Addressing nonignorable missing data and heterogeneity in prognostic biomarker assessment.

Covariate-specific and time-dependent area-under-curve (AUC) is often used to evaluate the discriminative performance of biomarkers with time-to-event outcomes, particularly when certain covariates influence biomarkers' accuracy. In biomarker research, despite extensive efforts, missing data remain unavoidable, with nonignorable missingness posing significant challenges. This article focuses on estimating the impact of covariates on time-dependent AUC in the presence of nonignorable missing biomarkers. Assuming a parametric model on the missing probability, we leverage instrumental variables to address the identifiable issue and estimate the unknown parameters. We integrate the inverse probability weighting approach into the score equation of a pseudo partial likelihood for estimation and inference. Additionally, we establish the asymptotic properties of the proposed estimators. Through simulation studies, we evaluate finite sample performance of the proposed estimators, and apply the method to data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.