FWER and FDR control when testing multiple mediators

Motivation: The biological pathways linking exposures and disease risk are often poorly understood. To gain insight into these pathways, studies may try to identify biomarkers that mediate the exposure/ disease relationship. Such studies often simultaneously test hundreds or thousands of biomarkers. Results: We consider a set of m biomarkers and a corresponding set of null hypotheses, where the jth null hypothesis states that biomarker j does not mediate the exposure/disease relationship. We propose a Multiple Comparison Procedure (MCP) that rejects a set of null hypotheses or, equivalently, identifies a set of mediators, while asymptotically controlling the Family-Wise Error Rate (FWER) or False Discovery Rate (FDR). We use simulations to show that, compared to currently available methods, our proposed method has higher statistical power to detect true mediators. We then apply our method to a breast cancer study and identify nine metabolites that may mediate the known relationship between an increased BMI and an increased risk of breast cancer.