Compute Product Limit Estimate (PLE) of F(x) and Confidence Limits for data with nondetects (left censored data).
1  plekm(dd,gam)

dd 
An n by 2 matrix or data frame with 
gam 
onesided confidence level γ. Default is 0.95 
R function survreg
is used to calculate KaplanMeier estimate
of S(z), where z = k  x and k is greater than the largest x value.
This technique of "reversing the data" to convert left censored data
to right censored data was first suggested by Nelson (1972). conf.type
= "plain" is required in survreg for correct CLs. The value of S(z)
is then used to calculate F(x). Note that if γ = 0.95 the 90%
twosided CLs are calculated.
Data frame with columns
a 
is the value of jth detect (ordered) 
ple 
is PLE of F(x) at 
stder 
standard error of F(x) at 
lower 
lower CL for PLE at 
upper 
upper CL for PLE at 
n 
number of detects or nondetects ≤ 
d 
number of detects equal to 
In survival analysis S(x) = 1  F(x) is the survival function i.e., S(x) = P [X > x]. In environmental and occupational situations S(x) is the "exceedance" function, i.e., S(x) = is the proportion of X values that exceed x. The PLE is the sample estimate of F(x), i.e., the proportion of values in the sample that are less than x.
E. L. Frome
Nelson, W.(1972), "Theory and Application of Hazard Plotting for Censored Failure Data", Technometrics, 14, 94566
Frome, E. L. and Wambach, P.F. (2005) "Statistical Methods and Software for the Analysis of Occupational Exposure Data with NonDetectable Values", ORNL/TM2005/52,Oak Ridge National Laboratory, Oak Ridge, TN 37830. Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM200552.pdf
Schmoyer, R. L., J. J. Beauchamp, C. C. Brandt and F. O. Hoffman, Jr. (1996), "Difficulties with the Lognormal Model in Mean Estimation and Testing," Environmental and Ecological Statistics, 3, 8197.
plend
, pleicf
1 2 3 4 
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