A new cure model accounting for longitudinal data and flexible patterns of hazard ratios over time

With the advancement of medical treatments, many historically incurable diseases have become curable. An accurate estimation of the cure rates is of great interest. When there are no clear biomarker indicators for cure, the estimation of cure rate is intertwined with and influenced by the specification of hazard functions for uncured patients. Consequently, the commonly used proportional hazards (PH) assumption, when violated, may lead to biased cure rate estimation. Meanwhile, longitudinal biomarker measurements for individual patients are usually available. To accommodate non-PH functions and incorporate individual longitudinal biomarker trajectories, we propose a new joint model for cure, survival, and longitudinal data, with hazard ratios between different covariate subgroups flexibly varying over time. The proposed joint model has individual random effects shared between its longitudinal and cure-survival submodels. The regression parameters are estimated by maximization of the non-parametric likelihood via the Monte Carlo expectation-maximization algorithm. The standard error estimation applies a jackknife resampling method. In simulation studies, we consider crossing and non-crossing survival curves, and the proposed model provides unbiased estimates for the cure rates. Our proposed joint cure model is illustrated via a study of chronic myeloid leukemia.