A Bayesian Prevalence Incidence Cure model for estimating survival using Electronic Health Records with incomplete baseline diagnoses

Retrospective cohorts can be extracted from Electronic Health Records (EHR) to study prevalence, time until disease or event occurrence, and cure proportion in real world scenarios. However, EHR are collected for patient care rather than research, and thus typically have complexities, such as patients with missing baseline disease status. Prevalence-Incidence (PI) models, which use a two-component mixture model to account for this missing data, have been proposed. However, PI models are biased in settings in which some individuals will never experience the endpoint (they are 'cured'). To address this, we propose a Prevalence-Incidence-Cure (PIC) model, a 3-component mixture model that combines the PI model framework with a cure model. Our PIC model enables estimation of the prevalence rate, time-to-incidence, and the cure proportion, and allows for covariate effects. We adopt a Bayesian inference approach, and focus on the interpretability of the prior. We show in a simulation study that the PIC model has smaller bias than PI and cure models for the survival probability; and we compare inference under vague, informative and misspecified priors. We illustrate our PIC model using a dataset of 1,964 patients who underwent treatment for Diabetic Macular Oedema, and demonstrate improved fit under our model.