Multiple Hypothesis Testing by Clustering Treatment Effects

Abstract

Multiple hypothesis testing and clustering have been the subject of extensive research in high-dimensional inference, yet these problems usually have been treated separately. By defining true clusters in terms of shared parameter values, we could improve the sensitivity of individual tests, because more data bearing on the same parameter values are available. We develop and evaluate a hybrid methodology that uses clustering information to increase testing sensitivity and accommodates uncertainty in the true clustering. To investigate the potential efficacy of the hybrid approach, we first study a stylized example in which each object is evaluated with a standard z score but different objects are connected by shared parameter values. We show that there is increased testing power when the clustering is estimated sufficiently well. We next develop a model-based analysis using a conjugate Dirichlet process mixture model. The method is general, but for specificity we focus attention on microarray gene expression data, to which both clustering and multiple testing methods are actively applied. Clusters provide the means for sharing information among genes, and the hybrid methodology averages over uncertainty in these clusters through Markov chain sampling. Simulations show that the hybrid method performs substantially better than other methods when clustering is heavy or moderate and performs well even under weak clustering. The proposed method is illustrated on microarray data from a study of the effects of aging on gene expression in heart tissue.