Semiparametric estimation of major gene and family-specific random effects for age of onset.

Analysis of familial diseases with variable age of onset is a common problem in human genetics. Most existing methods make some parametric distributional assumption on age of onset, and few methods have been designed with the goal of testing the hypothesis of a Mendelian gene against other hypotheses of familial dependence. We introduce the Cox model with major genetic and random familial effects to model age-of-onset dependence patterns among family members and to incorporate family heterogeneity. This model allows testing for and estimating major gene effects in the presence of residual correlations. Generalized maximum likelihood estimation using a Monte Carlo EM algorithm is used for parameter estimation. The methods are illustrated by a simulated data set and a data set from a case-control family study of breast cancer.