Practical exercise 9

 

From 1962 to 1969, 488 patients with liver cirrhosis at several hospitals in Copenhagen were included in a randomized clinical trial. The purpose of the study was to investigate whether patients treated with the hormone prednisone had a better survival than patients who got an inactive placebo treatment. 251 of the patients received prednisone while 237 received placebo.

 

You may read the cirrhosis data into R by the command:

 

cirrhosis=read.table("http://www.uio.no/studier/emner/matnat/math/STK4080/h12/cirrhosis.txt",header=T)

 

The data are organized with one line for each of the 488 patients, and with the following variables in the eight columns:

pas:              patient number (not to be used in the analysis)

status:       indicator for death/censoring (1=dead; 0=censored)

time:            time in days from start of treatment to death/censoring

treat:         treatment (0=prednisone; 1=placebo)

sex:              gender (0=female; 1=male)

asc:              ascites at start of treatment (0=none; 1=slight; 2=marked)

age:              age in years at start of treatment

prot:            prothrombin index

 

In the trial project, we analysed the cirrhosis data using Cox regression. In this exercise we will perform similar analyses using additive regression. For the additive regression we will not distinguish between slight and marked ascites, so we define a new ascites variable that is 0 for no ascites and 1 for slight or marked ascites:

 

cirrhosis$newasc=as.numeric(cirrhosis$asc>=1)

 

We will first consider additive regressions for one covariate at a time. For the treatment covariate we then give the commands:

fit.treat=aareg(Surv(time,status)~factor(treat),data=cirrhosis)

par(mfrow=c(1,2))

print(fit.treat)

plot(fit.treat)

 

a) Fit the additive model for each of the covariates (treatment, sex, ascites, age, and prothombin index) and discuss the results. It is useful to centre the numeric covariates age and prothrombin index (by subtracting their means).

 

b) Fit an additive regression model with all the covariates. Determine which covariates have a significant effect on the mortality and interpret the estimates of the cumulative regression functions.

 

c) Fit a model with interaction between treatment and ascites. Is there a significant interaction? Interpret the estimates for the model with interaction.