In time-course experiments, it is often desirable to identify genes that exhibit a specific pattern of differential expression over time and thus gain insights into the mechanisms of the underlying biological processes. Two challenging issues in the pattern identification problem are: (i) how to combine the simultaneous inferences across multiple time points and (ii) how to control the multiplicity of Type I errors while accounting for the strong dependence. We formulate a compound decision-theoretic framework for set-wise multiple testing and propose a data-driven procedure that aims to minimize the missed set rate (MSR) subject to a constraint on the false set rate (FSR). The hidden Markov model (HMM) proposed in Yuan and Kendziorski (2006) is generalized to capture the temporal correlation in the gene expression data. Both theoretical and numerical results are presented to show that our data-driven procedure controls the multiplicity, provides an optimal way of combining simultaneous inferences across multiple time points, and greatly improves the conventional combined p-value methods. In particular, we demonstrate our method in an application to a study of systemic inflammation in humans for detecting early and late response genes.
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