Some Discussions On Long - Term Survival Model Under Generalized Linear Mixed Model

In recent years with the improvement of medical instruments and conditions, cured individuals can be found in some diseases which were thought uncured before. That is, some patients will no longer be affected by the diseases after medical treatment. We call them long-term survivors. Therefore, the long-term survival model is proposed to analyze the survival data with a cure fraction in clinical trial studies.In this paper, we mainly discuss the long-term survival model with clustered and interval-censored survival time data. In the model, we integrates the logistic regression model for the proportion of cured subjects and the Cox proportional hazards model for uncured subjects. And random effects are incorporated to analyze the survival time data with a cure fraction.A long-term survival model based on Cox’s semi-parametric PH is considered to avoid the risk of model misspecification. Adopting the GLMM approach and EM algorithm, the estimation of regression parameters can be achieved by maximizing a BLUP-type log-likelihood function at the initial step, and then used to find the REML estimation for the variance component parameters. And then a simulation study is conducted to evaluate the performance of the proposed method in various practical situations.Furthermore, as the survival time of cure individuals is obviously greater than the trial observation time, so how to identify the cured individuals from the censored data has became a very important task. Interests then lies in the development of a score for testing the presence of cured subjects in clustered and interval-censored survival data. Through simulation, we evaluate the sampling distribution and power behavior of the score test.