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Abstract:
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Mediation effect of an exposure on an outcome via a mediator can be expressed as a product of two parameters, one for the exposure-mediator association and the other for the mediator-outcome association conditional the exposure. We study various hypothesis tests of the mediation effect in the settings of a single test and multiple tests. Under a single test, we show that joint significance test examining the two parameters separately is an intersection-union test with size alpha, and has smaller p-values than normality-based or normal product-based tests for the product. However, in the setting with multiple tests, the joint significance test has low power because it fails to account for the composition of different null hypotheses. We propose a test assessing the product of two normally distributed test statistics under the composite null hypothesis, i.e., either one parameter is zero or both are zero. The proposed method accounts for the composition by variances of test statistics without directly estimating the proportion of respective null hypotheses. Advantages of the proposed test are demonstrated in numerical simulation and an epigenome-wide mediation study.
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