A Multivariate Empirical Bayes Statistic for Replicated Microarray Time Course Data

Abstract

The analysis of replicated microarray time course data has been a great challenge for several reasons. The number of time points is typically very few compared to standard time series data, due to cost or available resources. The series are so short that traditional techniques for the analysis of standard time series data (e.g. Fourier transform, wavelet, and ARMA methods) are infeasible in this context. In addition, there are usually very few replicates (3-5) or sometimes no replicates at all. This may result in poorly estimated replicate variances or covariances. The sampling times are determined by the investigator's judgement concerning the specific biological event of interest. They are frequently irregularly spaced for developmental time courses, or equally spaced for periodic ones. Finally, for longitudinal time course experiments, gene expression levels are correlated over time, which complicates the analysis. In this talk, I will describe several multivariate empirical Bayes statistics (MB-statistics) we have developed for ranking genes from replicated longitudinal developmental experiments. We do this by treating them as one-sample, (paired) two-sample, or multi-sample problems, where genes of interest are those which change over time, maybe in some specific pattern, or change differently across biological conditions over time. The use of the empirical Bayes approach allows us to borrow information across the whole gene set, and hence reduces the numbers of false positives and false negatives.