Multivariate logistic regression for familial aggregation in age at disease onset

Familial aggregation studies seek to identify diseases that cluster in families. These studies are often carried out as a first step in the search for hereditary factors affecting the risk of disease. It is necessary to account for age at disease onset to avoid potential misclassification of family members who are disease-free at the time of study participation or who die before developing disease. This is especially true for late-onset diseases, such as prostate cancer or Alzheimer's disease. We propose a discrete time model that accounts for the age at disease onset and allows the familial association to vary with age and to be modified by covariates, such as pedigree relationship. The parameters of the model have interpretations as conditional log-odds and log-odds ratios, which can be viewed as discrete time conditional cross hazard ratios. These interpretations are appealing for cancer risk assessment. Properties of this model are explored in simulation studies, and the method is applied to a large family study of cancer conducted by the National Cancer Institute-sponsored Cancer Genetics Network (CGN).