermediate variables which are effected by the
exposure and which effect the outcome are known as mediators. There exists
extensive work on mediation analysis in the context of models with a single
mediator and continuous and binary outcomes. However these methods are often
not suitable for multi-omic data that include highly interconnected variables
measuring biological mechanisms and various types of outcome variables such as
censored survival responses. In this article, we develop a general framework
for causal mediation analysis with multiple exposures, multivariate mediators,
and continuous, binary, and survival responses. We estimate mediation effects
on several scales including the mean difference, odds ratio, and restricted
mean scale as appropriate for various outcome models. Our estimation method
avoids imposing constraints on model parameters such as the rare disease
assumption while accommodating continuous exposures. We evaluate the framework
and compare it to other methods in extensive simulation studies by assessing
bias, type I error and power at a range of sample sizes, disease prevalences,
and number of false mediators. Using Kidney Renal Clear Cell Carcinoma data
from The Cancer Genome Atlas, we identify proteins which mediate the effect of
metabolic gene expression on survival. Software for implementing this unified
framework is made available in an R package
(https://github.com/longjp/mediateR).
