  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.
