R-help to Exercise 11 in BSS

 

 

 

# QUESTION a)

 

# Read the data and variable names into a data frame, and take a look at the data

aserum<-read.table("http://www.uio.no/studier/emner/matnat/math/STK4900/v09/annet/serum.dat", header=T)

aserum

 

# Check that the data are the same as given in the table in the exercise

# Make sure that you understand how the data are coded.

 

# Attach the data frame

attach(aserum)

# Plot serum response against time for the different persons (identified by colors) and treatments 

# (identified by solid or dotted line) using the matplot command for multiple lines in a plot.

hours.mat<- matrix(c(1,2,3,6), nrow=4,ncol=10)

druga<-matrix(aserum$serum[drug==1], nrow=4)

drugb<-matrix(aserum$serum[drug==2], nrow=4)

serum.mat<-cbind(druga, drugb)

matplot(hours.mat, serum.mat, type="l", lty=c(1,1,1,1,1,2,2,2,2,2), col=c(1,2,3,4,5,1,2,3,4,5))

# Think about what the plot tells you!

# QUESTION b)

# This is a theoretical question (i.e. a discussion question)

# Here are three possible ways to approach the problem (cf. slides 8-9 & 14) 

# (i) Consider the model y_ijt = a_ij + b_ij * t + e_ijt, 

# where i in 1:5 is the subject number, 

# j in 1:2 is the drug number, and t in c(1,2,3,6) is time.

# Assume a_ij~N(alfa_j, sigma^2) and b_ij~N(beta_j, tau^2). 

# Check if alfa_1=alfa_2 or ?beta_1=beta_2. (Most interesting for the betas.)

# (ii) Same as above, but with ante-dependance:

# y_ijt = a_ij + b_ij * t + c_ij * y_ij,t-1 + e_ijt 

# Assumme again that the coefficients are drawn from the same distribution for each drug, 

# and check if those distributions are equal.

# (iii) Three-way ANOVA, with drug, time and individuals as factors

# QUESTION c)

# Here we consider approach (i) discussed above.

# Give the commands:

druga.coef<-array(NA,c(2,5))

drugb.coef<-array(NA,c(2,5))

hours<-c(1,2,3,6)

for(i in 1:5)

{

? druga.coef[,i]<-lm(druga[,i] ~hours)$coef

 ?drugb.coef[,i]<-lm(drugb[,i] ~hours)$coef

}

druga.coef

drugb.coef

# Make sure you understand the commands and what is computed!

# Make t-tests based on the estimated slopes? for each individual:

t.test(druga.coef[2,], drugb.coef[2,], var.equal=T)

# What you may conclude from this hypothesis testing?

# QUESTION d)

# Here we define? z_it=y_i2t - y_i1t, and consider the model z_it = a + b * t + noise

# Nullhypothesis: a=0 and b=0? (Of most interest: b=0)

# Give the commands:

drug.diff<- druga-drugb

diff.coef<-array(NA,c(2,5))

for(i in 1:5) diff.coef[,i]<-lm(drug.diff[,i]~hours)$coef

t.test(diff.coef[2,])

# Make sure you understand the commands and what is computed!

# What you may conclude from this hypothesis testing?

# QUESTION e)

# We may do a three-way analysis of variance:

mod1<-lm(serum~factor(subject)+factor(time)+factor(drug))

anova(mod1,test="Chi")

# What can you conclude from this anova analysis?

# QUESTION f)

# Summarise your conclusions. 

# Are the analyses consistent when it comes to the assessment of the treatment effect?

# Are there effects of subjects and/or time?