Semiparametric estimation for accelerated failure time mixture cure model allowing non-curable competing risk

The mixture cure model is the most popular model used to analyse the major event with a potential cure fraction. But in the real world there may exist a potential risk from other non-curable competing events. In this paper, we study the accelerated failure time model with mixture cure model via kernel-based nonparametric maximum likelihood estimation allowing non-curable competing risk. An EM algorithm is developed to calculate the estimates for both the regression parameters and the unknown error densities, in which a kernel-smoothed conditional profile likelihood is maximised in the M-step, and the resulting estimates are consistent. Its performance is demonstrated through comprehensive simulation studies. Finally, the proposed method is applied to the colorectal clinical trial data.