Graphical Tests for the Assumption of Gamma and Inverse Gaussian Frailty Distributions

Authors: Economou, P.¹; Caroni, C.²

Source: Lifetime Data Analysis, Volume 11, Number 4, December 2005 , pp. 565-582(18)

Publisher: Springer

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Abstract:

The common choices of frailty distribution in lifetime data models include the Gamma and Inverse Gaussian distributions. We present diagnostic plots for these distributions when frailty operates in a proportional hazards framework. Firstly, we present plots based on the form of the unconditional survival function when the baseline hazard is assumed to be Weibull. Secondly, we base a plot on a closure property that applies for any baseline hazard, namely, that the frailty distribution among survivors at time t has the same form as the original distribution, with the same shape parameter but different scale parameter. We estimate the shape parameter at different values of t and examine whether it is constant, that is, whether plotted values form a straight line parallel to the time axis. We provide simulation results assuming Weibull baseline hazard and an example to illustrate the methods.

Keywords: frailty; proportional hazards; diagnostic plots; Generalized Inverse Gaussian; Burr

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10985-005-5240-0

Affiliations: 1: Department of Mathematics, National Technical University of Athens, Greece, 2: Department of Mathematics, National Technical University of Athens, Greece, Email: ccaroni@central.ntua.gr

Publication date: 2005-12-01