An improved empirical bayes approach to estimating differential gene expression in microarray time-course data: BETR (Bayesian Estimation of Temporal Regulation)

Abstract

Background: Microarray gene expression time-course experiments provide the opportunity to observe the evolution of transcriptional programs that cells use to respond to internal and external stimuli. Most commonly used methods for identifying differentially expressed genes treat each time point as independent and ignore important correlations, including those within samples and between sampling times. Therefore they do not make full use of the information intrinsic to the data, leading to a loss of power.

Results: We present a flexible random-effects model that takes such correlations into account, improving our ability to detect genes that have sustained differential expression over more than one time point. By modeling the joint distribution of the samples that have been profiled across all time points, we gain sensitivity compared to a marginal analysis that examines each time point in isolation. We assign each gene a probability of differential expression using an empirical Bayes approach that reduces the effective number of parameters to be estimated.

Conclusions: Based on results from theory, simulated data, and application to the genomic data presented here, we show that BETR has increased power to detect subtle differential expression in time-series data. The open-source R package betr is available through Bioconductor. BETR has also been incorporated in the freely-available, open-source MeV software tool available from http://www.tm4.org/mev.html.

Figure 1

Time-course expression profiles of two illustrative genes. Log-ratio of expression between two treatment groups for a) a gene without differential expression, and b) an illustrative differentially expressed gene. I is an indicator of differential expression. δ represents the log-fold change at the four time points.

Figure 2

Performance assessment: ROC curves. ROC curves showing the true positive/false positive rates for detecting differentially expressed genes using simulated data.

Figure 3

Performance assessment: True positive rate vs. number of time points with differential expression. True positive rate as a function of the number of the four time points with differential expression. The significance cutoff is chosen to maintain a false positive rate of 5%.

Figure 4

An example of a gene uniquely identified by BETR. BETR has greater power than existing methods to detect genes with subtle and noisy differential expression patterns that are sustained over time. GNA13 is expressed at subtly higher levels in the TB resistant C57BL/6 mice compared to the more susceptible C3H.B6-sst1 mice.