On a class of non-linear transformation cure rate models

In this paper, we propose a generalization of the mixture (binary) cure rate model, motivated by the existence of a zero-modified (inflation or deflation) distribution, on the initial number of causes, under a competing cause scenario. This non-linear transformation cure rate model is in the same form of models studied in the past; however, following our approach, we are able to give a realistic interpretation to a specific class of proper transformation functions, for the cure rate modeling. The estimation of the parameters is then carried out using the maximum likelihood method along with a profile approach. A simulation study examines the accuracy of the proposed estimation method and the model discrimination based on the likelihood ratio test. For illustrative purposes, analysis of two real life data-sets, one on recidivism and another on cutaneous melanoma, is also carried out.