Brazilian Journal of Probability and Statistics

The generalized time-dependent logistic frailty model: An application to a population-based prospective study of incident cases of lung cancer diagnosed in Northern Ireland

Eder A. Milani, Vera L. D. Tomazella, Teresa C. M. Dias, and Francisco Louzada

Full-text: Open access

Abstract

Survival models with univariate frailty may be used when there is no information on covariates that are important to explain the failure time. The lack of information may be with respect to covariates that were not observed or even covariates which for some reason we can not measure, for instance, environmental or genetic factors. In this paper, we extend the generalized time-dependent logistic model proposed by Mackenzie (The Statistician 45 (1996) 21–34), by including a frailty term in the modeling. The proposed methodology uses the Laplace transform to find the survival function unconditional on the individual frailty. A simulation study examines the bias, the mean squared errors and the coverage probabilities. Estimation is based on maximum likelihood. A real example on lung cancer illustrates the applicability of the methodology, which is compared to the modeling without frailty via selection criteria to determine which model best fits the data.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 1 (2015), 132-144.

Dates
First available in Project Euclid: 30 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1414674779

Digital Object Identifier
doi:10.1214/13-BJPS232

Mathematical Reviews number (MathSciNet)
MR3299111

Zentralblatt MATH identifier
1329.62432

Keywords
Generalized time-dependent logistic model survival models with univariate frailty non-proportional hazard model

Citation

Milani, Eder A.; Tomazella, Vera L. D.; Dias, Teresa C. M.; Louzada, Francisco. The generalized time-dependent logistic frailty model: An application to a population-based prospective study of incident cases of lung cancer diagnosed in Northern Ireland. Braz. J. Probab. Stat. 29 (2015), no. 1, 132--144. doi:10.1214/13-BJPS232. https://projecteuclid.org/euclid.bjps/1414674779


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