The power series Pareto IV cure rate model

• Grant number: 14/16829-7
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: April 28, 2015
• End date: July 27, 2015
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Antonio Carlos Pedroso de Lima
• Grantee: Diego Ignacio Gallardo Mateluna
• Supervisor: Barry Charles Arnold
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of California, Riverside (UCR), United States
• Associated to the scholarship: 13/23684-2 - Extending the Destructive Negative Binomial cure rate model with a latent activation scheme., BP.PD

Abstract

Survival models with cure rate have an exponential growth in last years. In the initial work of Berkson e Gage (1952) was simply supposed two groups in population, susceptible and cured. This idea was extended in the work of Chen et al. (1999), assuming a biological context which each individual have a latent quantity M of cells which can produce the event of interest in the individual. Of course, M=0 (M>0) indicates that the individual is cured (susceptible). Inthat work, was assumed that M have Poisson distribution. Later, Rodrigues et al. (2009) extended that idea assuming the Negative Binomial distribution for the variable M. A more interesting approach is proposed in Cancho et al. (2013a), where it is assumed a more general structure for M although the Power Series distribution that include, among others, the Negative Binomial, Poisson, Binomial and Logarithmic distributions. It is usual in this context assume the Weibull model for the distribution of the concurrent causes, principally by the mathematical convenience of this distribution. Other approach can be seen in Cancho et al. (2013b), where was used the Birnbaum Saunders distribution for those causes and M with Geometric distribution, proposing the Geometric Birnbaum Saunders model. However, up to this moment, we have not found the use of other distributions in this context. The use of the Pareto IV distribution for the concurrent causes merits investigation since it is a flexible model which includes other popular models as limiting and/or special cases. For this reason, we propose the Power Series Pareto IV cure rate model and study in details the correspondent distribution for the non-cured individuals (that is a proper distribution). Interesting results can be obtained to this model denominated the Power Series Pareto IV. (AU)