This article presents semiparametric joint models to analyze longitudinal measurements and survival data with a cure fraction. We consider a broad class of transformations for the cure-survival model, which includes the popular proportional hazards structure and the proportional odds structure as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we demonstrate the good performance of the method through extensive simulation studies and a real-data application.
Keywords: Cure-survival data; Joint models; Longitudinal data; Nonparametric maximum likelihood; Random effects; Transformation models.