# PRACTICAL EXERCISE 2
# ====================

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

# The survival library must be loaded

# Kaplan-Meier estimates and summary for for all patients:
fit.mel0=survfit(Surv(lifetime,status==1)~1,data=melanoma,conf.type="plain")
plot(fit.mel0, mark.time=F, xlab="Years after operation")
summary(fit.mel0)

 
# Question a
# ----------
# We compute Kaplan-Meier estimates for females and males with standard confidence intervals:
fit.sex=survfit(Surv(lifetime,status==1)~sex,data=melanoma,conf.type="plain")

# We then make a plot of the estimates:
plot(fit.sex, mark.time=F, xlab="Years after operation",lty=1:2)
legend("bottomleft",c("females","males"),lty=1:2)

# We may use the summary command to obtain the estimated survival with confidence intervals
summary(fit.sex)

# From the summary we may read of an estimate for the lower quartile 
# with confidence limits, cf. section 3.2.3 and exercise 3.8 in the ABG-book. 

# For females the lower quartile becomes 8.33 years with 95% confidence limits 
# from 5.30 years and upwards (no upper limit can be obtained)

# For males the lower quartile becomes 3.36 years with 95% confidence limits from 2.17 to 5.76 years.

# We may also obtain the lower quartile with confidence limits from the command:
quantile(fit.sex,probs=0.25)


# Questions b and c

# The commands are as for question a, but using "ulcer" and "grthick" 
# instead of "sex" when computing the Kaplan-Meier estimates