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Abstract:
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Important properties of diagnostic methods are their sensitivity, specificity, and positive and negative predictive values (PPV and NPV). These methods are often assessed via case-control samples, which include one cohort of cases, known to have the disease, and a second control cohort of disease-free subjects. Such studies give direct estimates of sensitivity and specificity, but only indirect estimates of PPV and NPV, which also depend on the disease prevalence in the tested population. We develop formulas for optimal allocation of the sample between the case and control cohorts and for computing sample size when the goal of the study is to prove that the test procedure exceeds pre-stated bounds for PPV and/or NPV for prespecified prevalence range. Surprisingly, the optimal sampling schemes for many purposes are highly unbalanced, even when information is desired on both PPV and NPV.
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