The accuracy of a binary-scale diagnostic test can be represented by sensitivity (Se), specificity (Sp) and positive and negative predictive values (PPV and NPV). Although Se and Sp measure the intrinsic accuracy of a diagnostic test that does not depend on the prevalence rate, they do not provide information on the diagnostic accuracy of a particular patient. To obtain this information we need to use PPV and NPV. Since PPV and NPV are functions of both the intrinsic accuracy and the prevalence of the disease, constructing confidence intervals for PPV and NPV for a particular patient in a population with a given prevalence of disease using data from a case-control study is not straightforward. In this paper, a novel method for the estimation of PPV and NPV is developed using estimates of sensitivity and specificity in a case-control study. For PPV and NPV, standard, adjusted and their logit transformed based confidence intervals are compared using coverage probabilities and interval lengths in a simulation study. These methods are then applied to two examples: a diagnostic test assessing the ability of the ApoE4 allele on distinguishing patients with late-onset Alzheimer's disease and a prognostic test assessing the predictive ability of a 70-gene signature on breast cancer metastasis.
Statistical Methodology | Statistical Theory
Mercaldo, Nathaniel David; Zhou, Xiao-Hua; and Lau, Kit F., "Confidence Intervals for Predictive Values Using Data from a Case Control Study" (December 2005). UW Biostatistics Working Paper Series. Working Paper 271.