Sequential Design for Microarray Experiments

Abstract

This article features online supplementary material.A critical aspect in the design of microarray studies is the determination of the sample size necessary to declare genes differentially expressed across different experimental conditions. In this article, we propose a sequential approach where the decision to stop the experiment depends on the accumulated microarray data. The study could stop whenever sufficient data have been accumulated to identify gene expression changes across several experimental conditions. The gene expression response is modeled by a robust linear regression model. We then construct a sequential confidence interval for the intercept of this model, which represents the median gene expression at a given experimental condition. We derive the stopping rule of the experiment for both continuous and discrete sequential approaches and give the asymptotic properties of the stopping variable. We demonstrate the desirable properties of our sequential approach, both theoretically and numerically. In our application to a study of hormone responsive breast cancer cell lines, we estimated the stopping variable for the sample size determination to be smaller than the actual sample size available to conduct the experiment. This means that we can obtain an accurate assessment of differential gene expression without compromising the cost and size of the study. Altogether, we anticipate that this approach could have an important contribution to microarray studies by improving the usual experimental designs and methods of analysis.