Practical exercise 7

In this exercise we will use the data on causes of death and mortality in three Norwegian counties described in example 1.12 ABG-book. The data are also described at the course web-page and they are used for illustration in examples 3.3, 3.15, 4.1, and 4.4.

The data may be read into R by the command:

We disregard the 71 individuals who smoke pipe or cigar, so we give the command:

norw.death=norw.death[norw.death\$smkgr!=6,]

In this exercise we will not consider the different causes of death, but focus on total mortality (i.e. mortality due to any cause). Example 4.1 gives results of a Cox regression for total mortality using sex and smoking habit as covariates. You obtain the results of example 4.1 by the commands:

summary(fit0)

a) Perform the commands and make sure that you get the same results as in example 4.1. Read the example carefully!

b) We also want to study the effect of systolic blood pressure and body mass index. Perform a Cox regression model with the covariates sex, smoking habit, systolic blood pressure, and body mass index. Interpret the estimated regression coefficients.

c) We will also check if there are interactions between some of the covariates. Do this by fitting models with first order interaction between two and two covariates, and use the likelihood ratio test to check if the interactions are significant.

Example 4.4 gives estimated survival functions for the model of question a) for men and women who has never smoked and men and women who smoke 20 or more cigarettes per day (at the time of the health screening exam). You obtain the plot in Figure 4.3 by the commands:

new.cov=data.frame(sex=c(1,1,2,2),smkgr=c(1,5,1,5))

surv0=survfit(fit0,newdata=new.cov)

plot(surv0,mark.time=F,xlim=c(40,70),xlab="Age",ylab="Survival",lty=c(1,1,2,2))

d) Perform the commands and make sure that you get the same plot as in Figure 4.3. Read the example 4.4 carefully!

e) We then consider the model of question c) with sex, smoking habit, systolic blood pressure, and body mass index as covariates. Compute and plot the survival function for some selected values of these covariates. Try to find combination of covariate values that in a good way illustrates the effects of the covariates.