Querying multiple sets of P-values through composed hypothesis testing

Abstract

Motivation Combining the results of different experiments to exhibit complex patterns or to improve statistical power is a typical aim of data integration. The starting point of the statistical analysis often comes as sets of p-values resulting from previous analyses, that need to be combined in a flexible way to explore complex hypotheses, while guaranteeing a low proportion of false discoveries. Results We introduce the generic concept of composed hypothesis, which corresponds to an arbitrary complex combination of simple hypotheses. We rephrase the problem of testing a composed hypothesis as a classification task, and show that finding items for which the composed null hypothesis is rejected boils down to fitting a mixture model and classify the items according to their posterior probabilities. We show that inference can be efficiently performed and provide a thorough classification rule to control for type I error. The performance and the usefulness of the approach are illustrated on simulations and on two different applications. The method is scalable, does not require any parameter tuning, and provided valuable biological insight on the considered application cases. Availability The QCH methodology is implemented in the qch R package hosted on CRAN.

metaGE: Investigating Genotype × Environment interactions through meta-analysis

“…This mixture distribution can be inferred by a kernel method. Then, the filtering consists in considering only the markers m whose a posteriori probabilities of being under H 1 are lower than a certain threshold [40]. For the applications detailed in the Section 2, the filtering method was performed with a threshold fixed at 0.8.…”

“…By definition, the distribution to be estimated is a mixture between a N (0, 1) distribution corresponding to the markers under H 0 and a second unknown distribution corresponding to those under H 1 This mixture distribution can be inferred by a kernel method. Then, the filtering consists in considering only the markers m whose a posteriori probabilities of being under H 1 are lower than a certain threshold [40]. For the applications detailed in the Section 2, the filtering method was performed with a threshold fixed at 0.8.…”

ioSearch: a tool for searching disease-associated interacting omics; application on breast cancer data

“…According to IUT, the overall null hypothesis can be rejected only if each of the individual hypotheses can be rejected. Here, we use a testing method QCH 28 where IUT holds as a particular case. QCH is a scalable method that fits a mixture model to the p-values obtained from individual null hypotheses and the rejection rule is based on the posterior probabilities.…”

“…The inclusion of pathway information also facilitates the exploration of long-range functional relations between and within different omics as opposed to single gene-based biomarker identification methods. Besides, a compre-hensive testing algorithm for querying composed hypothesis 28 embedded in our algorithm generates conveniently interpretable p-values from an asymptotic distribution that reduces computation cost compared to permutation-based techniques. Simulation results show that our method is statistically powerful with a controlled type I error rate.…”

ioSearch: An approach for identifying interacting multiomics biomarkers using a novel algorithm with application on breast cancer data sets

“…The inclusion of pathway information also facilitates the exploration of long‐range functional relations between and within different omics as opposed to single gene‐based biomarker identification methods. Besides, a comprehensive testing algorithm for querying composed hypothesis (Mary‐Huard et al, 2022) embedded in our algorithm generates conveniently interpretable p values from an asymptotic distribution that reduces computational cost compared with permutation‐based techniques. Simulation results show that our method is statistically powerful.…”