Title: More powerful tests of the composite null hypothesis arising in mediation analysis
Authors: Caleb Miles - Columbia University (United States) [presenting]
Antoine Chambaz - Universite Paris 5 Rene Descartes (France)
Abstract: The indirect effect of an exposure on an outcome through an intermediate variable is identified by a product of regression coefficients under standard causal mediation assumptions and linear models for the outcome and intermediate variable. Thus, the null hypothesis of no indirect effect is a composite null hypothesis, as the null holds if either regression coefficient is zero. A consequence is that existing hypothesis tests are either severely underpowered near the origin (i.e., both coefficients being small with respect to standard errors) or invalid. We propose hypothesis tests that (i) preserve level alpha type 1 error, (ii) meaningfully improve power when both true underlying effects are small relative to sample size, and (iii) preserve power when at least one is not. One approach uses sparse linear programming to produce an approximately optimal test for a Bayes risk criterion. Another gives a closed-form test that is minimax optimal with respect to local power over the alternative parameter space.