Abstract
Micro-array technology allows investigators the opportunity to measure expression levels of thousands of genes simultaneously. However, investigators are also faced with the challenge of simultaneous estimation of gene expression differences for thousands of genes with very small sample sizes. Traditional estimators of differences between treatment means (ordinary least squares estimators or OLS) are not the best estimators if interest is in estimation of gene expression differences for an ensemble of genes. In the case that gene expression differences are regarded as exchangeable samples from a common population, estimators are available that result in much smaller average mean-square error across the population of gene expression difference estimates. We have simulated the application of such an estimator, namely an empirical Bayes (EB) estimator of random effects in a hierarchical linear model (normal-normal). Simulation results revealed mean-square error as low as 0.05 times the mean-square error of OLS estimators (i.e., the difference between treatment means). We applied the analysis to an example dataset as a demonstration of the shrinkage of EB estimators and of the reduction in mean-square error, i.e., increase in precision, associated with EB estimators in this analysis. The method described here is available in software that is available at http://www.soph.uab.edu/ssg.asp?id=1087.
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Acknowledgements
We wish to acknowledge Dr Eva Gropp for her contributions to earlier versions of this manuscript and Dr Alfred Bartolucci for reading two versions of this manuscript and providing many helpful comments. This research was supported in part by NSF grants 0217651 and 0090286, NIH grants T32AR007450, P01AG11915, and R01AG18922, an intramural award from the University of Alabama Health Services Foundation, and the Frederick Gardner Cottrell Foundation. Mention of trade names or commercial products in this article is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the US Department of Agriculture.
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Edwards, J.W., Page, G.P., Gadbury, G. et al. Empirical Bayes estimation of gene-specific effects in micro-array research. Funct Integr Genomics 5, 32–39 (2005). https://doi.org/10.1007/s10142-004-0123-0
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DOI: https://doi.org/10.1007/s10142-004-0123-0