Power-Enhanced Two-Sample Mean Tests for High-Dimensional Compositional Data with Application to Microbiome Data Analysis

Testing differences in mean vectors is a fundamental task in the analysis of high-dimensional compositional data. Existing methods may suffer from low power if the underlying signal pattern is in a situation that does not favor the deployed test. In this work, we develop two-sample power-enhanced mean tests for high-dimensional compositional data based on the combination of $p$-values, which integrates strengths from two popular types of tests: the maximum-type test and the quadratic-type test. We provide rigorous theoretical guarantees on the proposed tests, showing accurate Type-I error rate control and enhanced testing power. Our method boosts the testing power towards a broader alternative space, which yields robust performance across a wide range of signal pattern settings. Our theory also contributes to the literature on power enhancement and Gaussian approximation for high-dimensional hypothesis testing. We demonstrate the performance of our method on both simulated data and real-world microbiome data, showing that our proposed approach improves the testing power substantially compared to existing methods.