The receiver-operating characteristic surface is frequently used for presenting the accuracy of a diagnostic test for three-category classification problems. One common problem that can complicate the estimation of the volume under receiver-operating characteristic surface is that not all subjects receive the verification of the true disease status. Estimation based only on data from subjects with verified disease status may be biased, which is referred to as verification bias. In this article, we propose new verification bias correction methods to estimate the volume under receiver-operating characteristic surface for a continuous diagnostic test. We assume the verification process is missing not at random, which means the missingness might be related to unobserved clinical characteristics. Three classes of estimators are proposed, namely, inverse probability weighted, imputation-based, and doubly robust estimators. A jackknife estimator of variance is derived for all the proposed volume under receiver-operating characteristic surface estimators. The finite sample properties of the new estimators are examined via simulation studies. We illustrate our methods with data collected from Alzheimer’s disease research.
Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface
