# A Unified Combination Framework for Dependent Tests with Applications to Microbiome Association Studies

arXiv: https://arxiv.org/abs/2404.09353 · HTML: https://mlsanity.com/paper/2404.09353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 14 Apr 2024.

## Builds on (most cited first, 7 of 7)

- [Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures](https://mlsanity.com/paper/1808.09011/) (2018)
- [Power Enhancement in High Dimensional Cross-Sectional Tests](https://mlsanity.com/paper/1310.3899/) (2013)
- [Multiple-Splitting Projection Test for High-Dimensional Mean Vectors](https://mlsanity.com/paper/2110.15480/) (2021)
- [Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing](https://mlsanity.com/paper/2109.15287/) (2021)
- [Fisher's combined probability test for high-dimensional covariance matrices](https://mlsanity.com/paper/2006.00426/) (2020)
- [The Cauchy Combination Test under Arbitrary Dependence Structures](https://mlsanity.com/paper/2107.06040/) (2021)
- [Heavy-tailed distribution for combining dependent p-values with asymptotic robustness](https://mlsanity.com/paper/2103.12967/) (2021)

## Abstract (arXiv)

We introduce a novel meta-analysis framework to combine dependent tests under a general setting, and utilize it to synthesize various microbiome association tests that are calculated from the same dataset. Our development builds upon the classical meta-analysis methods of aggregating p-values and also a more recent general method of combining confidence distributions, but makes generalizations to handle dependent tests. The proposed framework ensures rigorous statistical guarantees, and we provide a comprehensive study and compare it with various existing dependent combination methods. Notably, we demonstrate that the widely used Cauchy combination method for dependent tests, referred to as the vanilla Cauchy combination in this article, can be viewed as a special case within our framework. Moreover, the proposed framework provides a way to address the problem when the distributional assumptions underlying the vanilla Cauchy combination are violated. Our numerical results demonstrate that ignoring the dependence among the to-be-combined components may lead to a severe size distortion phenomenon. Compared to the existing p-value combination methods, including the vanilla Cauchy combination method, the proposed combination framework can handle the dependence accurately and utilizes the information efficiently to construct tests with accurate size and enhanced power. The development is applied to Microbiome Association Studies, where we aggregate information from multiple existing tests using the same dataset. The combined tests harness the strengths of each individual test across a wide range of alternative spaces, %resulting in a significant enhancement of testing power across a wide range of alternative spaces, enabling more efficient and meaningful discoveries of vital microbiome associations.