Applications of Procedures Controlling the Tail Probability of the False Discovery Proportion

Abstract

Multiple testing has been an active area of statistical research in the past decade mainly because of its wide scope of applicability in modern scientific investigations. One major application area of multiple testing is in identifying differentially expressed genes from massive biological data generated by high-throughput genomic technologies where the expression profiles of genes are compared across two or more experimental conditions on a genomic scale. This dissertation briefly reviews modern multiple testing methodologies including types of error control, and multiple testing procedures, before focusing on one of its objectives of identifying differentially expressed genes from high-throughput genomic data. More specifically, we apply multiple testing procedures that control the γ-FDP, the probability of false discovery proportion (FDP) exceeding γ, given some γ∈ [0,1), on two types of high-throughput genomic data, namely, microarray and digital gene expression (DGE) data. In addition, we propose four newer step-up procedures controlling the γ-FDP. The first of these procedures is developed by modifying the Benjamini and Hochberg (1995, J. Roy. Statist. Soc., Ser. B) critical constants, which controls the γ-FDP under both independent and positively dependent test statistics. The second one is a two-stage adaptive procedure developed from these modified Benjamini and Hochberg critical constants and controls the γ-FDP under independence. The third and fourth procedures are also two-stage adaptive procedures controlling the γ-FDP under independence, but developed using critical constants in Lehmann and Romano (2005, Ann. of Statist.) and Delattre and Roquain (2015, Ann. of Statist.) respectively. Results of simulation studies examining performances of our procedures relative to their relevant competitors are presented. We also present a heuristic approach to investigating an unusual problem in the detection of differentially expressed genes from a microarray data. This problem arises when the marginal p-value distribution is an unknown mixture distribution rendering some multiple testing procedures incompetent of eliciting differentially expressed genes. We illustrate why the control of the γ-FDP is preferred in those instances. Future research problems are also discussed.