A cure rate survival model under a hybrid latent activation scheme

In lifetimes studies, the occurrence of an event (such as tumor detection or death) might be caused by one of many competing causes. Moreover, both the number of causes and the time-to-event associated with each cause are not usually observable. The number of causes can be zero, corresponding to a cure fraction. In this article, we propose a method of estimating the numerical characteristics of unobservable stages (such as initiation, promotion and progression) of carcinogenesis from data on tumor size at detection in the presence of latent competing causes. To this end, a general survival model for spontaneous carcinogenesis under a hybrid latent activation scheme has been developed to allow for a simple pattern of the dynamics of tumor growth. It is assumed that a tumor becomes detectable when its size attains some threshold level (proliferation of tumorais cells (or descendants) generated by the malignant cell), which is treated as a random variable. We assume the number of initiated cells and the number of malignant cells (competing causes) both to follow weighted Poisson distributions. The advantage of this model is that it incorporates into the analysis characteristics of the stage of tumor progression as well as the proportion of initiated cells that had been 'promoted' to the malignant ones and the proportion of malignant cells that die before tumor induction. The lifetimes corresponding to each competing cause are assumed to follow a Weibull distribution. Parameter estimation of the proposed model is discussed through the maximum likelihood estimation method. A simulation study has been carried out in order to examine the coverage probabilities of the confidence intervals. Finally, we illustrate the usefulness of the proposed model by applying it to a real data involving malignant melanoma.