bootstrap (version 2015.2)

patch: The Patch Data

Description

Eight subjects wore medical patches designed to infuse a naturally-occuring hormone into the blood stream.

Usage

data(patch)

Format

A data frame with 8 observations on the following 6 variables.

subject

a numeric vector

placebo

a numeric vector

oldpatch

a numeric vector

newpatch

a numeric vector

z

a numeric vector, oldpatch - placebo

y

a numeric vector, newpatch - oldpatch

Source

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

Details

Eight subjects wore medical patches designed to infuse a certain naturally-occuring hormone into the blood stream. Each subject had his blood levels of the hormone measured after wearing three different patches: a placebo patch, an "old" patch manufactured at an older plant, and a "new" patch manufactured at a newly opened plant.

The purpose of the study was to show bioequivalence. Patchs from the old plant was already approved for sale by the FDA (food and drug administration). Patches from the new facility would not need a full new approval, if they could be shown bioequivalent to the patches from the old plant.

Bioequivalence was defined as $$\frac{|E(\text{new})-E(\text{old})|}{E(\text{old})-E(\text{placebo})}\le .20$$

The book uses this to investigate bias of ratio estimation.

Examples

str(patch) 
 theta <- function(ind){
      Y <- patch[ind,"y"]
      Z <- patch[ind,"z"]
      mean(Y)/mean(Z) }
patch.boot <- bootstrap(1:8, 2000, theta)
names(patch.boot)          
hist(patch.boot$thetastar)
abline(v=c(-0.2, 0.2), col="red2")
theta(1:8) #sample plug-in estimator
abline(v=theta(1:8) , col="blue")
# The bootstrap bias estimate:
mean(patch.boot$thetastar) - theta(1:8)
sd(patch.boot$thetastar) # bootstrapped standard error