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We suggest a clear distinction between the accuracy measures of the detection of a disease in a screening setting in populations, using data on persons with and without known disease status, vs. accuracy measures of diagnosis in a clinical setting in individuals when the disease status is unknown. In the first situation, a researcher is conducting a study in which the prevalence of the disease is artificial: it is determined by the researcher based on the number of persons with and without the disease who are included in the study. For example, if in a study one examines the sensitivity and specificity of a test in 100 persons with a disease (for example, AIDS) and 100 persons without the disease, the prevalence of AIDS in this particular study is 50%, which is of course far from the true prevalence of AIDS. The sensitivity and specificity are used to describe the technical characteristics of a test, i.e., how many persons with a disease or without a disease will be detected correctly by a test in a population with known diagnoses. These measures are important in public health and health planning. For example, one might need to know the percentage of sick persons (the sensitivity) or healthy persons (the specificity) that will be detected among travelers at an airport and thus plan preventive measures in times of a communicable disease epidemic. The second situation is a clinical setting when the diagnoses are as yet unknown and the test is used to diagnose the disease in individuals: the positive predictive value (PPV) and the negative predictive value (NPV) are an estimate of the accuracy of the test, i.e., of the fractions of patients who are diagnosed correctly as positive or negative, respectively. Let us explain the need to use two different approaches for the two distinct situations described above, with specific analogous notations (italic lowercase and uppercase) and the derived equations.
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Grunau et al. (2018) studied this question.
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