A Bivariate Model for Simultaneous Testing in Bioinformatics Data

We develop a novel approach for testing treatment effects in high-throughput data. Most previous works on this topic focused on testing for differences between the means, but recently it has been recognized that testing for differential variation is probably as important. We take it a step further, and introduce a bivariate model modeling strategy which accounts for both differential expression and differential variation. Our model-based approach, in which the differential mean and variance are considered random effects, results in shrinkage estimation and powerful tests as it borrows strength across levels. We show in simulations that the method yields a substantial gain in the power to detect differential means when differential variation is present. Our case studies show that the model is realistic in a wide range of applications. Furthermore, a hierarchical estimation approach implemented using the EM algorithm results in a computationally efficient method which is particularly well-suited for "multiple testing" situations. Finally, we develop a power and sample size calculation tool that mirrors the estimation and inference method described in this article, and can be used to design experiments involving thousands of simultaneous tests.