kmms: Kaplan-Meier (KM) Mean and Standard Error

In STAND: Statistical Analysis of Non-Detects

Description

Kaplan- Meier Estimate of Mean and Standard Error of the Mean for Left Censored Data

Usage

kmms(dd, gam = 0.95)

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

The product limit estimate (PLE) of the cumulative distribution function was first proposed by Kaplan and Meier (1958) for right censored data. Turnbull (1976) provides a more general treatment of nonparametric estimation of the distribution function for arbitrary censoring. For randomly left censored data, the PLE is defined by Schmoyer et al. (1996)–see plend.

The mean of the PLE is a censoring-adjusted point estimate of E(X) the mean of X. An approximate standard error of the PLE mean can be obtained using the method of Kaplan and Meier (1958), and the 100γ\% UCL is KM.mean + t(γ -1, m-1) sp, where sp is the Kaplan-Meier standard error of the mean adjusted by the factor m/(m-1), where m is the number of detects in the sample. When there is no censoring this reduces to the second approximate method described by Land (1972).

Value

A LIST with components:

KM.mean	Kaplan- Meier(KM) estimate of mean E(X)
KM.LCL	KM estimate of lower confidence limit
KM.UCL	KM estimate of upper confidence limit
KM.se	estimate of standard error of KM-mean
gamma	one-sided confidence level γ. Default 0.95

Note

Error in KM.se corrected on 12 June 2007. KM standard error is adjusted by multiplying by sqrt(m/(m-1)) where m is number of detected values. Error occurred if there were ties in detected values by calculating the number of unique detected values. For example, for beTWA sqrt(m/(m-1)) is 1.004796 . Due to error 1.008032 was used. The sqrt(m/(m-1)) will always be smaller after correction, depending on value of m and the number of ties. See the example.

Author(s)

E. L. Frome

References

Kaplan, E. L. and Meier, P. (1958), "Nonparametric Estimation from Incomplete Observations," Journal of the American Statistical Association, 457-481.

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, plekm

Examples

# results for beTWA data using kmms in stand Ver 1.1 with error
#    KM.mean      KM.LCL      KM.UCL       KM.se       gamma 
# 0.018626709 0.014085780 0.023167637 0.002720092 0.950000000
#
data(beTWA) # Use data from Example 2 in ORNLTM2002-51
unlist(kmms(beTWA))

Example output

Loading required package: survival
    KM.mean      KM.LCL      KM.UCL       KM.se       gamma 
0.018626709 0.014126267 0.023127150 0.002711702 0.950000000 

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