A frailty approach for modelling diseases with variable age of onset in families: The NHBLI Family Heart Study

We use frailty models to analyse the effect of latent genetic and environmental risk factors on hazard functions in nuclear families. The approach expresses latent risk factors (frailties) as functions of the effects of a single major gene and shared familial risk. The latter may result from shared polygenes and/or a common environment. Genetic frailties are modelled using a two-point distribution, and residual frailities (shared environment, polygenes) using a gamma distribution. The two-point distribution follows the laws of Mendelian transmission, under either dominant or recessive gene action. We describe a robust EM approach for the joint estimation of the magnitude of genetic, covariate, gene by covariate interaction effects while allowing residual familiar correlation. We illustrate the method on coronary heart disease data from the National Heart, Lung, and Blood Institute Family Heart Study. In addition, a simulation study shows that ignoring possible residual correlation in disease status due to a shared familial environment leads to an overestimate of the relative risk associated with a latent genotype.