kmms {STAND}

Kaplan-Meier (KM) Mean and Standard Error

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 \gamma. 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 100\gamma\% UCL is KM.mean + t(\gamma -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 \gamma. 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))