Frailty Models with Applications in Linkage Analysis

The paper presents the Frailty Model using the hazard function in a logistic form. The model developed here is a survival analysis method which aggregates linkage analysis role. The model structure is based on a Cox model extension. The hazard function has a parametric form, the logistic one (Mackenzie, 1996). The censure is defined using the current age and the age at onset , thus if one has the age at onset greater than the current age, then a censured observation is characterized. The additive frailties are constructed from a gamma densities and it incorporates genetic and environmental contributions on the trait of interest.The use of these techniques in a unified way has been shown to be efficient, once the age at onset is usually collected in genetic mapping studies, moreover it is shown to be associated to complex diseases. Then,this is a useful model, which is able to be applied to Cox model situations and genetic mapping cases. The model is adjusted by maximization of retrospective likelihood (Whittemore, 1996), using an iterative algorithm based on the Kuhn-Tucker equations. The proposed model is ascertained by the analysis of simulated data created using G.A.S.P. package and by comparisons with the results from the joint analysis with SAS and GeneHunter softwares.