Confidence intervals for predictive values with an emphasis to case–control studies

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 accuracy of the test and the prevalence of the disease, constructing their confidence intervals for a particular patient is not straightforward. In this paper, a novel method for the estimation of PPV and NPV, as well as their confidence intervals, is developed. For both predictive values, 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 case-control studies: a diagnostic test assessing the ability of the e4 allele of the apolipoprotein E gene (ApoE.e4) on distinguishing patients with late-onset Alzheimer's disease (AD) and a prognostic test assessing the predictive ability of a 70-gene signature on breast cancer metastasis.