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Abstract:
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Cure models refer to survival models incorporating a cure fraction. As medical treatments progress, cure models have been applied to time-to-event data for diseases where a proportion of patients are at no risk of the disease following treatment. In most of the current work on cure models it is assumed that the cure status is determined, if unknown, at the beginning of the follow up (t=0). In practice though, patients often receive treatments or other events during the follow up. In this case it is natural to expect the chance of cure to change in response to dynamic factors. To account for this situation, we propose a joint dynamic model for the cure process and a terminal event. Two separate baseline hazards are estimated nonparametrically in the model to allow different time scales for the time to cure and time to failure processes. An EM algorithm is developed to estimate the two infinite dimensional parameters. Covariates are modeled parametrically and estimated using the profile likelihood. Large-sample properties are obtained. Simulation studies are presented to illustrate the finite-sample properties. The proposed model is applied to prostate cancer data from the SEER.
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