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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\u2013Downton 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.<\/jats:p>","DOI":"10.1177\/09622802261489815","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:52:11Z","timestamp":1790682731000},"update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["A new bivariate cure rate model and its application to diabetic retinopathy"],"prefix":"10.1177","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-1266-1586","authenticated-orcid":false,"given":"Matilda","family":"Pitt","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8054-6844","authenticated-orcid":false,"given":"Katherine","family":"Davies","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Statistics for biology and health survival analysis a self-learning text","author":"Kleinbaum DG","year":"1996","unstructured":"Kleinbaum DG, Klein M. 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