Marshall–Olkin frailty survival models for bivariate right-censored failure time data

ABSTRACT

The aim of this paper is to explore multivariate survival techniques for the analysis of bivariate right-censoring failure time data. In particular, a new family of parametric bivariate frailty models is investigated. To take into account the correlation between two survival times, the Marshall–Olkin Bivariate Exponential Distribution (MOBVE) is exploited to model the joint distribution of two frailties. The reason is twofold: on the one hand, it allows one to model shocks that affect individual-specific frailties; on the other hand, the parameter underlying the Poisson process characterizing the common shock is used to capture the dependence between two lifetimes. The proposed methodology is applied to the investigation of association in death on different-sex couples followed within the Cache County Study on Memory Health and Aging (CCSMHA). A cure rate extension of the model is also described.

KEYWORDS:

• Frailty models
• Marshall–Olkin distribution
• cache county study
• survival analysis

Acknowledgements

The authors are very grateful to Dr. Maria Norton for having shared the Cache County Study in Memory Health and Aging data, and to the two anonymous Referees whose comments have greatly improved the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.