A simple frailty model for family studies with covariates.

A simple, easily analysed frailty model based on logistic regression and employing only binary frailties is developed and analysed. Methods for testing for frailty and estimates of frailty parameters and covariate effects are presented. The effects of ignoring or mis-specifying frailty are examined in detail and shown to downwardly bias the estimates of covariate effects in a variety of situations, even when frailty is over-estimated. When the true frailty is large it can be difficult to estimate accurately because of the flatness of the likelihood. However, it is shown that this does not have a large influence on the estimates of the effects of the observed covariates. Methods for dealing with multiple frailties, for example, sibships and spouse pairs, are also developed. The results are illustrated on a large data set examining the risk factors associated with palmar keratoses.