title: Graphical tests for the assumption of gamma and inverse Gaussian frailty distributions.
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.
authors.affiliation: Department of Mathematics, National Technical University of Athens, Greece.
authors.forename: P
authors.initials: P
authors.lastname: Economou
authors.forename: C
authors.initials: C
authors.lastname: Caroni
mesh_terms: D006115:Greece; D006801:Humans; D015993:Life Tables; D016011:Normal Distribution; D016016:Proportional Hazards Models; D013223:Statistics as Topic; D016019:Survival Analysis