Cure models with adaptive activation for modeling cancer survival

We propose a class of cure rate models motivated by analysis of colon cancer and triple-negative breast cancer survival data. This class is indexed by an adaptive activation parameter and a function. We establish that the class is stochastically ordered in the activation parameter and also establish two identifiability results for this class. The first- and last-activation models are members of this class whereas many cure rate models proposed in the literature are also part of this class. We illustrate that while first- and last-activation models may perform poorly under model misspecifications, the proposed model with adaptive activation provides appropriate inference in these cases. We apply the proposed approach to assess treatment-sex interaction on cure rate in a colon cancer study and to assess role of tumor heterogeneity and ethnic disparity in breast cancer.