8.10 In section 1.3, 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 Breslow's method for handling ties to answer the following exercises.

(a) Using an appropriate Cox model test the hypothesis of no difference 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) 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-riskfirst remission (54 patients) and high-risksecond 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) Test for the possibility of an interaction effect on AGVHD between the disease categories and the use MTX. (d) Using the factors of age, sex, CMV status, FAB class, waiting time to transplant, and disease category as defined in Example 8.5, 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.

Use the "KMsurv" package in R to access the "bmt" data set. The reference for the data set variables can be found using this link:

https://cran.r-project.org/web/packages/KMsurv/KMsurv.pdf