Empirical Bayes Screening (EBS) of Many P-values with Applications to Microarray Studies
by
Susmita Datta
Georgia State University
Coauthors: Somnath Datta

Statistical tests for the detection of differentially expressed genes lead to a large collection of p-values one for each gene comparison. Without any further adjustment, these p-values may lead to a large number of false positives, simply because the number of genes to be tested is huge, which might mean wastage of laboratory resources. To account for multiple hypotheses, these p-values are typically adjusted using a single step method or a step-down method in order to achieve an overall control of the error rate (the so called familywise error rate). In many applications, this may lead to an overly conservative strategy leading to too few genes being flagged.

In this talk, we introduce a novel empirical Bayes screening (EBS) technique to inspect a large number of p-values in an effort to detect additional positive cases. In effect, each case borrows strength from an overall picture of the alternative hypotheses computed from all the p-values, while the entire procedure is calibrated by a step-down method so that the familywise error rate at the complete null hypothesis is still controlled. It is shown that the empirical Bayes screening has substantially higher sensitivity than the standard step-down approach for multiple comparison at the cost of a modest increase in the FDR. The EBS procedure also compares favorably when compared with existing FDR control procedures for multiple testing. The EBS procedure is particularly useful in situation where it is important to identify all possible potentially positive cases which can be subjected to further confirmatory testing in order to eliminate the false positives. We illustrated this screening procedure using a data set on human colorectal cancer.

This novel empirical Bayes procedure is advantageous over our earlier proposed empirical Bayes adjustments due to the following reasons: (i) it offers an automatic screening of the p-values the user may obtain from a univariate (i.e., gene by gene) analysis package making it extremely easy to use for a nonstatistician, (ii) since it applies to the p-values, the tests don't have to be t-tests; in particular they could be F-tests which might arise in certain ANOVA formulation with expression data or even nonparametric tests, (iii) the empirical Bayes adjustment uses nonparametric function estimation techniques to estimate the marginal density of the transformed p-values rather than using a parametric model for the prior distribution and is therefore robust against model mis-specification.

Date received: October 17, 2004