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

Abstract

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 [nDP] and disease-negative patients [nDN] from the apparent number of disease-positive and disease-negative patients (anDP and anDN), and the Se and Sp of the RS (SeR, SpR): nDP = (anDP × SpR + anDN × SpR − anDN)/JR; nDN = (anDP × SeR + anDN × SeR − anDP)/JR, where JR is Youden’s Index for the RS (JR = SeR + SpR − 1). The following derived formulas give the correct Se and Sp of an investigational test (SeI and SpI): SeI = (anTPI × SpR − nDP × SeR × SpR + nDP × JR + nDN × SpR2 − nDN × SpR − SpR × anTNI + anTNI)/(nDP × JR); SpI = (anTPI − anTPI × SeR + nDP × SeR2 − nDP × SeR − SeR × nDN × SpR + nDN × JR + SeR × anTNI)/(nDN × JR), where anTPI is the apparent number of true-positive test results, and anTNI 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.