Measures of influence and weighted partial likelihood estimation for cox proportional hazards regression

In this study, we consider the development of influential diagnostics to assess case influence for the Cox proportional hazards model and stratified Cox proportional hazards regression model. We examine various residuals previously proposed for these models and develop a diagnostics method using the case-deletion technique. However, existing diagnostics methods are affected by masking effect. This effect may cause diagnostics methods to fail to correctly detect influential cases. Therefore, we propose an influential diagnostics method that has lower masking effect as compared to other methods. The proposed influential diagnostics method is approximately Chi-square distribution with p degress of freedom. The simulation study is implemented to evaluate the performance of the proposed influential diagnostics method via comparison with existing diagnostics method. Then, the diagnostics methods are applied into the real data such as kidney catheter data, Worcester Heart Attack study and also Stanford Heart Transplant study. The performance of the proposed influential detection method is better than that of the existing influential detection method. The partial likelihood estimation for the Cox regression model is biased when there are measurement errors in the covariate. Therefore, a weighted partial likelihood estimation for Cox regression model is proposed when there is violation of underlying assumptions due to measurement error in the covariates. In the simulation study, the proposed weighted partial likelihood estimations for parameter coefficients have smaller bias, root mean square errors, and ratio of bias over standard error than the existing parameter estimators, both with and without contamination of the covariates. The demonstrated performance of the proposed influential methods and weighted partial likelihood estimators are superior to existing influential detection methods and parameter estimators.

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