Outlier and Time-Dependent Covariate in Survival Analysis, A Simulation Based Study

The Cox regression model is widely used in Survival Analysis, also related to medical fields. The Cox regression model is further extended to tackle problems such as non-proportionality and time-dependent covariates. This paper focuses on the behavior of the Cox proportional hazard model in the presence of outliers and time-dependent covariates. To compare the performance of widely used existing time-to-event models in the presence of Outliers and time-dependent covariates and propose a modified Cox model in case of outliers and time-dependent covariates. The algorithm used in the Cox and time-dependent Cox model is extended to tackle the problem of outlier and time-dependent covariates jointly in a model. The estimated model's betas, RMSE, MAE, and MAPE, were compared among the different models. The study concluded that the modified Cox model outperformed the existing time-to-event methodology if the model simultaneously has an Outlier and time-dependent covariates problem.