IEOR 156/256: Healthcare Analytics
Homework 7
March 14th, Thursday, 11:59pm PST
For this homework, we will use the data from a study of 6-mercaptopurine (6-MP) as maintenance
therapy for children in remission from acute lymphoblastic leukemia (ALL)12. One crucial characteristic of
these survival times is that for the 12 patients in the 6-MP group who remained in remission at the time of
the analysis, the exact time to relapse was unobserved; it was only known to exceed the follow-up time. For
example, one patient had only been under observation for three weeks, so we only know that the relapse time
is longer than that. At the time of the analysis, all 21 patients in the placebo group had relapsed, whereas
only 9 of 21 patients in the 6-MP group had.
The below are lists of time to remission, for each group:
• 6-MP: 3,3,3,3*,4,5,5*,5*,6*,7,8,9*,10*, 10*,11,12,13*,16*,16*,17*,18*
• Placebo: 1,1,1,1,2,2,2,3,3,4,4,4,4,6,6,6,6,8,9,11,12
The * symbol indicates that the subject is lost to follow-up.
Problem 1 Kaplan-Meier estimator [20 points]
1. Compute the survival function for the weeks 1 - week 12, using the Kaplan-Meier estimator for each
group. (10 points)
2. What are the median survival time for the two groups, 6-MP and placebo? (4 points)
3. Perform logrank test to compare the survival distributions, using R. (6 points)
> library(survival)
> data <- read.csv("directory-to-csv/leuk.csv")
> surv_obj <- with(data, Surv(time, cens, type = "right"))
> logrank_test <- survdiff(surv_obj ~ group, data = data)
> print(logrank_test)
What is the conclusion of the logrank test?
1Vittinghoff et al., 2012
2Freireich, E. J., Gehan, E., Frei, E. I., Schroeder, L. R., Wolman, I. J., Anbari, R., Burgert, E. O., Mills, S. D., Pinkel,
D., Selawry, O. S., Moon, J. H., Gendel, B. R., Spurr, C. L. and Storrs, R. (1963). The effect of 6-mercaptopurine on the
duration of steroid-induced remissions in acute leukemia: a model for the evaluation of other potentially useful therapy. Blood,
21, 699–716.