In many practical situations, some subjects may never experience the event of interest in their lifetime. These subjects are referred to as the cured or non-susceptible subjects. In the context of chronic disease treatment, this is referred to as a cure fraction. In this work, we extend the generalized time-dependent logistic (GTDL) model proposed by MacKenzie (1996) to a flexible family of models which accommodates not only non-proportional hazards, but also long-term survivors. Inferential methods are then developed for the proposed model and a Monte Carlo simulation study is also carried out to evaluate the performance of the model as well as the inferential method developed here. A real data example on gastric cancer is then used to illustrate the usefulness of the proposed model.
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