Comparing the predictive values of diagnostic tests: sample size and analysis for paired study designs

Abstract

Although statistical methodology is well developed for comparing diagnostic tests in terms of their sensitivities and specificities, comparative inference about predictive values is not. In this paper we consider the design and analysis of studies comparing the positive and negative predictive values of two diagnostic tests that are measured on all subjects. We focus on comparing tests using the relative positive and negative predictive values. We discuss directly estimating these quantities from the data and derive analytic variance expressions. Sample size formulas for study design ensue. We analyze data on patients with cystic fibrosis to illustrate the methodology. This approach is compared and contrasted with an existing regression framework that can also be used for similar analysis purposes and yields similar results. We have developed a new approach for comparing the predictive values of two tests that gives rise to sample size formulas for study design.