KENDL (version 1.1)

KRKM:

Description

Calculate the exposure distribution based on the kernel reverse Kaplan-Meier(KRKM) estimator proposed by Yang et al. (2017).

Usage

KRKM(obs, bdl, lod, method='formula', b=1000)

Arguments

obs

A vector of observations which are the exposure levels if the subject's exposure level can be detected, and the detection limits otherwise.

bdl

A logical vector indicating TRUE if the subject's exposure level is below the detection limit, and FALSE otherwise.

lod

A vector of detection limits.

method

The method of variance estimation. Either `formula' or `bootstrap' can be used. The default value is `formula'.

b

The number of bootstrap replicates for the bootstrap-based variance estimation method. The default value is 1000.

Value

unique.obs

A vector of unique observations in the argument obs.

cdf

A vector of estimates for the cumulative distribution function (cdf) at the points given by unique.obs.

se

A vector of standard error estimates for the cdf estimates

lower

A vector of 95% lower confidence limits of the cdf values

upper

A vector of 95% upper confidence limits of the cdf values

Details

The KRKM estimator is a nonparametric estimator for the exposure distribution. It is valid regardless of whether the exposure level and detection limit are independent or not. This method requires the data come from simple random sampling and the detection limit is available for each subject. This function provides either formula-based or bootstrap-based variance estimation. The formula-based variance estimation method is computationally faster than the bootstrap-based method, but may underestimate the variance and thus yield poor coverage probabilities at the points below which there are few observations.

References

Yang Y, Shelton BJ, Tucker TC, Li L, Kryscio RJ, Chen L. (2017). Estimation of Exposure Distribution Adjusting for Association between Exposure Level and Detection Limit. Statistics in Medicine. Provisionally Accepted.

See Also

plot.KRKM

Examples

# simulated data set from a lognormal regression model
 lod <- exp(rnorm(200, -2.79, 1.12))
 e   <- rnorm(200, 0 , 1.21 )
 t   <- exp(-3.05+0.42*lod+e)
 obs <- pmax(t, lod)
 bdl <- t<lod
# KRKM estimator 
 fit <- KRKM(obs=obs, bdl=bdl, lod=lod)