Environmental exposure measurements are, in general, positive and may be subject to left censoring; i.e., the measured value is less than a "detection limit", and is referred to as a non-detect or "less than" value. This package calculates the censored data equivalent of a number of statistics that are used in the analysis of environmental data that do not contain non-detects, i.e. the usual complete data case.
|License:||GPL version 2 or newer|
In occupational monitoring, strategies for assessing workplace exposures typically focus on the mean exposure level or the probability that any measurement exceeds a limit. Parametric methods used to determine acceptable levels of exposure are based on a two parameter lognormal distribution. The mean exposure level, an upper percentile, the exceedance fraction, and confidence limits for each of these statistics are calculated. Statistical methods for random samples (without non-detects) from the lognormal distribution are well known for each of these situations–see e.g., Lyles and Kupper (1996). In this package the maximum likelihood method for randomly left censored lognormal data is used to calculate these statistics, and graphical methods are provided to evaluate the lognormal assumption. Nonparametric methods based on the product limit estimate for left censored data are used to estimate the mean exposure level, and the upper confidence limit on an upper percentile (i.e., the upper tolerance limit) is obtained using a nonparametric approach.
The American Industrial Hygiene Association (AIHA) has published a
consensus standard with two basic strategies for evaluating an
exposure profile—see Mulhausen and Damiano(1998), Ignacio and
Bullock (2006). Most of the AIHA methods are based on the assumptions
that the exposure data does not contain non-detects, and that a
lognormal distribution can be used to describe the data. Exposure
monitoring results from a compliant workplace tend to contain a high
percentage of non-detected results when the detection limit is close
to the exposure limit, and in some situations, the lognormal
assumption may not be reasonable. The function
IH.summary calculates most of the statistics proposed by
AIHA for exposure data with non-detects. All of the methods are
described in the report Frome and Wambach (2005).
This work was supported in part by the Office of Health, Safety, and Security of the U. S. Department of Energy and was performed in the Computer Science and Mathematics Division (CSMD) at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725. Additional funding and oversight have been provided through the Occupational Exposure and Worker Studies Group, Oak Ridge Institute for Science and Education, which is managed by Oak Ridge Associated Universities under Contract No. DE-AC05-060R23100.
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
The work has been authored by a contractor of the U.S. Government. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this work, or to allow others to do so for U. S. Government purposes.
Throughout this document and the online help files the greek letter γ is used to represent the confidence level for a one-sided confidence limit (default value 0.95). This is represented by
gamma in the argument list and value of functions that compute confidence limits.
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# Example 1 from Frome and Wambach (2005) ORNL/TM-2005/52 # NOTE THAT FUNCTIONS NAMES AND DETAILS HAVE BEEN REVISED IN THIS PACKAGE # the results are the same. For example lnorm.ml() replaces mlndln(). data(SESdata) mle<-lnorm.ml(SESdata) unlist(mle[1:4]) # ML estimates mu sigma E(X) and sigma^2 unlist(mle[5:8]) # ML Estimates of standard errors unlist(mle[9:13]) # additional output from ORNL/TM-2005/52 IH.summary(SESdata,L=0.2) # All sumarry statistics for SESdata # lognormal q-q plot for SESdata Figure in ORNL/TM-2005/52 qq.lnorm(plend(SESdata),mle$mu,mle$sigma) title("SESdata: Smelter-Elevated Surfaces")
Loading required package: survival mu sigma logEX Sigmasq -2.290764 1.276000 -1.476678 1.628180 se.mu se.sigma se.logEX se.Sigmasq 0.2311395 0.1754489 0.3137301 0.4477474 cov.musig m n m2log(L) convergence -0.002005525 28.000000000 31.000000000 -12.852885390 0.000000000 SESdata mu -2.2907643 se.mu 0.2311395 sigma 1.2760000 se.sigma 0.1754489 GM 0.1011891 GSD 3.5822818 EX 0.2283952 EX.LCL 0.1338480 EX.UCL 0.3897286 KM.mean 0.2030645 KM.LCL 0.1254281 KM.UCL 0.2807009 KM.se 0.0455803 Xp.obs 0.6502500 Xp 0.8253637 Xp.LCL 0.4464973 Xp.UCL 1.5257099 NpUTL NA Maximum 1.1400000 NonDet% 9.7000000 n 31.0000000 Rsq 0.9830338 m 28.0000000 f 29.6686380 f.LCL 19.4593597 f.UCL 41.8076231 fnp 29.0322581 fnp.LCL 16.0611091 fnp.UCL 45.1904417 m2logL -12.8528854 L 0.2000000 p 0.9500000 gamma 0.9500000
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