LLR test to identify genes whose expression is informed by various model features

For each of the three models (M1, M2, and M3), we assess for each gene whether its expression predictability has significant contribution from WBGE, (WBGE+WBSp), and (WBGE+WBSp+eSNPs), respectively, above and beyond age, race, and sex. For each gene, we compare the model (M1, M2, or M3) with the null model M0 using the LLR test using R package “lmtest.” The P value indicates the significance of the contribution by the additional features. We apply FDR ≤ 0.05 to select the genes, henceforth called the “significant gene” with respect to a particular model. With regard to finding the significant genes that has significant contribution from eSNPs above and beyond WBT, we compare model M4 with M3 using the LLR test as above.