MODELING HAZARD FUNCTIONS IN FAMILIES

A genetic frailty model is presented for censored age of onset data in nuclear families where individuals carrying a genetic susceptibility gene have an increased risk of becoming affected. We use maximum likel ihood via the EM algorithm to estimate the genetic relative risk and t he allele frequency under a dominant susceptibility type and a proport ional hazards model. When sampling is from a disease registry, likelih ood corrections are necessary for reducing bias in the parameter estim ates. In these biased samples, the full conditional likelihood is appr oximated by a Likelihood conditional on the proband's age of onset. Fo r unbiased samples, simulations show the distributions of the estimate s are similar under both a semiparametric and the correctly specified parametric likelihoods. For biased samples, simulations under the appr oximate conditional likelihood show the median estimates of the allele frequency and genetic relative risk tend to under-and overestimate, r espectively, the true values; however, the approximation is better for rarer allele frequencies (0.0033 vs. 0.01). In practice, large sample s or more complex ascertainment corrections are recommended. Using the approximate conditional likelihood on familial breast cancer onset da ta collected as part of a case-control study at the Fred Kutchinson Ca ncer Research Center in Seattle, Washington, we estimate an allele fre quency of 0.0009 (approximate 95% CI 0.0006-0.002) and a genetic relat ive risk of 104 (approximate 95% CI 55-181). (C) 1998 Wiley-Liss, Inc.