Analyze paired case-control data prospectively in comparing two predictive values

Various test statistics have been proposed for comparing the predictive values of two binary diagnostic tests. However, these existing test statistic were derived based on a paired random sample where both diagnostic tests are administered on each subject in a random sample. It is not immediately clear whether or not they can be applied to a paired case-control sample where both diagnostic tests are administered on each subject in a case-control sample. In this paper, we propose a Wald test statistic and a weighted generalized score test statistic for comparing two predictive values based on a paired case-control sample and show that both test statistics can be calculated by applying their respective counterparts based on the paired random sample as if the paired case-control sample were a paired random sample. We further derive an optimal case-control ratio and demonstrate that when the disease is rare, the paired case-control sampling design with optimal case-control allocation achieves a substantial variance reduction, compared with a paired random sampling design.