title: A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data.
abstract: Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the β-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X0.95) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the β-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the β-substitution method, but use of more informative priors generally improved the Bayesian method's performance, making both the bias and the rMSE more comparable to the β-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the β-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications.
authors.affiliation: Division of Environmental Health Sciences, University of Minnesota, Minneapolis, MN 55455, USA;
authors.forename: Tran
authors.initials: T
authors.lastname: Huynh
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA;
authors.forename: Harrison
authors.initials: H
authors.lastname: Quick
authors.affiliation: Division of Environmental Health Sciences, University of Minnesota, Minneapolis, MN 55455, USA; ramac002@umn.edu.
authors.forename: Gurumurthy
authors.initials: G
authors.lastname: Ramachandran
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA;
authors.forename: Sudipto
authors.initials: S
authors.lastname: Banerjee
authors.affiliation: Exposure Assessment Applications, LLC, Arlington, VA 22207, USA;
authors.forename: Mark
authors.initials: M
authors.lastname: Stenzel
authors.affiliation: Epidemiology Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, USA;
authors.forename: Dale P
authors.initials: DP
authors.lastname: Sandler
authors.affiliation: Epidemiology Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, USA; Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA;
authors.forename: Lawrence S
authors.initials: LS
authors.lastname: Engel
authors.affiliation: Epidemiology Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, USA;
authors.forename: Richard K
authors.initials: RK
authors.lastname: Kwok
authors.affiliation: National Cancer Institute, Gaithersburg, MD 20892, USA;
authors.forename: Aaron
authors.initials: A
authors.lastname: Blair
authors.affiliation: Stewart Exposure Assessments, LLC, Arlington, VA 22207, USA.
authors.forename: Patricia A
authors.initials: PA
authors.lastname: Stewart
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D006801:Humans; D057230:Limit of Detection; D015233:Models, Statistical; D016273:Occupational Exposure / Q000032:analysis / Q000706:statistics & numerical data*; D016272:Occupational Health; D018570:Risk Assessment / Q000379:methods; D018401:Sample Size
keywords: Bayesian; exposure assessment; left-censored data; β-substitution