Augmented composite likelihood for copula modeling in family studies under biased sampling

Abstract

The heritability of chronic diseases can be effectively studied by examining the nature and extent of within-family associations in disease onset times. Families are typically accrued through a biased sampling scheme in which affected individuals are identified and sampled along with their relatives who may provide right-censored or current status data on their disease onset times. We develop likelihood and composite likelihood methods for modeling the within-family association in these times through copula models in which dependencies are characterized by Kendall's \tau . Auxiliary data from independent individuals are exploited by augmentating composite likelihoods to increase precision of marginal parameter estimates and consequently increase efficiency in dependence parameter estimation. An application to a motivating family study in psoriatic arthritis illustrates the method and provides some evidence of excessive paternal transmission of risk.