Distance-correlation based gene set analysis in longitudinal studies

Longitudinal gene expression profiles of subjects are collected in some clinical studies to monitor disease progression and understand disease etiology. The identification of gene sets that have coordinated changes with relevant clinical outcomes over time from these data could provide significant insights into the molecular basis of disease progression and lead to better treatments. In this article, we propose a Distance-Correlation based Gene Set Analysis (dcGSA) method for longitudinal gene expression data. dcGSA is a non-parametric approach, statistically robust, and can capture both linear and nonlinear relationships between gene sets and clinical outcomes. In addition, dcGSA is able to identify related gene sets in cases where the effects of gene sets on clinical outcomes differ across subjects due to the subject heterogeneity, remove the confounding effects of some unobserved time-invariant covariates, and allow the assessment of associations between gene sets and multiple related outcomes simultaneously. Through extensive simulation studies, we demonstrate that dcGSA is more powerful of detecting relevant genes than other commonly used gene set analysis methods. When dcGSA is applied to a real dataset on systemic lupus erythematosus, we are able to identify more disease related gene sets than other methods.