The logistic modeling of sensitivity, specificity, and predictive value of a diagnostic test

Abstract

A method is described for modeling the sensitivity, specificity, and positive and negative predictive values of a diagnostic test. To model sensitivity and specificity, the dependent variable (Y) is defined to be the dichotomous results of the screening test, and the presence or absence of disease, as defined by the "gold standard", is included as a binary explanatory variable (X1), along with variables used to define the subgroups of interest. The sensitivity of the screening test may then be estimated using logistic regression procedures. Modeled estimates of the specificity and predictive values of the screening test may be similarly derived. Using data from a population-based study of peripheral arterial disease, the authors demonstrated empirically that this method may be useful for obtaining smoothed estimates of sensitivity, specificity, and predictive values. As an extension of this method, an approach to the modeling of the relative sensitivity of two screening tests is described, using data from a study of screening procedures for colorectal disease as an example.