Semiparametric estimation for proportional hazards mixture cure model allowing non-curable competing risk

With advancements in medical research, broader range of diseases may be curable, which indicates some patients may not die owing to the disease of interest. The mixture cure model, which can capture patients being cured, has received an increasing attention in practice. However, the existing mixture cure models only focus on major events with potential cures while ignoring the potential risks posed by other non-curable competing events, which are commonly observed in the real world. The main purpose of this article is to propose a new mixture cure model allowing non-curable competing risk. A semiparametric estimation method is developed via an EM algorithm, the asymptotic properties of parametric estimators are provided and its performance is demonstrated through comprehensive simulation studies. Finally, the proposed method is applied to a prostate cancer clinical trial dataset.