Statistics and Its Interface

Volume 4 (2011)

Number 1

A likelihood ratio test for the proportion of non-differentially expressed genes

Pages: 37 – 50



Yinglei Lai (Department of Statistics and Biostatistics Center, The George Washington University, Washington D.C., U.S.A.)

Anastasios Markitsis (Department of Statistics, The George Washington University, Washington D.C., U.S.A.)


The proportion of non-differentially expressed genes ($\pi_0$) is an important quantity in microarray data analysis. Although there is a wealthy literature about the estimation of $\pi_0$, the issue of hypothesis testing for $\pi_0$ has not been well addressed. In this study, we develop a likelihood ratio test for $\pi_0$ based on our recently proposed censored beta mixture model, and evaluate its power through a comprehensive simulation study. In order to understand the performance of our method for general experimental data, we simulate gene expression measurements based on a widely used data simulation scheme. The results confirm that a satisfactory power can still be achieved when there is a considerable sample size, a considerable number of genes, or a relatively large proportion of non-differentially expressed genes. Based on two experimental datasets, we illustrate that our method can be particularly useful for testing the hypothesis of no differentially expressed genes and calculating the sample size in an experimental design.


proportion of true null hypothesis, likelihood ratio test, mixture model, censored beta distribution, power, microarray gene expression data

2010 Mathematics Subject Classification

Primary 62F03, 62F40. Secondary 62F30.

Published 28 February 2011