A Multi-Center Competing Risks Model and Its Absolute Risk Calculation Approach

In the competing risks frame, the cause-specific hazard model (CSHM) can be used to test the effects of some covariates on one particular cause of failure. Sometimes, however, the observed covariates cannot explain the large proportion of variation in the time-to-event data coming from different areas such as in a multi-center clinical trial or a multi-center cohort study. In this study, a multi-center competing risks model (MCCRM) is proposed to deal with multi-center survival data, then this model is compared with the CSHM by simulation. A center parameter is set in the MCCRM to solve the spatial heterogeneity problem caused by the latent factors, hence eliminating the need to develop different models for each area. Additionally, the effects of the exposure factors in the MCCRM are kept consistent for each individual, regardless of the area they inhabit. Therefore, the coefficient of the MCCRM model can be easily explained using the scenario of each model for each area. Moreover, the calculating approach of the absolute risk is given. Based on a simulation study, we show that the estimate of coefficients of the MCCRM is unbiased and precise, and the area under the curve (AUC) is larger than that of the CSHM when the heterogeneity cannot be ignored. Furthermore, the disparity of the AUC increases progressively as the standard deviation of the center parameter (SDCP) rises. In order to test the calibration, the expected number (E) of strokes is calculated and then compared with the corresponding observed number (O). The result is promising, so the SDCP can be used to select the most appropriate model. When the SDCP is less than 0.1, the performance of the MCCRM and CSHM is analogous, but when the SDCP is equal to or greater than 0.1, the performance of the MCCRM is significantly superior to the CSHM. This suggests that the MCCRM should be selected as the appropriate model.