Microarray data analysis: A hierarchical t-test to handle heteroscedasticity

The analysis of differential gene expression in microarray experiments requires the development of adequate statistical tools. This article describes a simple statistical method for detecting differential expression between two conditions with a low number of replicates. When comparing two group means using a traditional t-test, gene-specific variance estimates are unstable and can lead to wrong conclusions. We construct a likelihood ratio test while modelling these variances hierarchically across all genes, and express it as a t-test statistic. By borrowing information across genes we can take advantage of their large numbers, and still yield a gene-specific test statistic. We show that this hierarchical t-test is more powerful than its traditional version and generates less false positives in a simulation study, especially with small sample sizes. This approach can be extended to cases where there are more than two groups.