Solution: Leukemia treatment study (Exam 2021)

Eksempel

The Kaplan-Meyer estimates and corresponding confidence intervals may be found and plotted by the following R commands:

library(survival)
TPlacebo = c(1,1,2,2,3,4,4,5,5,8,8,8,8,11,11,12,12,15,17,22,23)
CensPlacebo = 1 - c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
T6MP = c(6,6,6,6,7,9,10,10,11,13,16,17,19,20,22,23,25,32,32,34,35)
Cens6MP = 1 - c(0,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,1,1,1)

KMPlacebo =  survfit(Surv(TPlacebo,CensPlacebo)~1, conf.type="log-log")
pdf("KMPlacebo.pdf")
plot(KMPlacebo,col="red")
graphics.off()
    
KM6MP = survfit(Surv(T6MP,Cens6MP)~1, conf.type="log-log")
pdf("KM6MP.pdf")
plot(KM6MP,col="blue",new=FALSE)
graphics.off()

Code for creating Kaplan-Meier curves.

The resulting plots are shown in Figure 1 and 2.

KMPlacebo — Figure 1: Kaplan-Meyer estimates with confidence intervals for the placebo group.

KM6MP — Figure 2: Kaplan-Meyer estimates with confidence intervals for the 6MP group.

Confidence intervals for the median survival times can be found by drawing a horisontal line at survival probability equal to \(0.5\) and reading off at which times \(t\) this line crosses the confidence interval curves. The process is illustrated by green lines in the two plots in Figure 1 and 2.

Kopier

# For the placebo plot: 
lines(c(0,25), c(0.5,0.5), col="green")
lines(c(4,4), c(0,0.5), col="green")
lines(c(11,11), c(0,0.5), col="green")

# For the 6MP plot:
lines(c(0,35),c(0.5,0.5),col="green")
lines(c(13,13),c(0,0.5),col="green")

Code for producing the green lines for the placebo and 6Mp group (insert code after the respective plots' code).

Note that for the 6MP group the upper limit in the confidence interval is equal to infinity. The numerical values for the confidence intervals can either be read off from the plots or they can be found by inspecting the R variables KMPlacebo and KM6MP produced in the R code above, which can be done by the R commands below.

Kopier

KMPlacebo
KM6MP

Printing out the numerical values for the confidence interval.

The confidence interval for the Placebo group becomes \(\underline{\underline{[4,11]}}\) and for the 6MP group it becomes \(\underline{\underline{[13,\infty)}}\).