Estimating genetic parameters of survival distributions: a multifactorial model.

For a number of genetically influenced illnesses, age of onset is correlated between relatives. In some cases, age of onset also serves as an index of an individual's inherited liability to an illness. Typically, survival models for age of onset distributions do not allow for these effects. We have used the gamma distribution as the basis of a model which specifies genetic variability in age of onset. Specifically, we allow the hazard frequency parameter of the gamma distribution to be a monotonic function of an individual's inherited liability to an illness. Simulations under various gamma models indicate that age of onset correlations may be strikingly different from correlations in liability. Maximum likelihood estimation procedures were used to obtain parameter estimates from simulated data sets and to determine whether it is possible to discriminate between gamma processes of different order. The results of 1,000 pairs of twins (500 monozygotic and 500 dizygotic) gave parameter estimates that were fairly accurate but that decreased in precision as the order of the gamma process increased. We discuss the effect this may have on inferences made about age of onset.