# R-commands for additve regression
# =================================

# For illustration we will use the melanoma data 


# We first read the data:
melanoma=read.table("http://www.uio.no/studier/emner/matnat/math/STK4080/h12/melanoma.txt",header=T)


# We use the survival library, so this has to be loaded.


# We first estimate the marginal effect sex:
fit.sex=aareg(Surv(lifetime,status==1)~factor(sex),data=melanoma)
par(mfrow=c(1,2))
plot(fit.sex)

# Here the estimated cumulative baseline equals the Nelson-Aalen estimate for females
# while the estimated cumulative regression function for sex equals the difference 
# between the Nelson-Aalen estimates for males and females (exercise 4.4)


# We will also look at the marginal effect tumor thickness. 
# First we center the thickness values by subtracting their means
# (since that will make the cumulative baseline more meaningful)
melanoma$cthick=melanoma$thickn-mean(melanoma$thickn)
fit.thick=aareg(Surv(lifetime,status==1)~cthick,data=melanoma)
par(mfrow=c(1,2))
plot(fit.thick)

# Here the cumulative baseline corresponds to the hazard for an individual with mean tumor thickness (=2.92 mm),
# while the cumulative regression function shows the effect of 1 med mer increase in tumor thickness.
# We see that there is a clear effect of thickness the first 5 years or so, but not later on.


# Finally we fit a model with sex, ulceration anf thickness (centered)
fit.all=aareg(Surv(lifetime,status==1)~factor(sex)+factor(ulcer)+cthick,data=melanoma)
par(mfrow=c(2,2))
plot(fit.all)

# Here the cumulative baseline corresponds to the cumulative hazard of a female with ulceration and mean tumor thickness (=2.92 mm).
# The other cumulative regression functions show 
#   - the effect of being a male (compared to a female),
#   - of not having ulcetation (compared to having it)
#   - of 1 mm increase of tumor thickness


# To test the if the covariates have an effect, we give the command:
print(fit.all)

# The TST test statistic (cf top of page 165 in the ABG-book) is given in the second last column 
# of the out put, with the corresponding p-value in the last column 
# (we only consider the last two columns of the output)

# We see that ulcetarion is higly significant, that thickness is significant (p-value 2.9%), 
# and that sex is not significant (p-value 12.1%)