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Cure models have been widely developed to estimate the cure fraction when some subjects never experience the event of interest. However, these models were rarely focused on the estimation of the time‐to‐cure, that is, the delay elapsed between the diagnosis and "the time from which cure is reached," an important indicator, for instance, to address the question of access to insurance or loans for subjects with personal history of cancer. We propose a new excess hazard regression model that includes the time‐to‐cure as a covariate‐dependent parameter to be estimated. The model is written similarly to a Beta probability distribution function and is shown to be a particular case of the non–mixture cure models. Parameters are estimated through a maximum likelihood approach and simulation studies demonstrate good performance of the model. Illustrative applications to three cancer data sets are provided and some limitations as well as possible extensions of the model are discussed. The proposed model offers a simple and comprehensive way to estimate more accurately the time‐to‐cure. [ABSTRACT FROM AUTHOR]