Linear regression with an independent variable subject to a detection limit

• Published in: Epidemiology (Cambridge, Mass.) Vol. 21 Suppl 4; p. S17
• Main Authors: Nie, Lei, Chu, Haitao, Liu, Chenglong, Cole, Stephen R, Vexler, Albert, Schisterman, Enrique F
• Format: Journal Article
• Language: English
• Published: United States 01.07.2010
• Subjects: Computer Simulation; Female; Fertility - physiology; Humans; Likelihood Functions; Limit of Detection; Linear Models; Monte Carlo Method; Normal Distribution; Oxidative Stress - physiology; Sex Hormone-Binding Globulin - metabolism; Statistics, Nonparametric
• ISSN: 1531-5487
• DOI: 10.1097/EDE.0b013e3181ce97d8

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). 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. 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. Recommendations are given based on theoretical and simulation results. These recommendations are illustrated with one case study.