Linear Regression With an Independent Variable Subject to a Detection Limit
- 1 July 2010
- journal article
- research article
- Published by Ovid Technologies (Wolters Kluwer Health) in Epidemiology
- Vol. 21 (4), S17-S24
- https://doi.org/10.1097/ede.0b013e3181ce97d8
Abstract
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.Keywords
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