Assess predictive values of a binary diagnostic test under a nested case-control design

Predictive values of a binary diagnostic test are often evaluated under a random sample design. When the disease is rare, however, such a design might not be as efficient as a nested case-control design where the cases are oversampled from a large existing cohort. Under a nested case-control design, direct proportion estimators of predictive values are biased because cases are oversampled. Consistent estimates of predictive values can be easily obtained by inverse probability weighting (IPW) method. The only difficulty with these IPW estimators has been the absence of expressions for their variances. To fill this gap, in the current paper, we obtain the asymptotic variance formulas for the IPW estimators of predictive values. Unlike their counterparts from weighted logistic regression, our variance formulas take into account the variance of the estimated weights in the IPW estimators of predictive values. We further use the proposed variance formulas to examine the gain in efficiency under a nested case-control design compared with a simple random sampling design. Our results clearly show that when the disease is rare, a nested case-control design can achieve a substantial amount of variance reduction by oversampling cases, compared with a random sample design. Finally, we compare via simulation the accuracy of the proposed variance formulas with the existing methods and illustrate the proposed method by a real data example evaluating the accuracy of D-dimer test.