# PRACTICAL EXERCISE 10
# =====================

# Read data:
path="http://www.uio.no/studier/emner/matnat/math/STK4080/h14/lungcancer.txt"
lungcancer=read.table(path,header=T)


# Question a
# ----------

# Compute number of lung cancer cases and person years aggregated over cities:
lung.aggr=aggregate(lungcancer,list(age.group=lungcancer$age),sum)
cancer.cases=lung.aggr$cancer
pyears=4*lung.aggr$population


# Question b
# ----------

# Compute the lung cancer rates and their standard errors: 
occexp=cancer.cases/pyears
occexp.se=occexp/sqrt(cancer.cases)
?
# Plot lung rates per 1000 person-years with 95% standard confidence limits:
plot(c(47.5,57.5,62.5,67.5,72.5), 1000*occexp,type='l', ylim=c(0,6), xlim=c(45,75),  
        xlab="Age",ylab="Lung cancer rates per 1000")
lines(c(47.5,57.5,62.5,67.5,72.5), 1000*(occexp-1.96*occexp.se), lty=2)
lines(c(47.5,57.5,62.5,67.5,72.5), 1000*(occexp+1.96*occexp.se), lty=2)


# Question c
# ----------

# Add 95% log-transformed confidence limits:
lines(c(47.5,57.5,62.5,67.5,72.5), 1000*occexp*exp(-1.96/sqrt(cancer.cases)), lty=2,col='red')
lines(c(47.5,57.5,62.5,67.5,72.5), 1000*occexp*exp(1.96/sqrt(cancer.cases)), lty=2,col='red')