Gene set differential analysis of time course expression profiles via sparse estimation in functional logistic model...

High-throughput time course expression profiles have been available in the last decade due to developments in measurement techniques and devices. Functional data analysis, which treats smoothed curves instead of originally observed discrete data, is effective for the time course expression profiles in terms of dimension reduction, robustness, and applicability to data measured at small and irregularly spaced time points. However, the statistical method of differential analysis for time course expression profiles has not been well established. We propose a functional logistic model based on elastic net regularization (F-Logistic) in order to identify the genes with dynamic alterations in case/control study. We employ a mixed model as a smoothing method to obtain functional data; then F-Logistic is applied to time course profiles measured at small and irregularly spaced time points. We evaluate the performance of F-Logistic in comparison with another functional data approach, i.e. functional ANOVA test (F-ANOVA), by applying the methods to real and synthetic time course data sets. The real data sets consist of the time course gene expression profiles for long-term effects of recombinant interferon β on disease progression in multiple sclerosis. F-Logistic distinguishes dynamic alterations, which cannot be found by competitive approaches such as F-ANOVA, in case/control study based on time course expression profiles. F-Logistic is effective for time-dependent biomarker detection, diagnosis, and therapy.