efraction.exact: Exceedance Fraction and Exact Confidence Limits

In STAND: Statistical Analysis of Non-Detects

Description

Calculate estimate of the exceedance fraction FL = Pr [X > L] and exact confidence limits for random sample from normal/lognormal distribution. This function should only be used for complete samples.

Usage

efraction.exact(x, gam = 0.95, L=NA ,logx=TRUE,wpnt=FALSE)

Arguments

x	vector of data values
gam	one-sided confidence level γ. Default is 0.95
L	L is specified limit for the exceedance fraction; e.g., the occupational exposure limit
logx	If TRUE, sample is from lognormal, else normal. Default is TRUE
wpnt	if TRUE, show warning from pnt. Default is FALSE

Details

The exceedance fraction represent the proportion of the X's that exceed a given limit Lp. The null hypothesis of interest is Ho: F ≥ Fo = 1-p; i.e., Fo is the maximum proportion of the population that can exceed the limit Lp. The null hypothesis is rejected if the 100 γ\% UCL for FL is less than Fo , indicating that the exposure profile is acceptable. The type I error rate for this test is less than or equal to α = 1 - γ.

Value

A LIST with components:

f	estimate of exceedance fraction for lognormal distribution as %
fe.LCL	100*γ% exact lower confidence limit % units
fe.UCL	100*γ% exact upper confidence limit % units
L	L is specified limit for the exceedance fraction, e.g. the occupational exposure limit
gam	one-sided confidence level γ. Default is 0.95
Logx	If TRUE, sample is from lognormal, else normal. Default is TRUE

Note

(fe.LCL, fe.UCL) is an approximate 100(2γ -1) percent confidence interval for F. The R function uniroot is used to find the noncentrality parameter of noncentral t distribution to calculate CL's for U = (L - μ) / σ where F = pnorm(U). In some versions of R this may cause a warning message. See R bug report RP 9171 full precision was not achieved in 'pnt'. This warning message may occur in uniroot calls to pt and does not effect the precision of the final result

Author(s)

E. L. Frome

References

Johnson, N. L. and B. L. Welch (1940), "Application of the Non-Central t-Distribution," Biometrika, 31(3/4), 362-389.

Lyles, R. H. and L. L. Kupper (1996), "On strategies for comparing occupational exposure data to limits," American Industrial Hygiene Association Journal. 57:6-15.

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 Assessing and Managing Occupational Exposures, Second Edition, AIHA Press, Fairfax, VA.

See Also

Help files for efraction.ml,efclnp, percentile.exact, efraction.exact, aihand

Examples

# calculate exceedance fraction and exact CLs for Example data
# Appendix  Mulhausen and Damiano(1998) Ignacion and Bullock (2006
data(aihand)
x <- aihand$x ;  det <- rep(1,length(x))
aiha<-data.frame(x,det) #  complete data
unlist(efraction.exact(x,gam=0.95,L=5) ) #  exact CLs
unlist(efraction.ml(aiha,gam=0.95,L=5))  #  ML CLs
unlist(efclnp(aiha,L=5))                 #  nonparametric CLs 

Example output

Loading required package: survival
        fe     fe.LCL     fe.UCL          L        gam       Logx 
 4.2410699  0.8570166 15.2826865  5.0000000  0.9500000  1.0000000 
         f      f.LCL      f.UCL          L        gam 
 3.7227271  0.5937415 14.6450772  5.0000000  0.9500000 
       fnp    fnp.LCL    fnp.UCL          L      gamma 
 6.6666667  0.3413713 27.9396194  5.0000000  0.9500000 

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