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

1
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 γ. 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

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).

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-γ

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-γ

gam

one-sided confidence level γ. Default is 0.95

Author(s)

E. L. Frome

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

1
2
3
4
5
6
7
# 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)

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker.