Joint longitudinal and time-to-event cure models for the assessment of being cured

Medical time-to-event studies frequently include two groups of patients: those who will not experience the event of interest and are said to be "cured" and those who will develop the event and are said to be "susceptible". However, the cure status is unobserved in (right-)censored patients. While most of the work on cure models focuses on the time-to-event for the uncured patients (latency) or on the baseline probability of being cured or not (incidence), we focus in this research on the conditional probability of being cured after a medical intervention given survival until a certain time. Assuming the availability of longitudinal measurements collected over time and being informative on the risk to develop the event, we consider joint models for longitudinal and survival data given a cure fraction. These models include a linear mixed model to fit the trajectory of longitudinal measurements and a mixture cure model. In simulation studies, different shared latent structures linking both submodels are compared in order to assess their predictive performance. Finally, an illustration on HIV patient data completes the comparison.