# load data
mel <- read.table("http://publicifsv.sund.ku.dk/~pka/epidata/melanom-surv.txt", header = TRUE)

# rescale age and thick
mel$age <- mel$age/10
mel$thick <- mel$thick/100

# 1.: slide 17
library(survival)
fit <- coxph(Surv(days, dc != 2) ~ factor(sex) + (ulc == 1) + thick + age, data = mel)
summary(fit)

# 2.: proportionality for ulc
# since a time-dependent interaction term cannot be added as easily as in SAS, we use the cox.zph function. Proportional hazards can be
# assumed for non-significant variables
tmp <- cox.zph(fit)
tmp
# suggests proportionality for all variables

# 3.: linear splines for thick
mel$thick2 <- (mel$thick -2)*(mel$thick>2)
mel$thick5 <- (mel$thick -5)*(mel$thick>5)
fit3 <- coxph(Surv(days, dc != 2) ~ factor(sex) + (ulc == 1) + thick + age + thick2 + thick5, data = mel)
summary(fit3)

anova(fit, fit3, test = "LRT")

# 4.: interaction of sex and thick
fit4 <- coxph(Surv(days, dc != 2) ~ factor(sex) + (ulc == 1) + thick + age + factor(sex):thick, data = mel)
summary(fit4)