# Exponentiated Weibull Models Applied to Medical Data in Presence of Right-censoring, Cure Fraction and Covariates

• Edson Zangiacomi Martinez Universidade de Sao Paulo, Brazil
• Bruno Caparroz Lopes de Freitas State University of Maringa, Master Program in Biostatistics, Maringa, Brazil
• Jorge Alberto Achcar Ribeirao Preto Medical School, University of Sao Paulo (USP), Ribeirao Preto, Brazil
• Davi Casale Aragon Ribeirao Preto Medical School, University of Sao Paulo (USP), Ribeirao Preto, Brazil
• Marcos Vinicius de Oliveira Peres Ribeirao Preto Medical School, University of Sao Paulo (USP), Ribeirao Preto, Brazil
Keywords: Weibull distribution, Survival analysis, Cure fraction, Censored data

### Abstract

Cure fraction models have been widely used to analyze survival data in which a proportion of the individuals isnot susceptible to the event of interest. This article considers frequentist and Bayesian methods to estimate the unknown model parameters of the exponentiated Weibull (EW) distribution considering right-censored survival data with a cure fraction and covariates. The EW distribution is as an extension to the Weibull distribution by considering an additional shape parameter to the model. We consider four types of cure fraction models: the mixture cure fraction (MCF), the nonmixture cure fraction (NMCF), the complementary promotion time cure (CPTC), and the cure rate proportional odds (CRPO) models. Bayesian inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods. A simulation study was conducted to examine the performance of the maximum likelihood estimators for different sample sizes. Two real datasets were considered to illustrate the applicability of the proposed model. The EW distribution and its sub-models have the flexibility to accommodate different shapes for the hazard function and should be an attractive choice for survival data analysis when a cure fraction is present.

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Published
2021-11-29
How to Cite
Martinez, E. Z., Lopes de Freitas, B. C., Achcar, J. A., Aragon, D. C., & Peres, M. V. de O. (2021). Exponentiated Weibull Models Applied to Medical Data in Presence of Right-censoring, Cure Fraction and Covariates. Statistics, Optimization & Information Computing, 10(2), 548-571. https://doi.org/10.19139/soic-2310-5070-1266
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Research Articles