Analysis of secondary failure time responses in studies with response-dependent sampling schemes

Response-dependent sampling is routinely used as an enrichment strategy in the design of family studies investigating the heritable nature of disease. In addition to the response of primary interest, investigators often wish to investigate the association between biomarkers and secondary responses related to possible comorbidities. Statistical analysis regarding genetic biomarkers and their association with the secondary outcome must address the biased sampling scheme involving the primary response. In this article, we develop composite likelihoods and two-stage estimation procedures for such secondary analyses in which the within-family dependence structure for the primary and secondary outcomes is modeled via a Gaussian copula. The dependence among responses within family members is modeled based on kinship coefficients. Auxiliary data from independent individuals are exploited by augmenting the composite likelihoods to increase precision of marginal parameter estimates and enhance the efficiency of estimators of the dependence parameters. Simulation studies are carried out to evaluate the finite sample performance of the proposed method, and an application to a motivating family study in psoriatic arthritis is given for illustration.