Joint modeling of longitudinal proportional measurements and survival time with a cure fraction

In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event (survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.