
Frailty Models with Applications in Linkage Analysis
Benilton de Sá Carvalho^{a}, Hildete P. Pinheiro^{b}
and Mariza de Andrade^{c}
^{a} Department of
Biostatistics, University of Johns Hopkins, USA
^{b} Departamento de
Estatística, UNICAMP  SP, Brazil
^{c} Division of
Biostatistics, Mayo Clinic Rochester, MN, USA
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 KuhnTucker 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.
