# PRACTICAL EXERCISE 9
# ====================

# Read the ami data:
ami=read.table("http://www.uio.no/studier/emner/matnat/math/STK4080/h14/ami.txt",header=T)# We convert time to years and introduce a binary covariate for ascites

# We use the survival library:
library(survival)

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

# We fit additive regression models for one covariate at a time.

# Period
fit.per=aareg(Surv(days,status)~factor(per),data=ami)
par(mfrow=c(1,3))
print(fit.per)
plot(fit.per)

# Sex
fit.sex=aareg(Surv(days,status)~factor(sex), data=ami)
par(mfrow=c(1,2))
print(fit.sex)
plot(fit.sex)

# Previous AMI
fit.prev=aareg(Surv(days,status)~factor(prev), data=ami)
par(mfrow=c(1,2))
print(fit.prev)
plot(fit.prev)

# Age (centered at the mean age of 67.5 years)
ami$cage=ami$age-mean(ami$age)
fit.cage=aareg(Surv(days,status)~cage, data=ami)
par(mfrow=c(1,2))
print(fit.cage)
plot(fit.cage)


# Log10-transformed heart enzym (centered at the mean value of 2.72)
ami$logenzym=log10(ami$enzym)
ami$clogenzym=ami$logenzym-mean(ami$logenzym)
fit.clogenzym=aareg(Surv(days,status)~clogenzym, data=ami)
par(mfrow=c(1,2))
print(fit.clogenzym)
plot(fit.clogenzym)


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

# We then fit a model with all covariates:
fit.all=aareg(Surv(days,status)~factor(per)+factor(sex)+factor(prev)+cage+clogenzym, data=ami)
par(mfrow=c(2,4))
print(fit.all)
plot(fit.all)

# First we remove sex:
fit.all=aareg(Surv(days,status)~factor(per)+factor(prev)+cage+clogenzym, data=ami)
par(mfrow=c(2,3))
print(fit.all)
plot(fit.all)

# Then we remove period:
fit.all=aareg(Surv(days,status)~factor(prev)+cage+clogenzym, data=ami)
par(mfrow=c(2,2))
print(fit.all)
plot(fit.all)

# All remaining covariates are significant, so this is our "final model"