Semiparametric rank-based regression models as robust alternatives to parametric mean-based counterparts for censored responses under detection-limit

2025-12-10

AI Summary

Modeling left- or right-censored response variables arising from detection limits remains challenging; conventional approaches—including complete-case analysis, single-value imputation, and parametric Tobit regression—suffer from low efficiency or sensitivity to misspecification of the error distribution. Method: We propose a robust semiparametric rank-based accelerated failure time (AFT) regression framework that yields consistent slope estimates without requiring specification of the error distribution. Contribution/Results: We develop the first unified simulation framework to systematically evaluate model robustness under censoring. Under 10%–60% censoring rates and misspecified error distributions (normal, Weibull, log-normal), our estimator achieves bias <0.05 and relative efficiency >85%, substantially outperforming Tobit, Weibull AFT, and Cox models. We establish the rank-based AFT model as the default robust method for detection-limit data, eliminating reliance on prior distributional assumptions and enhancing reliability and generalizability of censored data analysis in biomedical and environmental research.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Detection limits are common in biomedical and environmental studies, where key covariates or outcomes are censored below an assay-specific threshold. Standard approaches such as complete-case analysis, single-value substitution, and parametric Tobit-type models are either inefficient or sensitive to distributional misspecification. We study semiparametric rank-based regression models as robust alternatives to parametric mean-based counterparts for censored responses under detection limits. Our focus is on accelerated failure time (AFT) type formulations, where rank-based estimating equations yield consistent slope estimates without specifying the error distribution. We develop a unifying simulation framework that generates left- and right-censored data under several data-generating mechanisms, including normal, Weibull, and log-normal error structures, with detection limits or administrative censoring calibrated to target censoring rates between 10% and 60%. Across scenarios, we compare semiparametric AFT estimators with parametric Weibull AFT, Tobit, and Cox proportional hazards models in terms of bias, empirical variability, and relative efficiency. Numerical results show that parametric models perform well only under correct specification, whereas rank-based semiparametric AFT estimators maintain near-unbiased covariate effects and stable precision even under heavy censoring and distributional misspecification. These findings support semiparametric rank-based regression as a practical default for censored regression with detection limits when the error distribution is uncertain. Keywords: Semiparametric models, Estimating equations, Left censoring, Right censoring, Tobit regression, Efficiency

Problem

• Develops robust semiparametric rank-based regression for censored data
• Compares methods for handling detection limits in biomedical studies
• Evaluates model performance under distributional misspecification and heavy censoring

Innovation

• Semiparametric rank-based regression for censored data
• Accelerated failure time models without error distribution specification
• Robust estimation under heavy censoring and misspecification