Statistical Analysis For Mixture Cure Competing Risk Models

With advancements in medical research,more and more diseases,especially chronic disease may be curable,which indicates some patients may not die from the disease of interest.Thus,increasingly scholars are interested in these survival data with nonnegligible cure rates and have proposed appropriate statistical models.The most common model is the mixture cure model,which can capture patients being cured,attracts an increase attention in practice.However,because of the increased rate of cure,some patients may not die from diseases of interest,but from other diseases or events.The existing mixture cure models only focused on the major event with a potential cure while ignoring the potential risk from other non-curable competing events,which are commonly seen in real world.In this paper,a new mixed cure competing risk model is proposed,which analysis the cure ratio of diseases or events of interest,as well competition with other diseases or events.The main content is as follows:(1)The main purpose of this article is to develop a new mixture cure model allowing non-curable competing risk.A semiparametric estimation method is developed via an EM algorithm and its performance is demonstrated through comprehensive simulation studies.Finally,the proposed method is applied to the prostate cancer clinical trial data.(2)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 maximized 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.(3)We develop a Bayesian approach to estimate a proportional hazards mixture cure(PHMC)model allowing non-curable competing risk.Data augmentation method with latent binary cure indicators and event indicators are adopted to simplify the Markov chain Monte Carlo implementation.Given the event indicators,the PHMC model reduces to two standard Cox models and two logistic regression models.The baseline cumulative hazards for the PHMC model are explained by counting processes with gamma process priors.Its performance is demonstrated through comprehensive simulation studies.Finally,the proposed method is applied to the prostate cancer clinical trial data.