# PRACTICAL EXERCISE 11
# =====================

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


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

# Use the glm-command to compute the logarithm of the occurrence/exposure rates:
fit.age=glm(cancer~offset(log(4*population))+factor(age)-1, family=poisson, data=lungcancer)
summary(fit.age)


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

# Read a function that computes the exponentials of the coefficients 
# from a glm-fit with corresponding confidence intervals:

expcoef=function(glmobj)
{ 
regtab=summary(glmobj)$coef 
expcoef=exp(regtab[,1]) 
lower=expcoef*exp(-1.96*regtab[,2]) 
upper=expcoef*exp(1.96*regtab[,2]) 
cbind(expcoef,lower,upper)
}

# Compute occurrence/exposure rates with log-transformed confidence limits: 
expcoef(fit.age)


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

# Fit a model with age and city:
fit.age.city=glm(cancer~offset(log(4*population))+factor(age)+factor(city)-1, family=poisson, data=lungcancer)
summary(fit.age.city)
expcoef(fit.age.city)


# Question d
# ----------

# Test if there is an effect of city:
anova(fit.age,fit.age.city,test="Chisq")