Bivariate Birnbaum-Saunders accelerated lifetime model: estimation and diagnostic analysis

Abstract

In this paper, we discuss the bivariate Birnbaum-Saunders accelerated lifetime model, in which we have modeled the dependence structure of bivariate survival data through the use of frailty models. Specifically, we propose the bivariate model Birnbaum-Saunders with the following frailty distributions: gamma, positive stable and logarithmic series. We present a study of inference and diagnostic analysis for the proposed model, more concisely, are proposed a diagnostic analysis based in local influence and residual analysis to assess the fit model, as well as, to detect influential observations. In this regard, we derived the normal curvatures of local influence under different perturbation schemes and we performed some simulation studies for assessing the potential of residuals to detect misspecification in the systematic component, the presence in the stochastic component of the model and to detect outliers. Finally, we apply the methodology studied to real data set from recurrence in times of infections of 38 kidney patients using a portable dialysis machine, we analyzed these data considering independence within the pairs and using the bivariate Birnbaum-Saunders accelerated lifetime model, so that we could make a comparison and verify the importance of modeling dependence within the times of infection associated with the same patient.

Keywords:

• Dependence
• frailty
• local influence
• residual analysis
• survival data

2010 Mathematics Subject Classifications:

• 62N01
• 62N02
• 62J20

Acknowledgements

This work was supported by FACEPE and CNPq, Brazil. The authors are grateful to the Associate Editor and reviewers for their constructive comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the FACEPE (Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco) [grant number IBPG-0872-1.02/17]; and Conselho Nacional de Desenvolvimento Científico e Tecnológico [grant numbers 310359/2017-1, 302767/2018-5], Brazil.