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Abstract:
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Statistical inference based on false discovery rate (FDR) is challenging when the assumptions of p-value distribution are violated. The basic assumptions are continuity, uniformity, and independence of p-values. We are particularly interested in investigating the assumption of independence when using a paired sample test under compositionality. For example, microbiome data produce the output with the relative abundances based on hundreds of taxon counts. Such data, generally referred to as high dimensional compositional data are vulnerable to the independence assumption by nature because of the sum-to-one constraint. Another source of dependency is the paired samples from the matched pairs or repeated measures experiment. Situation can be a mixture of both. For instance, when large-scale hypotheses are constructed from four-group comparison experiments (6 pairwise tests) over 500 hundreds of taxa, the independence of 3000 tests are not warranted. In this walk, we aim to examine the FDR procedure under compositional responses with dependent samples. The specific goals include evaluation of weak dependency and development of an alternative method robust to dependency.
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