Using Copula to Model Dependence When Testing Multiple Hypotheses in DNA Microarray Experiments: A Bayesian Approximation

Abstract

Many experiments require simultaneously testing many hypotheses. This is particularly relevant in the context of DNA microarray experiments, where it is common to analyze many genes to determine which of them are differentially expressed under two conditions. Another important problem in this context is how to model the dependence at the level of gene expression. In this paper, we propose a Bayesian procedure for simultaneously testing multiple hypotheses, modeling the dependence through copula functions, where all available information, both objective and subjective, can be used. The approach has the advantage that it can be used with different dependency structures. Simulated data analysis was performed to examine the performance of the proposed approach. The results show that our procedure captures the dependence appropriately classifying adequately a high percentage of true and false null hypotheses when choosing a prior distribution beta skewed to the right for the initial probability of each null hypothesis, resulting in a very powerful procedure. The procedure is also illustrated with real data.

Mathematical Biology: Modeling, Analysis, and Simulations

“…The present volume contains the 12 articles accepted and published in 2021 in the Special Issue, "Mathematical Biology: Modeling, Analysis, and Simulations" of the MDPI Mathematics journal, which covers a wide range of topics connected to the mathematical modeling of different biologically inspired and motivated problems. These topics include, among others, elements from processes in developmental biology [1]; equilibria and bifurcations in cardiac [2], tumoral [3] and regulatory cell [4] models; complexity in human pupillary light reflexes [5] and visual disorders [6]; a descriptive geometrical method as a model for motion [7]; statistical analysis applied to lactation model fitting [8]; DNA microarray experiments [9]; the transmission dynamics of HIV [10]; and mathematical models of the phosphorylation of glucose [11] and the transmission of tuberculosis [12].…”