Environmental toxicology studies often involve sample values that fall below a laboratory procedure's limit of quantification. Such left-censored data give rise to several problems for regression analyses. First, both covariates and outcome may be left censored. Second, the transformed toxicant levels may not be normal but mixtures of normals because of differences in personal characteristics, e.g. exposure history and demographic factors. Third, the outcome and covariates may be linear functions of left-censored variates, such as averages and differences. Fourth, some toxicant levels may be functions of other toxicant levels resulting in a recursive system. In this paper marginal and pseudo-likelihood based methods are proposed for estimation of the means and covariance matrix of variates found in these four settings. Next, linear regression methods are developed allowing outcomes and covariates to be linear combinations of left-censored measures. This is extended to a recursive system of modeling equations. Bootstrap standard errors and confidence intervals are used. Simulation studies demonstrate the proposed methods are accurate for a wide range of study designs and left-censoring probabilities. The proposed methods are illustrated through the analysis of an on-going community-based study of polychlorinated biphenyls, which motivated the proposed methodology.

中文翻译：

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使用伪似然方法使用左删失协变量和结果的线性回归

环境毒理学研究通常涉及低于实验室程序量化限制的样本值。这种左删失数据给回归分析带来了几个问题。首先，协变量和结果都可以进行左删失。其次，由于个人特征（例如接触史和人口统计因素）的差异，转化后的毒物水平可能不是正常值，而是正常值的混合。第三，结果和协变量可以是左删失变量的线性函数，例如平均值和差异。第四，一些毒物水平可能是导致递归系统的其他毒物水平的函数。在本文中，提出了基于边际和伪似然的方法来估计在这四种设置中发现的变量的均值和协方差矩阵。下一个，开发了线性回归方法，允许结果和协变量是左删失度量的线性组合。这被扩展到建模方程的递归系统。使用 Bootstrap 标准误差和置信区间。模拟研究表明，所提出的方法对于广泛的研究设计和左删失概率是准确的。通过对一项正在进行的基于社区的多氯联苯研究的分析来说明所提议的方法，该研究推动了所提议的方法。模拟研究表明，所提出的方法对于广泛的研究设计和左删失概率是准确的。通过对一项正在进行的基于社区的多氯联苯研究的分析来说明所提议的方法，该研究推动了所提议的方法。模拟研究表明，所提出的方法对于广泛的研究设计和左删失概率是准确的。通过对一项正在进行的基于社区的多氯联苯研究的分析来说明所提议的方法，该研究推动了所提议的方法。