Analysis of Unbalanced Microarray Data

This paper investigates statistical procedures for analyzing microarray gene expression data obtained from studies with an unbalanced experimental design. We demonstrate the methods using microarray data from a study of opioid dependence in mice. The experiment was designed to investigate how morphine dependence alters gene expression in spinal cord mRNA. The aim was to identify genes that characterize the tolerance, withdrawal and two abstinence stages of dependence and to describe how gene expression is altered in moving from one stage to the next. The study design was unbalanced in several respects. First, for mice receiving morphine, arrays were made for four dependence stages, while for mice receiving placebo, arrays were made for only three stages. Second, administrative error led to an omitted replication for one treatment combination. Third, some expression readings were missing. Extending the two-stage ANOVA model of Lee et al (2000, 2002a) this paper first uses a chi-square statistic to identify a small set of genes that exhibit differential expression over one or more treatment combinations. This gene set is then examined further using cluster analysis and novel inference methods to uncover specific genes and gene clusters that play a role at different stages of opioid dependence and, in particular, a role in the persistence of effect into the late abstinence stage. The latter effect implies that morphine dependence has a long-term genetic impact. The statistical power of the study to uncover differentially expressed genes is calculated as a prelude to further investigation. The analytical results proved useful to scientists in understanding the link between opioid dependence and gene function.