Study of Ordinary Time to Event (OTE) residual in CPH model and its application in the genomic-wide time-to-event data analysis

Abstract

This study critically explored the Vieland et al. (2020) article, which introduced the Ordinary Time to Event (OTE) residual. The primary objective of this study was to validate the claims made in the article regarding the superior performance of OTE residuals compared to Martingale Residual (MR) and Deviance Residual (DR) in the context of downstream analysis for Genome-Wide Association Studies (GWAS) focused on time-to-event data, which inherently contains censored information. In the context of Cox Proportional Hazards (CPH) regression, MR represents the difference between observed and expected cumulative hazards, while DR quantifies the discrepancy between observed and predicted event probabilities, providing insights into model fit and potential outliers. OTE is computed by making three changes in the DR residual computation. To comprehensively assess these claims, this research undertook a rigorous evaluation involving genetic data simulations with various influencing factors, providing a robust foundation for a comprehensive GWAS using OTE as the phenotype. Comparative analysis of residuals showed that the properties of residuals were almost similar in this case and as presented in the article. When these residuals were used for downstream analysis using linear regression, with residuals as the dependent variable and genotype data as the independent variable (Vieland et al. (2020)) used a Bayesian approach for downstream analysis), 25 different models were examined, including the 8 models reported in the article. In this study, OTE performed better in most cases, but in a few instances, MR performed better, which contrasted with the article where OTE consistently outperformed MR and DR. Additionally, this study extended the analysis by considering four different allele frequencies (0.05, 0.1, 0.2, and 0.5), while the reference article used a fixed allele frequency of 0.5 for genotype data. Notably, model performance improved as allele frequency increased; for example, in Model 3, power increased from 65.8% when the allele frequency was 0.05 to 100% when the allele frequency was 0.5. Compared with the model performance reported in the article, where OTE outperformed MR and DR, the findings in this study revealed a degree of inconsistency in OTE's performance, emphasizing the significance of considering allele frequency as a contributing factor in GWAS analysis.