Product Limit Estimate for Non-detects Using Kaplan-Meier

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Description

Compute Product Limit Estimate (PLE) of F(x) and Confidence Limits for data with non-detects (left censored data).

Usage

1
plekm(dd,gam)

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

gam

one-sided confidence level γ. Default is 0.95

Details

R function survreg is used to calculate Kaplan-Meier 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% two-sided CLs are calculated.

Value

Data frame with columns

a

is the value of jth detect (ordered)

ple

is PLE of F(x) at a

stder

standard error of F(x) at a

lower

lower CL for PLE at a

upper

upper CL for PLE at a

n

number of detects or non-detects a

d

number of detects equal to a

Note

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.

Author(s)

E. L. Frome

References

Nelson, W.(1972), "Theory and Application of Hazard Plotting for Censored Failure Data", Technometrics, 14, 945-66

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

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, 81-97.

See Also

plend, pleicf

Examples

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data(SESdata) ## use SESdata data set Example 1 from ORNLTM-2005/52
pkm<- plekm(SESdata)
qq.lnorm(pkm) #  lognormal q-q plot based on PLE
round(pkm,3)

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