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We view this as a two\u2010phase study and propose the use of an efficient selection model for the recruitment of families to form a phase II sample subject to budgetary constraints. Simple random sampling, balanced sampling and use of an approximately optimal selection model are considered where the latter is chosen to minimize the variance of parameters of interest. We consider the setting where family members provide current status data with respect to the disease and use copula models to address within\u2010family dependence. The efficiency gains from the use of an optimal selection model over simple random sampling and balanced sampling schemes are investigated as is the robustness of optimal sampling to model misspecification. 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