Limitations of relative sensitivity in detecting differential misclassification in case-control studies.

Apparent relative sensitivity, based on an investigator's external standard, is the ratio of observed case to control exposure sensitivity. An apparent relative sensitivity different from 1.0 is usually interpreted as evidence for differential misclassification of exposure status. We undertook this investigation to determine the conditions under which an apparent relative sensitivity exceeding 1.0 is actually due to differential misclassification. We also consider whether apparent relative sensitivity correctly quantifies the degree of differential misclassification. To achieve these goals, we derived an algebraic relation involving apparent relative sensitivity, true sensitivities and specificities, true odds ratio, an index of how well the external standard classifies true exposure, and the incidence of the disease among the nonexposed. We found that an apparent relative sensitivity greater than 1.0 correctly indicates differential misclassification when either (1) the investigator's external standard classifies true exposure perfectly, or (2) the investigator's external standard is imperfect, but the true odds ratio equals 1.0, true relative sensitivity is greater than 1.0, and true relative specificity is less than 1.0. We also found that apparent relative sensitivity greater than 1.0 falsely suggests differential misclassification when true relative sensitivity equals 1.0, the investigator's external standard is imperfect, and the true odds ratio is greater than 1.0. Furthermore, even when apparent relative sensitivity correctly detects the presence of differential misclassification, it may misrepresent the degree.