Power-Enhanced Two-Sample Mean Tests for High-Dimensional Compositional Data with Application to Microbiome Data Analysis
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917948153659392 |
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| author | Li, Danning Xue, Lingzhou Yang, Haoyi Yu, Xiufan |
| author_facet | Li, Danning Xue, Lingzhou Yang, Haoyi Yu, Xiufan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Power-Enhanced Two-Sample Mean Tests for High-Dimensional Compositional Data with Application to Microbiome Data Analysis Li, Danning Xue, Lingzhou Yang, Haoyi Yu, Xiufan Methodology Statistics Theory Applications 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. |
| title | Power-Enhanced Two-Sample Mean Tests for High-Dimensional Compositional Data with Application to Microbiome Data Analysis |
| topic | Methodology Statistics Theory Applications |
| url | https://arxiv.org/abs/2405.02551 |