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A Comparison of the ?-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 ?-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 ?-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 ?-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 ?-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 ?-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.

SUBMITTER: Huynh T

PROVIDER: S-EPMC4715251 | biostudies-literature | 2016 Jan

REPOSITORIES: biostudies-literature

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A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data.

Huynh Tran T Quick Harrison H Ramachandran Gurumurthy G Banerjee Sudipto S Stenzel Mark M Sandler Dale P DP Engel Lawrence S LS Kwok Richard K RK Blair Aaron A Stewart Patricia A PA

The Annals of occupational hygiene 20150724 1

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 mix ...[more]

PMID: 26209598

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Project description:The National Institute for Environmental Health Sciences (NIEHS) is conducting an epidemiologic study (GuLF STUDY) to investigate the health of the workers and volunteers who participated from April to December of 2010 in the response and cleanup of the oil release after the Deepwater Horizon explosion in the Gulf of Mexico. The exposure assessment component of the study involves analyzing thousands of personal monitoring measurements that were collected during this effort. A substantial portion of these data has values reported by the analytic laboratories to be below the limits of detection (LOD). A simulation study was conducted to evaluate three established methods for analyzing data with censored observations to estimate the arithmetic mean (AM), geometric mean (GM), geometric standard deviation (GSD), and the 95th percentile (X0.95) of the exposure distribution: the maximum likelihood (ML) estimation, the β-substitution, and the Kaplan-Meier (K-M) methods. Each method was challenged with computer-generated exposure datasets drawn from lognormal and mixed lognormal distributions with sample sizes (N) varying from 5 to 100, GSDs ranging from 2 to 5, and censoring levels ranging from 10 to 90%, with single and multiple LODs. Using relative bias and relative root mean squared error (rMSE) as the evaluation metrics, the β-substitution method generally performed as well or better than the ML and K-M methods in most simulated lognormal and mixed lognormal distribution conditions. The ML method was suitable for large sample sizes (N ≥ 30) up to 80% censoring for lognormal distributions with small variability (GSD = 2-3). The K-M method generally provided accurate estimates of the AM when the censoring was <50% for lognormal and mixed distributions. The accuracy and precision of all methods decreased under high variability (GSD = 4 and 5) and small to moderate sample sizes (N < 20) but the β-substitution was still the best of the three methods. When using the ML method, practitioners are cautioned to be aware of different ways of estimating the AM as they could lead to biased interpretation. A limitation of the β-substitution method is the absence of a confidence interval for the estimate. More research is needed to develop methods that could improve the estimation accuracy for small sample sizes and high percent censored data and also provide uncertainty intervals.

Dataset Information

A Comparison of the ?-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data.

Publications

A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data.

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