Estimating sensitivity and specificity from positive predictive value, negative predictive value and prevalence: application to surveillance systems for hospital-acquired infections

Sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) are terms usually associated with diagnostic testing. Although these concepts have been expanded from diagnostic assays to surveillance systems, these systems are not like diagnostic assays. In attempting to estimate the sensitivity and specificity of surveillance systems, situations may arise where only the PPV, NPV and prevalence are known. We aim to demonstrate the equivalence of two methods for calculating sensitivity and specificity from PPV, NPV and prevalence. The formulae for sensitivity and specificity are calculated from first principles and compared with the adjustment of a standard contingency table. We have illustrated this method using a review of a sample of surgical site infection cases following coronary artery bypass grafting. The derived prevalence from the sample is an estimate of the population prevalence and is the value that must be used in the formulae for sensitivity and specificity as functions of PPV, NPV and prevalence to obtain the same estimates as those obtained from the adjusted contingency table. The general proof of this principle is provided as an Appendix. The sensitivity and specificity of surveillance systems can be calculated by two equivalent methods when only PPV, NPV and prevalence are known.