A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data

Alex Mota (), Eder A. Milani, Jeremias Leão, Pedro L. Ramos, Paulo H. Ferreira, Oilson G. Junior, Vera L. D. Tomazella and Francisco Louzada
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Alex Mota: University of São Paulo
Eder A. Milani: Federal University of Goiás
Jeremias Leão: Federal University of Amazonas
Pedro L. Ramos: Pontificia Universidad Católica de Chile
Paulo H. Ferreira: Federal University of Bahia
Oilson G. Junior: University of São Paulo
Vera L. D. Tomazella: Federal University of São Carlos
Francisco Louzada: University of São Paulo

Statistical Methods & Applications, 2023, vol. 32, issue 3, No 8, 883-909

Abstract: Abstract In this paper, we propose a new cure rate frailty regression model based on a two-parameter weighted Lindley distribution. The weighted Lindley distribution has attractive properties such as flexibility on its probability density function, Laplace transform function on closed-form, among others. An advantage of proposed model is the possibility to jointly model the heterogeneity among patients by their frailties and the presence of a cured fraction of them. To make the model parameters identifiable, we consider a reparameterized version of the weighted Lindley distribution with unit mean as frailty distribution. The proposed model is very flexible in sense that has some traditional cure rate models as special cases. The statistical inference for the model’s parameters is discussed in detail using the maximum likelihood estimation under random right-censoring. Further, we present a Monte Carlo simulation study to verify the maximum likelihood estimators’ behavior assuming different sample sizes and censoring proportions. Finally, the new model describes the lifetime of 22,148 patients with stomach cancer, obtained from the Fundação Oncocentro de São Paulo, Brazil.

Keywords: Cure rate model; Frailty; Maximum likelihood estimation; Randomized residual analysis; Weighted Lindley distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10260-022-00673-y

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