Smith et al.1 compared the performance of a fecal immunochemical test (FIT) for hemoglobin to a sensitive, guaiac-based fecal occult blood test (GFOBT) in a large cohort of average-risk adults and found that the FIT was more sensitive for cancers and significant adenomas. They report that “…the FIT returned a true-positive result…in cancer…[of] 87.5%.” Readers should not mistake this result for the true sensitivity in the usual sense: the proportion of all patients with cancer who have a positive test.
The study by Smith et al was conducted in such a way that true sensitivity is necessarily overestimated and easily can approach 100%. Almost all participants in this study underwent colonoscopy only if 1 of the 2 fecal occult blood tests was positive. Patients with cancer who had negative tests—which would have been counted as false-negative results, causing lower sensitivity—systematically were excluded. This problem, known as diagnostic work-up bias,2 would have been avoided only by performing colonoscopy on all members of the cohort, regardless of the test results.3
The extent to which the reported “true-positive rate” may have overestimated true sensitivity is illustrated by the following example: The literature suggests that no more than half of colorectal cancers bleed at a given point in time. If so, then at least 48 of the 2512 study participants would have had cancer, not just the 24 that were diagnosed because they bled, causing 1 or both of the tests to be positive. The true sensitivity for FIT then would have been 21 of 48 (43.8%), and not the 21 of 24 (87.5%) reported. Taking into account statistical uncertainty (the 95% confidence interval), sensitivity would have been in the 29% to 58% range. The “true positive rate” used for comparing 2 tests within a study like the one by Smith et al1 is not a valid estimate of true sensitivity for comparison with the sensitivities of other tests reported in the literature.