带有检测限的自变量的线性回归。
Linear regression with an independent variable subject to a detection limit.
机构信息
Division of Biometrics IV, Office of Biometrics/OTS/CDER/FDA, Silver Spring, MD, USA.
出版信息
Epidemiology. 2010 Jul;21 Suppl 4(Suppl 4):S17-24. doi: 10.1097/EDE.0b013e3181ce97d8.
BACKGROUND
Linear regression with a left-censored independent variable X due to limit of detection (LOD) was recently considered by 2 groups of researchers: Richardson and Ciampi (Am J Epidemiol. 2003;157:355-363), and Schisterman et al (Am J Epidemiol. 2006;163:374-383).
METHODS
Both groups obtained consistent estimators for the regression slopes by replacing left-censored X with a constant, that is, the expectation of X given X below LOD E(X|X<LOD) in the former group and the sample mean of X given X above LOD in the latter.
RESULTS
Schisterman et al argued that their approach would be a better choice because the sample mean of X given X above LOD is available, whereas E(X|X<LOD) is unknown. Other substitution methods, such as replacing the left-censored values with LOD, or LOD/2,have been extensively used in the literature. Simulations were conducted to compare the performance under 2 scenarios in which the independent variable is normally and not normally distributed.
CONCLUSION
Recommendations are given based on theoretical and simulation results. These recommendations are illustrated with one case study.
背景
由于检测下限 (LOD) 的限制，两组研究人员最近考虑了带有左截断独立变量 X 的线性回归：Richardson 和 Ciampi（Am J Epidemiol. 2003;157:355-363），以及 Schisterman 等人（Am J Epidemiol. 2006;163:374-383）。
方法
两组研究人员都通过用常数替换左截断的 X 来获得回归斜率的一致估计量，即在前者中，LOD 以下 X 的 X 的期望 E(X|X<LOD)，而在后一种情况下，则是 LOD 以上 X 的 X 的样本均值。
结果
Schisterman 等人认为，他们的方法将是更好的选择，因为 LOD 以上 X 的样本均值是可用的，而 E(X|X<LOD)是未知的。其他替代方法，如用 LOD 或 LOD/2 替换左截断值，在文献中已被广泛使用。进行了模拟比较，以比较在独立变量正态和非正态分布的两种情况下的性能。
结论
根据理论和模拟结果给出了建议。通过一个案例研究来说明这些建议。
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