A growth curve approach to analyzing multiple-valued expression data

There is significant literature which explores methods for clustering timeseries gene-expression data sets, such as the classical data set due to Spellman et al. (1998). For instance James and Hastie (2001) use linear or quadratic discriminant functions on fitted curves, while Bar-Joseph et al. (2003) using a similar approach, do the clustering based on the coefficients of the fitted splines. In a series of papers, Liu et al. (2006), medvedovic et al. (2004) and Medvedovic and Sivaganesan (2002) present methods of clustering geneprofiles, by treating them as multivariate vectors. In this work we take a very different approach. Our goal is not exploratory as when one does clustering, but confirmatory viz. to verify if the mean profiles of the obtained clusters are significantly different. We treat the observed vector on each gene as multivariate Gaussian, and fit a mean curve to each group, based on the “growth curve” analysis. This approach coming from linear models for multivariate data, allows us to do proper statistical significance tests for checking if a mean profile fits to the data, and if these profiles differ for the different groups.