Estimation of the proportion of true null hypotheses under sparse dependence: Adaptive FDR controlling in microarray data

Abstract

The proportion of non-differentially expressed genes is an important quantity in microarray data analysis and an appropriate estimate of the same is used to construct adaptive multiple testing procedures. Most of the estimators for the proportion of true null hypotheses based on the thresholding, maximum likelihood and density estimation approaches assume independence among the gene expressions. Usually, sparse dependence structure is natural in modelling associations in microarray gene expression data and hence it is necessary to develop methods for accommodating the sparse dependence well within the framework of existing estimators. We propose a clustering based method to put genes in the same group that are not coexpressed using the estimated high dimensional correlation structure under sparse assumption as dissimilarity matrix. This novel method is applied to three existing estimators for the proportion of true null hypotheses. Extensive simulation study shows that the proposed method improves an existing estimator by making it less conservative and the corresponding adaptive Benjamini-Hochberg algorithm more powerful. The proposed method is applied to a microarray gene expression dataset of colorectal cancer patients and the results show gain in terms of number of differentially expressed genes. The R code is available at https://github.com/aniketstat/Proportiontion-of-true-null-under-sparse-dependence-2021 .

Estimating the proportion of true null hypotheses and adaptive false discovery rate control in discrete paradigm

“…For a reasonable estimate of 𝜋 0 , it is obvious that the ABH procedures reject more null hypotheses compared to the BH procedure. Storey (2002), Storey et al (2004), Langaas et al (2005), Pounds and Cheng (2006), Jiang and Doerge (2008), Blanchard and Roquain (2009), Wang et al (2010), Cheng et al (2015), Biswas et al (2021), and Biswas et al (2022), among many others, discuss the problem of estimating 𝜋 0 and thus formulating an ABH procedure. These estimators for 𝜋 0 were developed under the continuous framework.…”

Local false discovery rate estimation with competition‐based procedures for variable selection

“…Efron simultaneously estimates $$$ {\pi}_0 $$$ and the null density function ($$$ {f}_0 $$$) using $$$ z $$$‐values instead of $$$ P $$$‐values, employing several optional methods that assume the normality of $$$ {f}_0 $$$ 43 . Despite these advancements, achieving more accurate estimation of $$$ {\pi}_0 $$$ remains a primary objective in current FDR research 44,45 …”

“…43 Despite these advancements, achieving more accurate estimation of 𝜋 0 remains a primary objective in current FDR research. 44,45 In this paper, we propose a novel method called TDfdr for estimating fdr in error-controlled variable selection, utilizing competition-based procedures. Unlike traditional approaches that rely on P-values, TDfdr is designed to handle general scores or test statistics with or without known distributions.…”

Model-free Bias Reduction of Storey’s Estimator for the Proportion of True Null Hypotheses

“…Wang et al [14] introduced a new method, namely the sliding linear model (SLIM) to accommodate dependence among the p -values in Storey’s estimator, originally constructed for independent tests. Biswas et al [15] introduced a clustering based method for improving an estimator of π 0 under sparse dependence and implemented the same on Storey’s estimator. The above estimators are quite popular in handling genetic data but model based bias corrected estimators [8, 11, 12] are more efficient for suitable data if we agree to lose some generality.…”