A multivariate growth curve model for ranking genes in replicated time course microarray data

Gene ranking problem in time course microarray experiments is challenging since gene expression levels between different time points are correlated. This is because, expression values at successive time points are usually taken from the same organism, tissue or culture. Moreover, time dependency of gene expression values is usually of interest and often is the biological problem that motivates the experiment. We propose a multivariate growth curve model for ranking genes and estimating mean gene expression profiles in replicated time course microarray data. The approach takes the within individual correlation as well as the temporal ordering into consideration. Moreover, time is incorporated as a continuous variable in the model to account for the temporal pattern. Polynomial profiles are assumed to describe the time dependence and a transformation incorporating information across the genes is used. A moderated likelihood ratio test is then applied to the transformed data to get a statistic for ranking genes according to the difference in expression profiles among biological groups. The methodology is presented in a general setup and could be used for one sample as well as more than one sample problem. The estimation is done in a multivariate framework in which information from all the groups involved is used for better inference. Moreover, the within individual correlation as well as information across genes entered in the estimation through a moderated covariance matrix. We assess the performance of our method using simulation studies and illustrate the results with publicly available real time course microarray data.