On sample size for sensitivity and specificity in prospective diagnostic accuracy studies

The design of a study of disease screening tests may be based on hypothesis tests for the sensitivity and specificity of the tests. The case-control study requires knowledge of the disease status of patients at the time of enrollment. This may not be possible in a prospective setting, when the gold standard is obtained subsequent to the initial screening and the number of diseased individuals is random and can not be fixed by design. Several ad hoc procedures for determining the total sample size are commonly used by practitioners, for example, the prevalence inflation method. The properties of these methods are not well understood. We develop a formal method for sample size and power calculations based on the unconditional power properties of the test statistics. The approach provides novel insights into the behaviour of the commonly used methods. We find that the ad hoc prevalence inflation method may serve as a useful approximation to our rigorous framework for sample size determination in the prospective set-up. The design of a large population-based study of mammography for breast cancer screening illustrates the key issues.