Parametric frailty model based analysis of survival data with time-varying risk factors

Abstract

In the follow-up study, a covariate changing over time is known as a time-varying covariate. By using the frailty model, we can analyze the effect of such a variable on survival time. When heterogeneity is present, the statistical analysis of the survival data without considering frailty gives a less accurate estimate of parameters. The proportional hazard (PH) assumption of the Cox regression model for time-varying covariates does not hold. The PH assumption was tested using Schoenfeld residuals, and a p-value of less than 0.05 was deemed statistically significant. The covariates' p-value is less than 0.05, which suggests that they do not meet the PH assumption and shows that the covariate is time-varying. This article aims to illustrate how to carry out statistical analysis by using frailty models in the presence of time-varying covariates and to compare their performance. Two frailty models, namely the Gamma frailty model and the inverse-Gaussian frailty model with log-normal and Weibull as initial hazards, were used in this study. AIC and BIC were used to compare the performance of the models. An application to hospital readmission data for patients with colorectal cancer is illustrated.