Power analysis of approximation methods for parameter estimation in Cox regression model with longitudinal covariate and tied survival times

Cox regression model (CRM) with time-varying covariates is widely used in medical and health related studies to investigate the effects of longitudinal variables on survival. In this paper, tied survival refers to units in which different subjects have the same survival time, while the term interaction indicates the relationship between longitudinal covariate and survival time. Unlike previous studies, we calculate the statistical power of Wald χ2 statistics to test the interaction term based on Monte Carlo (MC) simulations when Breslow, Efron, Discrete, and Exact approximation methods are used for handling tied survival times. A linear mixed effect model (LMM) is used to generate longitudinal covariate such as time-varying covariate in simulations. A numerical example is provided to illustrate the CRM with the interaction term between longitudinal covariate and survival time. Using extensive MC simulations under different conditions for censored proportion, type I error, and number of subjects, statistical power of Wald χ2 statistics is calculated using four different methods in the CRM. Statistical power value calculated using Breslow method is usually lower than statistical power values calculated when the other three methods are used. The proportion of censored observations in survival analysis has an important effect on power calculations.