Statistical Analysis of Data with Non-Detectable Values

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Environmental exposure measurements are, in general, positive and may be subject to left censoring, i.e. the measured value is less than a ''limit of detection''. In occupational monitoring, strategies for assessing workplace exposures typically focus on the mean exposure level or the probability that any measurement exceeds a limit. A basic problem of interest in environmental risk assessment is to determine if the mean concentration of an analyte is less than a prescribed action level. Parametric methods, used to determine acceptable levels of exposure, are often based on a two parameter lognormal distribution. The mean exposure level and/or an upper ... continued below

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Frome, E.L. August 26, 2004.

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Description

Environmental exposure measurements are, in general, positive and may be subject to left censoring, i.e. the measured value is less than a ''limit of detection''. In occupational monitoring, strategies for assessing workplace exposures typically focus on the mean exposure level or the probability that any measurement exceeds a limit. A basic problem of interest in environmental risk assessment is to determine if the mean concentration of an analyte is less than a prescribed action level. Parametric methods, used to determine acceptable levels of exposure, are often based on a two parameter lognormal distribution. The mean exposure level and/or an upper percentile (e.g. the 95th percentile) are used to characterize exposure levels, and upper confidence limits are needed to describe the uncertainty in these estimates. In certain situations it is of interest to estimate the probability of observing a future (or ''missed'') value of a lognormal variable. Statistical methods for random samples (without non-detects) from the lognormal distribution are well known for each of these situations. In this report, methods for estimating these quantities based on the maximum likelihood method for randomly left censored lognormal data are described and graphical methods are used to evaluate the lognormal assumption. If the lognormal model is in doubt and an alternative distribution for the exposure profile of a similar exposure group is not available, then nonparametric methods for left censored data are used. The mean exposure level, along with the upper confidence limit, is obtained using the product limit estimate, and the upper confidence limit on the 95th percentile (i.e. the upper tolerance limit) is obtained using a nonparametric approach. All of these methods are well known but computational complexity has limited their use in routine data analysis with left censored data. The recent development of the R environment for statistical data analysis and graphics has greatly enhanced the availability of high quality nonproprietary (open source) software that serves as the basis for implementing the methods in this paper.

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  • Report No.: ORNL/TM-2004/146
  • Grant Number: DE-AC05-00OR22725
  • DOI: 10.2172/861676 | External Link
  • Office of Scientific & Technical Information Report Number: 861676
  • Archival Resource Key: ark:/67531/metadc791926

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Creation Date

  • August 26, 2004

Added to The UNT Digital Library

  • Dec. 19, 2015, 7:14 p.m.

Description Last Updated

  • Dec. 8, 2016, 11:11 p.m.

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Frome, E.L. Statistical Analysis of Data with Non-Detectable Values, report, August 26, 2004; [Tennessee]. (digital.library.unt.edu/ark:/67531/metadc791926/: accessed October 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.