Objective: As a result of the development of microarray technologies, gene expression levels of thousands of
genes involved in a given biological process can be measured simultaneously, and it is important to study their temporal
behavior to understand their mechanisms. Since the dependence between gene expression levels over time for a given
gene is often too complicated to model parametrically, sparse functional data analysis has received an increasing amount
of attention for analyzing such data.
Methods: We propose a new functional mixed-effects model for analyzing time-course gene expression data.
Specifically, the model groups individual functions with heterogeneous smoothness. The proposed method utilizes the
mixed-effects model representation of penalized splines for both the mean function and the individual functions. Given
noninformative or weakly informative priors, Bayesian inference on the proposed models was developed, and Bayesian
computation was implemented by using Markov chain Monte Carlo methods.
Results: The performance of our new model was studied by two simulation studies and illustrated using a yeast cell cycle
gene expression dataset. Simulation results suggest that our proposed methods can outperform the previously used
methods in terms of the mean integrated squared error. The yeast gene expression data application suggests that the
proposed model with two latent groups should be used on this dataset.