Comparing disease screening tests when true disease status is ascertained only for screen positives

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Abstract
Disease screening is a fundamental part of health care. To evaluate the accuracy of a new screening modality, ideally the results of the screening test are compared with those of a definitive diagnostic test in a set of study subjects. However, definitive diagnostic tests are often invasive and cannot be applied to subjects whose screening tests are negative for disease. For example, in cancer screening, the assessment of true disease status requires a biopsy sample, which for ethical reasons can only be obtained if a subject's screening test indicates presence of cancer. Although the absolute accuracy of screening tests cannot be evaluated in such circumstances, it is possible to compare the accuracies of screening tests. Specifically, using relative true positive rate (the ratio of the true positive rate of one test to another) and relative false positive rate (the ratio of the false positive rates of two tests) as measures of relative accuracy, we show that inference about relative accuracy can be made from such studies. Analogies with case‐control studies can be drawn where inference about absolute risk cannot be made, but inference about relative risk can. In this paper, we develop a marginal regression analysis framework for making inference about relative accuracy when only screen positives are followed for true disease. In this context factors influencing the relative accuracies of tests can be evaluated. It is important to determine such factors in order to understand circumstances in which one test is preferable to another. The methods are applied to two cancer screening studies, one concerning the effect of race on screening for prostate cancer and the other concerning the effect of tumour grade on the detection of cervical cancer with cytology versus cervicography screening.

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