Comparison of methods for handling outliers in Cox regression model

The Cox regression analysis is used to determine the relationship between a dependent variable and covariates in survival analysis involving censored data. The proportional hazards assumption is one of the most important assumptions of Cox regression. Outliers may have a strong influence on the Cox regression model's parameter estimates and lead to violation of the proportional hazard assumption. Therefore, having outliers in the data set is a problem for researchers. In this case, robust estimations are commonly used to infer the parameters in a more robust way. However, we explore a new approach consisting of considering an outlier as missing data and replacing it by the multiple imputation method. The aim of this study is to compare these two methods through simulation. Furthermore, an analysis of a lung cancer data set is considered for illustration. According to the results of the study carried out based on simulated data sets and a real data set, the multiple imputation method, which is a missing data analysis method, solves the problem of outliers better than the robust estimation method, as the outcome is closer to the results obtained through original data.