# Improving estimation of the volume under the ROC surface when data are missing not at random

## TL;DR

This paper introduces a new method for accurately estimating the volume under the ROC surface in diagnostic tests with missing data that are not at random, using a mean score equation approach and instrumental variables.

## Contribution

It proposes a novel verification bias correction method for VUS estimation under nonignorable missingness, incorporating instrumental variables and a parametric verification model.

## Key findings

- The new estimators are consistent and asymptotically normal.
- Simulation studies show improved finite sample performance.
- Application to ovarian cancer data demonstrates practical utility.

## Abstract

In this paper, we propose a mean score equation-based approach to estimate the the volume under the receiving operating characteristic (ROC) surface (VUS) of a diagnostic test, under nonignorable (NI) verification bias. The proposed approach involves a parametric regression model for the verification process, which accommodates for possible NI missingness in the disease status of sample subjects, and may use instrumental variables, which help avoid possible identifiability problems. In order to solve the mean score equation derived by the chosen verification model, we preliminarily need to estimate the parameters of a model for the disease process, but its specification is required only for verified subjects under study. Then, by using the estimated verification and disease probabilities, we obtain four verification bias-corrected VUS estimators, which are alternative to those recently proposed by To Duc et al. (2019), based on a full likelihood approach. Consistency and asymptotic normality of the new estimators are established. Simulation experiments are conducted to evaluate their finite sample performances, and an application to a dataset from a research on epithelial ovarian cancer is presented.