Editor—We would like to draw attention to two points, which Deeks in his review article simplified.1-1
Firstly, consider an example to illustrate the futility of what might be called the “reflex to fill the fourfold table” in research into diagnostic accuracy. Consider a study on an experimental test that claims to give clinicians more certainty in situations where they have only a few indications that disease may be present. But let us assume that the indications are not strong enough to justify the performance of truly invasive tests. Without the new experimental test these patients would be sent home. The value of the new test lies in its ability to identify those patients who have the disease and would benefit from treatment. In this scenario, the analysis of only those patients who test positively on the experimental test (two cells filled of the fourfold table) suffices to learn about its usefulness.
Secondly, Deeks ends his explanation of the application of the likelihood ratio by saying that knowledge of other characteristics of a particular patient that either increase or decrease their prior probability of endometrial cancer can be incorporated into the calculation by adjusting the pretest probability accordingly. This, however, assumes constancy of likelihood ratios, which should not be assumed because it is usually incorrect. In practice, the knowledge of other patient characteristics will have an influence on the magnitude of the likelihood ratios of following tests. This is so because when a chain of diagnostic tests (history taking, physical exam, lab tests, or imaging) is performed on a patient, certain results from his or her clinical history make the likelihood to find certain lab results more (or less) likely. This in turn influences the chances of finding certain imaging results. In other words, the results of the component tests are not mutually independent. For example, on average, women with a positive test on ultrasound (thickened endometrium) are more likely to test positively on hysteroscopy, in which the endometrial thickness is also assessed, albeit in a different manner.
The theoretical solution to this problem is the calculation of likelihood ratios that are conditional on the results of the preceding tests in the diagnostic test chain. In practice, this is usually not feasible owing to lack of data, and most investigators use logistic regression models to account for all these dependencies. These models, however, yield diagnostic odds ratios, not likelihood ratios. It is partly this complexity that hampers the application of simple diagnostic accuracy studies to clinical practice. In figure 2 the numerators in the second column of the right hand panel represent the number of false positives, not the true negatives.
References
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1-1.Deeks JJ. Systematic reviews of evaluations of diagnostic and screening tests. BMJ. 2001;323:157–162. doi: 10.1136/bmj.323.7305.157. . (21 July.) [DOI] [PMC free article] [PubMed] [Google Scholar]
