Title
Optimal Sample Size for Multiple Testing: the Case of Gene Expression Microarrays
Speaker
Dr. Peter Mueller, M.D., Anderson Cancer Center, Houston, TX
Abstract
We consider the choice of an optimal sample size for multiple comparison problems. The motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression. However, the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests. We discuss two decision problems in the context of this setup, the sample size selection and the decision about the multiple comparisons. We adopt a decision theoretic approach, using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible, while keeping the number of false discoveries manageable. We use the same loss function for both decisions, thus ensuring coherent practice. The decision rule that emerges for the multiple comparison problem takes a form based on controlling posterior expected false discovery rate (FDR). For the sample size selection we combine the expected utility argument with additional sensitivity analysis, reporting conditional expected utilities, conditioning on assumed levels of true differential expression. We recognize the resulting diagnostic as a form of statistical power, facilitating interpretation and communication.
As sampling model for observed gene expression densities across genes and arrays we use a variation of a hierarchical Gamma/Gamma model model proposed in recent literature. But the discussion of the decision problem is independent of the chosen probability model. The approach is valid for any model that includes positive prior probabilities for the null hypotheses in the multiple comparisons, and that allows efficient marginal and posterior simulation, possibly by dependent Markov chain Monte Carlo simulation.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.
