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STAT 533/633: Survival Models
Late assignments will be penalized by 50% per day up to 100%.
Well-presented assignments will receive 1% bonus.
• You can use existing functions in R packages or user-defined functions to answer the questions.
• For related questions, please write down correct hypotheses to be tested and provide details for
calculating values of test statistics using the formulas provided in textbook/lecture notes.
1. (18 points) In the Bone Marrow Transplantation for Leukemia study (see Section 1.3 in
Chapter 1-Examples of Survival Data of Klein and Moeschberger (2003) for details), the data is
available in R package KMSurv under the name bmt where several event times are described for
patients receiving a bone marrow transplant for leukemia. Consider the time to development
of acute graft-versus-host disease (AGVHD). As a prophylactic treatment, patients at two of
the hospitals were given a treatment combining methotrexate (MTX) with cyclosporine and
possibly methylprednisilone. Patients at the other hospitals were not given methotrexate but
rather a combination of cyclosporine and methylprednisilone. Of primary interest in studying
AGVHD is a test of the effectiveness of the MTX regime to prevent AGVHD. Use Breslows
method for handling ties to answer the following questions.
(a) (5 points) Using an appropriate Cox model test the hypothesis of nodifference in the rate
of development of AGVHD between MTX and no MTX patients. Find a point estimate
and a 95% confidence interval for the relative risk of AGVHD for patients on the MTX
protocol as compared to those not given MTX.
(b) (5 points) Patients were also grouped into risk categories based on their status at the time
of transplantation. These categories were as follows: acute lymphoblastic leukemia (ALL)
with 38 patients and acute myeloctic leukemia (AML). The latter category was further
subdivided into low-risk - first remission (54 patients) and high-risk - second remission or
untreated first relapse or second or greater relapse or never in remission (45 patients). Test
the hypothesis of interest (no effect of MTX on development of AGVHD) adjusting for the
three disease categories.
(c) (5 points) Test for the possibility of an interaction effect on AGVHD between the disease
categories and the use of MTX.
(d) (10 points) Using the factors of age, sex, CMV status, FAB class, waiting time to trans-
plant, and disease category as defined (see Example 8.5 Klein and Moeschberger (2003)
1
for details), find the best model to test the primary hypothesis of no MTX effect on the
occurrence of AGVHD. Test the primary hypothesis and find an estimate of the relative
risk of occurrence of AGVHD for an MTX patient as compared to a non-MTX patient.
(e) (10 points, for students in STAT 633 only) Summarize your findings from this data set in
a short report (up to one page).