An expectation-conditional maximization-based Weibull-Gompertz mixture model for analyzing competing-risks data: Using post-transplant malignancy data

The aim of this study is to introduce a parametric mixture model to analysis the competing-risks data with two types of failure. In mixture context, ith type of failure is ith component. The baseline failure time for the first and second types of failure are modeled as proportional hazard models according to Weibull and Gompertz distributions, respectively. The covariates affect on both the probability of occurrence and the hazards of the failure types. The probability of occurrence is modeled to depend on covariates through the logistic model. The parameters can be estimated by application of the expectation-conditional maximization and Newton-Raphson algorithms. The simulation studies are performed to compare the proposed model with parametric cause-specific and Fine and Gray models. The results show that the proposed parametric mixture method compared with other models provides consistently less biased estimates for low, mildly, moderately, and heavily censored samples. The analysis of post-kidney transplant malignancy data showed that the conclusions obtained from the mixture and other approaches have some different interpretations.