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

In STAND: Statistical Analysis of 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 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

# 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)

Example output

Loading required package: survival
         cansdata       A       B
mu         -5.001  -4.653  -5.186
se.mu       0.224   0.303   0.291
sigma       1.763   1.868   1.401
se.sigma    0.203   0.276   0.258
GM          0.007   0.010   0.006
GSD         5.827   6.478   4.060
EX          0.032   0.055   0.015
EX.LCL      0.019   0.025   0.009
EX.UCL      0.052   0.120   0.024
KM.mean     0.034   0.051   0.018
KM.LCL      0.018   0.019   0.013
KM.UCL      0.051   0.083   0.023
KM.se       0.010   0.019   0.003
Xp.obs      0.105   0.158   0.047
Xp          0.122   0.206   0.056
Xp.LCL      0.077   0.102   0.032
Xp.UCL      0.195   0.415   0.097
NpUTL       0.195   1.120   0.149
Maximum     1.120   1.120   0.149
NonDet%    59.200  51.700  66.700
n         120.000  60.000  60.000
Rsq         0.974   0.965   0.956
m          49.000  29.000  20.000
f           2.717   5.165   0.534
f.LCL       1.283   2.268   0.072
f.UCL       5.296  10.443   2.756
fnp         0.833   1.667   0.000
fnp.LCL     0.043   0.085   0.000
fnp.UCL     3.892   7.664   4.870
m2logL    -43.189 -17.915 -32.115
L           0.200   0.200   0.200
p           0.950   0.950   0.950
gamma       0.950   0.950   0.950

STAND documentation built on May 2, 2019, 3:39 p.m.