A general class of shared gamma frailty models for risk prediction, with application to breast cancer screening adherence

We introduce a new class of mixed models for longitudinal or clustered binary data. The formulation is inspired by the shared frailty multivariate survival model for clustered data, and it allows for closed forms for all the relevant quantities, which allows for an efficient and fast computational solution of the associated inferential and prediction problems. We focus on an easily interpretable specification of the model, discuss the associated individual risk prediction, and compare our results to the traditional GLMM model for binary data with random intercept. We implement the methods on a large motivating dataset on the individual longitudinal adherence to the breast cancer screening program of the Oslo region.