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.
Conclusion: The new Bayesian functional mixed-effects model that assumes multiple groups of
functions with different smoothing parameters provides an enhanced approach to analyzing timecourse
gene expression data.