title: Linear regression with an independent variable subject to a detection limit.
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.
  
  
  CONCLUSIONS
  Recommendations are given based on theoretical and simulation results. These recommendations are illustrated with one case study.
authors.affiliation: Division of Biometrics IV, Office of Biometrics/OTS/CDER/FDA, Silver Spring, MD, USA. lei.nie@fda.hhs.gov
authors.forename: Lei
authors.initials: L
authors.lastname: Nie
authors.forename: Haitao
authors.initials: H
authors.lastname: Chu
authors.forename: Chenglong
authors.initials: C
authors.lastname: Liu
authors.forename: Stephen R
authors.initials: SR
authors.lastname: Cole
authors.forename: Albert
authors.initials: A
authors.lastname: Vexler
authors.forename: Enrique F
authors.initials: EF
authors.lastname: Schisterman
mesh_terms: D003198:Computer Simulation; D005260:Female; D005298:Fertility / Q000502:physiology; D006801:Humans; D016013:Likelihood Functions; D057230:Limit of Detection; D016014:Linear Models; D009010:Monte Carlo Method; D016011:Normal Distribution; D018384:Oxidative Stress / Q000502:physiology; D012738:Sex Hormone-Binding Globulin / Q000378:metabolism; D018709:Statistics, Nonparametric
chemical_list: D012738:Sex Hormone-Binding Globulin