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

翻译：检测限在生物医学和环境研究中十分常见，其中关键协变量或结果变量在低于特定检测阈值时被删失。标准方法如完整案例分析、单值替代以及参数化Tobit型模型要么效率低下，要么对分布误设敏感。本文研究半参数秩回归模型作为检测限下删失响应参数化均值模型的稳健替代方法。我们聚焦于加速失效时间（AFT）型设定，其中基于秩的估计方程可在不指定误差分布的情况下得到一致的斜率估计。我们开发了一个统一的模拟框架，在多种数据生成机制（包括正态、威布尔和对数正态误差结构）下生成左删失和右删失数据，并通过检测限或管理性删失校准目标删失率在10%至60%之间。在不同场景中，我们从偏差、经验变异性和相对效率方面比较了半参数AFT估计量与参数化威布尔AFT、Tobit以及Cox比例风险模型。数值结果表明，参数化模型仅在正确设定下表现良好，而基于秩的半参数AFT估计量即使在重度删失和分布误设下仍能保持接近无偏的协变量效应和稳定的精度。这些发现支持将半参数秩回归作为误差分布不确定时检测限下删失回归的实用默认方法。关键词：半参数模型，估计方程，左删失，右删失，Tobit回归，效率