Efficient nonparametric estimators of discrimination measures with censored survival data

TL;DR

This paper introduces efficient nonparametric estimators for discrimination measures like AUC and concordance index in censored survival data, addressing bias and model misspecification issues.

Contribution

It proposes debiased, data-adaptive estimators for discrimination measures that do not require correct censoring model specification, improving accuracy in survival analysis.

Findings

Estimators outperform existing methods in simulations.

Proposed methods are robust to censoring model misspecification.

Application to brain cancer data demonstrates practical utility.

Abstract

Discrimination measures such as the concordance index and the cumulative-dynamic time-dependent area under the ROC-curve (AUC) are widely used in the medical literature for evaluating the predictive accuracy of a scoring rule which relates a set of prognostic markers to the risk of experiencing a particular event. Often the scoring rule being evaluated in terms of discriminatory ability is the linear predictor of a survival regression model such as the Cox proportional hazards model. This has the undesirable feature that the scoring rule depends on the censoring distribution when the model is misspecified. In this work we focus on linear scoring rules where the coefficient vector is a nonparametric estimand defined in the setting where there is no censoring. We propose so-called debiased estimators of the aforementioned discrimination measures for this class of scoring rules. The proposed estimators make efficient use of the data and minimize bias by allowing for the use of data-adaptive methods for model fitting. Moreover, the estimators do not rely on correct specification of the censoring model to produce consistent estimation. We compare the estimators to existing methods in a simulation study, and we illustrate the method by an application to a brain cancer study.