Long-term survival models with latent activation under a flexible family of distributions

. In this paper, we propose a new cure rate survival model under a flexible family of distributions. Our approach enables different underlying activation mechanisms that lead to the event of interest. The number of competing causes of the event of interest follows a power series distribution. This model includes the standard mixture cure model and the promotion time cure model. The model is parametrized in terms of the cured fraction, which is then linked to covariates. We carried out a simulation study to assess some properties of our proposal. An illustrative example with a real data set is pro-vided to illustrate the models. rate models stand out in the literature as being the pre-vailing approaches. Here we point out a distinguishing feature between them. In the standard mixture cure model (Boag, 1949; Berkson and Gage, 1952), the number of causes of the event of interest is a binary random variable on { 0 , 1 } , whereas in the promotion time cure model (Yakovlev and Tsodikov, 1996) this number follows a Poisson distribution. These models have been successfully applied to many real word problems. Our aim consists in pursuing some steps toward flexibility.