Abstract

We review Bayesian sample size arguments for microarray experiments, focusing on a decision theoretic approach. We start by introducing a choice based on minimizing expected loss as theoretical ideal. Practical limitations of this approach quickly lead us to consider a compromise solution that combines this idealized solution with a sensitivity argument. The finally proposed approach relies on conditional expected loss, conditional on an assumed true level of differential expression to be discovered. The expression for expected loss can be interpreted as a version of power, thus providing for ease of interpretation and communication

Introduction

We discuss approaches for a Bayesian sample size argument in microarray experiments. As is the case for most sample size calculations in clinical trials and other biomedical applications the nature of the sample size calculation is to provide the investigator with decision support, and allow an informed sample size choice, rather than providing a black-box method to deliver an optimal sample size.

Several classical approaches for microarray sample size choices have been proposed in the recent literature. Pan et al. (2002) develop a traditional power argument, using a finite mixture of normal sampling model for difference scores in a group comparison microarray experiment. Zien et al. (2002) propose to plot ROC-type curves to show achievable combinations of false-negative and falsepositive rates. Mukherjee et al. (2003) use a machine learning perspective. They consider a parametric learning curve for the empirical error rate as a function of the sample size, and proceed to estimate the unknown parameters in the learning curve.