Estimating Subject-Specific Dependent Competing Risk Profile With A Cure Fraction

In surival analysis, usually, we think that if the follow up period is long enough, all individ-uals will eventually experience the event of interest. However, with the advanced development of new cancer treatments in clinical trials, a substantial proportion of individuals may never ex-perience the event, that is, those individuals are cured. In this paper, we consider the predictive inference of dependent competing risks with a cure fraction, and argue that some patients are exposed only to the risk which can be cured, whereas the uncured patients are exposed to other hazards. Specifically, we employ AFT mixture cure model to create a univariate risk index s-core predictive to the event rate of the primary interest risk, using EM algorithm to estimate the parameters. We then use nonparameteric function estimation method, making joint inferences about the average competing risks for subjects who have the same index score through a local multinomial likelihood for nonparametric smoothing technique. Through the two-stage proce-dure, we could construct a reliable prediction rule for the future subject’s profile of all competing risks of interest for risk-benefit decision making. We show a simulation study to assess the per-formance of proposed estimation method, and the proposed inference procedure is applied to bone marrow transplant data and melanoma survival data.The organization of this paper is as follows. Section 1 is the introduction, will introduce some basis knowledge of survival analysis, competing risks and cure models, and the estimation method is also included. Section 2 describes the semiparametric AFT mixture cure model and competing risks frameworks, then the two-stage estimation method is proposed, showing the point-wise and simultaneous confidence intervals for event rates over the risk score. In section 3, we will show a simulation study to assess the performance of proposed estimation method. In section 4, the proposed inference procedure is applied to bone marrow transplant data and melanoma survival data. The paper is concluded with a discussion in section 5.