STAND (version 2.0)

IH.summary: Summary Statistic for Samples With Non-detects

Description

Summary statistic described by The American Industrial Hygiene Association (AIHA) for occupational exposure data are calculated for samples with non-detects (aka left censored data). Parametric estimates are based on a lognormal model using maximum likelihood (ML). Nonparametric methods are based on the product limit estimate (PLE) for left censored data.

Usage

IH.summary(dd,L, p = 0.95, gam = 0.95,bcol=NA)

Arguments

dd
An n by 2 matrix or data frame with x (exposure) variable in column 1, and det = 0 for non-detect or 1 for detect in column 2
L
L is specified limit for the exceedance fraction; e.g., the occupational exposure limit
p
p is probability for Xp the 100pth percentile. Default is 0.95
gam
one-sided confidence level $\gamma$. Default is 0.95
bcol
Column number that contains a BY variable. This column must contain a factor and the value of each of the summary statistics is calculated for each level of the factor. Default NA

Value

A data.frame with column names based on levels of the BY variable and row names:
mu
ML estimate of mean of y=log(x)
se.mu
Estimate of standard error of mu
sigma
ML estimate of sigma
se.sigma
Estimate of standard error of sigma
GM
MLE of geometric mean
GSD
MLE of geometric standard deviation
EX
MLE of E(X) the (arithmetic) mean
EX-LCL
Lower Confidence Limit for E(X)
EX-UCL
Upper Confidence Limit for E(X)
KM-mean
Kaplan-Meier(KM) Estimate of E(X)
KM-LCL
KM Lower Confidence Limit for E(X)
KM-UCL
KM Upper Confidence Limit for E(X)
KM-se
Standard Error of KM-mean
obs.Xp
Estimate of Xp from PLE
Xp
ML estimate of Xp the pth percentile
Xp.LCL
MLE of LX(p,gam) the LCL for Xp
Xp.UCL
MLE of UX(p,gam) the UCL for Xp
zL
MLE of the Z value for limit L
NpUTL
Nonparametric estimate of the UTL $p-\gamma$
Maximum
Largest value in the data set
NonDet
percent of X's that are left censored, i.e., non-detects
n
number of observations in the data set
Rsq
Square of correlation for the quantile-quantile (q-q) plot
m
number X's greater than the LOD
f
MLE of exceedance fraction F for limit L
f.LCL
LCf(L,gam) MLE of LCL for F
F.UCL
UCf(L,gam) MLE of UCL for F
fnp
Nonparametric estimate of F for limit L
fnp.LCL
Nonparametric estimate of LCL for F
fnp.UCL
Nonparametric estimate of UCL for F
m2log(L)
-2 times the log-likelihood function
L
L is specified limit for the exceedance fraction; e.g., the occupational exposure limit
p
percentile for UTL p-$\gamma$
gam
one-sided confidence level $\gamma$. Default is 0.95

Details

Regulatory and advisory criteria for evaluating the adequacy of occupational exposure controls are generally expressed as limits that are not to be exceeded in a work shift or shorter time-period if the agent is acutely hazardous. Exposure monitoring results above the limit require minimal interpretation and should trigger immediate corrective action. Demonstrating compliance with a limit is more difficult. AIHA has published a consensus standard with two basic strategies for evaluating an exposure profile---see Mulhausen and Damiano(1998), Ignacio and Bullock (2006). The first approach is based on the mean of the exposure distribution, and the second approach considers the "upper tail" of the exposure profile. Statistical methods for estimating the mean, an upper percentile of the distribution, the exceedance fraction, and the uncertainty in each of these parameters are provided by this package. 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. All of these methods are described in a companion report by Frome and Wambach (2005).

References

Frome, E. L. and Wambach, P. F. (2005), "Statistical Methods and Software for the Analysis of Occupational Exposure Data with Non-Detectable Values," ORNL/TM-2005/52,Oak Ridge National Laboratory, Oak Ridge, TN 37830. Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM2005-52.pdf

Ignacio, J. S. and W. H. Bullock (2006), A Strategy for Assesing and Managing Occupational Exposures, Third Edition, AIHA Press, Fairfax, VA.

Mulhausen, J. R. and J. Damiano (1998), A Strategy for Assesing and Managing Occupational Exposures, Second Edition, AIHA Press, Fairfax, VA.

See complete list of references at About-STAND

See Also

See Also lnorm.ml, efraction.ml, percentile.ml, kmms

Examples

Run this code
# Analysis for cansdata  Example 1 from ORNLTM2005-52
data(cansdata)
Allcans<- round(IH.summary(cansdata,L=0.2,bcol=NA),3)
# Example using cansdata with By variable
cansout <- round(IH.summary(cansdata,L=0.2,bcol=3),3)
#  combine out from both analysis
cbind(Allcans,cansout)

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