CD8 T cells are specialized immune cells that play an important role in the regulation of antiviral immune response and the generation of protective immunity. In this paper we investigate the differentiation of memory CD8 T cells in the immune response using a short time course microarray experiment. Structurally, this experiment is similar to many in that it involves measurements taken on independent samples, in one biological group, at a small number of irregularly spaced time points, and exhibiting patterns of temporal nonstationarity. To analyze this CD8 T-cell experiment, we develop a hierarchical state space model so that we can: (1) detect temporally differentially expressed genes, (2) identify the direction of successive changes over time, and (3) assess the magnitude of successive changes over time. We incorporate hidden Markov models into our model to utilize the information embedded in the time series and set up the proposed hierarchical state space model in an empirical Bayes framework to utilize the population information from the large-scale data. Analysis of the CD8 T-cell experiment using the proposed model results in biologically meaningful findings. Temporal patterns involved in the differentiation of memory CD8 T cells are summarized separately and performance of the proposed model is illustrated in a simulation study.
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