case1102 {Sleuth3}

The Blood–Brain Barrier

Description

The human brain is protected from bacteria and toxins, which course through the blood–stream, by a single layer of cells called the blood–brain barrier. These data come from an experiment (on rats, which possess a similar barrier) to study a method of disrupting the barrier by infusing a solution of concentrated sugars.

Usage

case1102

Format

A data frame with 34 observations on the following 9 variables.

Brain

Brain tumor count (per gm)

Liver

Liver count (per gm)

Time

Sacrifice time (in hours)

Treatment

Treatment received

Days

Days post inoculation

Sex

Sex of the rat

Weight

Initial weight (in grams)

Loss

Weight loss (in grams)

Tumor

Tumor weight (in 10^{-4} grams)

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

See Also

ex1416, ex1417

Examples

str(case1102)
attach(case1102)

## EXPLORATION
logRatio <- log(Brain/Liver)
logTime <- log(Time)
myMatrix <- cbind (logRatio, Days, Weight, Loss, Tumor, logTime)
if(require(car)){   # Use the car library
scatterplotMatrix(myMatrix,groups=Treatment,
  smooth=FALSE, diagonal="histogram", col=c("green","blue"), pch=c(16,17), cex=1.5)
}
 
myLm1 <- lm(logRatio ~ Treatment + logTime + Days + Sex + Weight + Loss + Tumor)
plot(myLm1, which=1)          
if(require(car)){   # Use the car library
  crPlots(myLm1) # Draw partial resdual plots. 
}                              

myLm2   <-  lm(logRatio ~ Treatment + factor(Time) + 
  Days + Sex + Weight + Loss + Tumor)  # Include Time as a factor.
anova(myLm1,myLm2)
if(require(car)){   # Use the car library
  crPlots(myLm2) # Draw partial resdual plots. 
}    

summary(myLm2)  # Use backard elimination 
myLm3 <- update(myLm2, ~ . - Days)   
summary(myLm3)  
myLm4 <- update(myLm3, ~ . - Sex)          
summary(myLm4)
myLm5 <- update(myLm4, ~ . - Weight)
summary(myLm5)
myLm6 <- update(myLm5, ~ . - Tumor)
summary(myLm6)                             
myLm7 <- update(myLm6, ~ . - Loss)
summary(myLm7)   # Final model for inference


## INFERENCE AND INTERPRETATION
myTreatment <- factor(Treatment,levels=c("NS","BD")) # Change level ordering 
myLm7a  <- lm(logRatio ~  factor(Time) + myTreatment)
summary(myLm7a) 
beta <- myLm7a$coef
exp(beta[5])         
exp(confint(myLm7a,5))
# Interpetation: The median ratio of brain to liver tumor counts for barrier-
# disrupted rats is estimated to be 2.2 times the median ratio for control rats 
# (95% CI: 1.5 times to 3.2 times as large). 

## DISPLAY FOR PRESENTATION 
ratio <- Brain/Liver
jTime <- exp(jitter(logTime,.2)) # Back-transform a jittered version of logTime
plot(ratio ~ jTime, log="xy",
  xlab="Sacrifice Time (Hours), jittered; Log Scale",
  ylab="Effectiveness: Brain Tumor Count Relative To Liver Tumor Count; Log Scale",
  main="Blood Brain Barrier Disruption Effectiveness in 34 Rats", 
  pch= ifelse(Treatment=="BD",21,24), bg=ifelse(Treatment=="BD","green","orange"),
  lwd=2, cex=2)
dummyTime     <- c(0.5, 3, 24, 72)
controlTerm   <- beta[1] + beta[2]*(dummyTime==3) + 
  beta[3]*(dummyTime==24) + beta[4]*(dummyTime==72)
controlCurve  <- exp(controlTerm)
lines(controlCurve ~ dummyTime, lty=1,lwd=2)
BDTerm        <- controlTerm + beta[5]
BDCurve       <- exp(BDTerm)
lines(BDCurve ~ dummyTime,lty=2,lwd=2)
legend(0.5,10,c("Barrier disruption","Saline control"),pch=c(21,22),
  pt.bg=c("green","orange"),pt.lwd=c(2,2),pt.cex=c(2,2), lty=c(2,1),lwd=c(2,2))

detach(case1102)