#Commands to practical exercise 5

 

#The commands below assume that the cirrhosis ("skrumplever") data set has been stored

# in the dataframe "skrumplever" and that the survival library has been attached

# (cf. the R commands to practical exercise 3).

 

# Define treatment, gender, and ascites to be factors:

skrumplever$beh<-factor(skrumplever$beh)

skrumplever$kjonn<-factor(skrumplever$kjonn)

skrumplever$asc<-factor(skrumplever$asc)

 

 

# One possible model for the data is (use years as time unit)

cox.fit<- coxph(Surv(tid/365.25,status)~ beh+kjonn+asc+alder+prot+beh:asc, data=skrumplever)

 

 

# To assess the appropriate functional form of a numeric covariate we may make a smoothed plot

# of the martingale residuals versus the covariate for a model fitted without the actual covariate.

 

# To check whether age has a log-linear form, we first fit a model without age

cox.fit0<- coxph(Surv(tid/365.25,status)~ beh+kjonn+asc+prot+beh:asc, data=skrumplever)

martres.fit0<-residuals(cox.fit0, type="mart")

 

#We then make a plot of the martingale residuals versus age and add a smoothed curve to the plot:

plot(skrumplever$alder, martres.fit0, xlab="Age",ylab=" ")

spline.fit<-smooth.spline(skrumplever$alder, martres.fit0)

lines(spline.fit$x, spline.fit$y)

 

#Similarily for prothrombin

cox.fit0<- coxph(Surv(tid/365.25,status)~ beh+kjonn+asc+alder+beh:asc, data=skrumplever)

martres.fit0<-residuals(cox.fit0, type="mart")

plot(skrumplever$prot, martres.fit0, xlab="Prothrombin",ylab=" ")

spline.fit<-smooth.spline(skrumplever$prot, martres.fit0)

lines(spline.fit$x, spline.fit$y)

 

 

#We finally check for proportionality of the covariates:

cox.zph(cox.fit)

 

#and make plots that suggest the (possible) time dependent effect of a covariate:

par(mfrow=c(2,4))

plot(cox.zph(cox.fit))