The Pareto IV power series cure rate model with applications

Abstract

Cutaneous melanoma is thought to be triggered by intense, occasional exposure to ultraviolet radiation, either from the sun or tanning beds, especially in people who are genetically predisposed to the disease. When skin cells are damaged by ultraviolet light in this way, often showing up as a sunburn, they are more prone to genetic defects that cause them to rapidly multiply and form potentially fatal (malignant) tumors. Melanoma originates in a type of skin cell called a melanocyte, such cells help produce the pigments of our skin, hair, and eyes. We propose a new cure rate survival regression model for predicting cutaneous melanoma. We assume that the unknown number of competing causes that can influence the survival time is governed by a power series Distribution and that the time until the tumor cells are activated follows the Pareto IV distribution. The parameter estimation is based on the EM algorithm which for this model can be implemented in a simple way in computational terms. Simulation studies are presented, showing the good performance of the proposed estimation procedure. Finally, two real applications related to a cutaneous melanoma and melanoma data sets are presented.