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Random effect bivariate survival models and stochastic comparisons

Part of: Applications Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Ramesh C. Gupta  and
Rameshwar D. Gupta
Ramesh C. Gupta*
Affiliation:
University of Maine
Rameshwar D. Gupta*
Affiliation:
University of New Brunswick
*
∗Postal address: Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, USA. Email address: ramesh_gupta@umit.maine.edu
∗∗Postal address: Department of Computer Science and Applied Statistics, University of New Brunswick, Saint John, E2L 4L5, Canada.
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Abstract

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In this paper we propose a general bivariate random effect model with special emphasis on frailty models and environmental effect models, and present some stochastic comparisons. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well-known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

Keywords

Frailty modelenvironmental effect modelhazard gradientbivarate multiplicative modelshared frailty model

MSC classification

Secondary: 62N99: None of the above, but in this section 62P99: None of the above, but in this section 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 426 - 440
Copyright
Copyright © Applied Probability Trust 2010 

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