A new bivariate cure rate model and its application to diabetic retinopathy.

Modeling the time until an event occurs is often of interest, and in particular when two events occur to one subject, often modeled via bivariate distributions. Further scenarios occur where some subjects in the population are cured and will not experience the event(s) of interest, often modeled via a cure rate mixture model. Various bivariate cure rate mixture models exist, with this article developing a further model using the Moran-Downton Weibull distribution. A method to fit distributions when there is a latent variable, in this case cure status, is to use an Expectation-Maximization (EM) algorithm however this has yet to be developed for bivariate cure rate models. This article suggests a new bivariate cure rate model, derives and develops an EM algorithm to fit the model and applies it to a dataset on diabetic retinopathy to suggest insight on the effect of laser treatment.