Sequential Bayesian designs for high-throughput studies Seminar

Traditional sample size calculations require making a priori guesses about the quantities of interest that one wishes to study, e.g. the size of the differences between groups is critical in power calculations for hypothesis testing, or similarly the amount of inherent variability plays a crucial role in the width of confidence/credibility intervals. We consider the case of high-throughput studies with a massive number of outcomes of interest (e.g. genomics studies with tens of thousands of genes) for which one wishes to perform simultaneous inference. In these settings researchers are unable to come up with reasonable a priori guesses, and even if they were one needs to extend the usual criteria related to statistical power or estimation precision. We propose a Bayesian framework for sequential design of experiments. Akin to sequential clinical trials, rather than deciding the sample size in advance we collect data in batches and decide to stop when continuing experimentation looks unpromising. The framework is embedded within Bayesian decision-theory, where the computational unfeasibility to maximize posterior expected utility exactly forces us to adopt certain simplifications. Specifically, we consider a reduction of the action space that leads to easy intuition and implementation. Throughout we shall emphasize applied considerations, providing examples from gene/protein expression studies as well as an interesting new application to RNA-sequencing studies, where additionally to the sample size one may consider other experimental settings (number and length of sequences etc.).