Granger Causality Analysis of Human Cell-Cycle Gene Expression Profiles

Abstract

Granger causality (GC) tests are ideally suited to investigate time series data generated by bivariate vector autoregressive (VAR) processes. Recent studies have applied GC analysis and its extensions for modeling functional relationships and network structure from temporal gene expression profiles. The present study investigates GC analysis of human cell-cycle gene expression profiles that can be modeled as a first-order bivariate VAR. Analytical results presented establish the contribution of the VAR process parameters, including auto-regulatory feedback and noise variance to the mean-squared forecast error, as a critical component in identifying statistically significant GC relationships. These results in turn discourage blind inference of functional relationship between a given pair of genes solely based on the result of the statistical tests for GC. The presence of significant auto-regulatory feedback and discrepancy in noise variance is demonstrated across the cell-cycle gene expression profiles by VAR parameter estimation. It is emphasized that discrepancies in noise variance can be due to artifacts and can lead to spurious existence of functional relationship between a given pair of genes. VAR parameter estimation is encouraged for better of GC interpretation of the results. Published case studies on GC analysis of the same publicly available cell-cycle gene expression data are reinvestigated for transparency.