Correcting Diagnostic Test Sensitivity and Specificity for Patient Misclassifications Resulting from Use of an Imperfect Reference Standard

Investigational diagnostic tests are validated by using a reference standard (RS). If the RS is imperfect (i.e., it has sensitivity [Se] and/or specificity [Sp] < 1), incorrect values for the investigational test’s Se and Sp may result because of patient misclassification by the RS. Formulas were derived to correct a test’s Se and Sp that were determined by using an imperfect RS. The following derived formulas correct for misclassification and give the true numbers of disease-positive [n(DP)] and disease-negative patients [n(DN)] from the apparent number of disease-positive and disease-negative patients (an(DP) and an(DN)), and the Se and Sp of the RS (Se(R), Sp(R)): n(DP) = (an(DP) × Sp(R) + an(DN) × Sp(R) − an(DN))/J(R); n(DN) = (an(DP) × Se(R) + an(DN) × Se(R) − an(DP))/J(R), where J(R) is Youden’s Index for the RS (J(R) = Se(R) + Sp(R) − 1). The following derived formulas give the correct Se and Sp of an investigational test (Se(I) and Sp(I)): Se(I) = (an(TPI) × Sp(R) − n(DP) × Se(R) × Sp(R) + n(DP) × J(R) + n(DN) × Sp(R)(2) − n(DN) × Sp(R) − Sp(R) × an(TNI) + an(TNI))/(n(DP) × J(R)); Sp(I) = (an(TPI) − an(TPI) × Se(R) + n(DP) × Se(R)(2) − n(DP) × Se(R) − Se(R) × n(DN) × Sp(R) + n(DN) × J(R) + Se(R) × an(TNI))/(n(DN) × J(R)), where an(TPI) is the apparent number of true-positive test results, and an(TNI) is the apparent number of true-negative test results. The derived formulas correct for patient misclassification by an imperfect RS and give the correct values of a diagnostic test’s Se and Sp.