Stochastic comparisons in frailty models
Classes of distributions, Frailty among survivors, Hazard rate, Heterogeneity, Stochastic orderings
Journal of Statistical Planning and Inference
The frailty model in survival analysis accounts for unobserved heterogeneity between individuals by assuming that the hazard rate of an individual is the product of an individual specific quantity, called "frailty" and a baseline hazard rate. It is well known that the choice of the frailty distribution strongly affects the nonparametric estimate of the baseline hazard as well as that of the conditional probabilities. This paper reviews the basic concepts of a frailty model, presents various probability inequalities and other monotonicity results which may prove useful in choosing among alternative specifications. More specifically, our main result lies in seeing how well known stochastic orderings between distributions of two frailities translate into orderings between the corresponding survival functions. Some probabilistic aspects and implications of the models resulting from competing choices of the distributions of frailty or the baseline are compared. © 2005 Elsevier B.V. All rights reserved.
Original Publication Date
DOI of published version
Gupta, Ramesh C. and Kirmani, S. N.U.A., "Stochastic comparisons in frailty models" (2006). Faculty Publications. 2758.