Weighted Lindley frailty model: estimation and application to lung cancer data

Alex Mota (), Eder A. Milani, Vinicius F. Calsavara, Vera L. D. Tomazella, Jeremias Leão, Pedro L. Ramos, Paulo H. Ferreira and Francisco Louzada
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Alex Mota: University of São Paulo
Eder A. Milani: Federal University of Goiás
Vinicius F. Calsavara: A.C.Camargo Cancer Center
Vera L. D. Tomazella: Federal University of São Carlos
Jeremias Leão: Federal University of Amazonas
Pedro L. Ramos: Pontificia Universidad Católica de Chile
Paulo H. Ferreira: Federal University of Bahia
Francisco Louzada: University of São Paulo

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2021, vol. 27, issue 4, No 2, 587 pages

Abstract: Abstract In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of São Paulo, Brazil.

Keywords: Lung cancer; Maximum likelihood method; Unobserved heterogeneity; Weighted Lindley distribution. (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10985-021-09529-1

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