A Unified Combination Framework for Dependent Tests with Applications to Microbiome Association Studies
arxiv(2024)
摘要
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,
enhancement of testing power across a wide range of alternative spaces,
enabling more efficient and meaningful discoveries of vital microbiome
associations.
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