Acute myelogenous leukemia (AML) is a cancer that starts inside bone marrow (the soft tissue inside bones that helps form blood cells). The cancer grows from cells that would normally turn into white blood cells. A clinical trial to evaluate the efficacy of maintenance chemotherapy for AML was conducted at Stanford University. After reaching a status of remission through treatment by chemo-therapy, the patients who entered the study were randomly assigned to two groups; the first group received maintenance chemotherapy, and the second group did not. The objective of the study was to investigate whether maintenance chemotherapy prolonged time until relapse (measured in weeks from the time of randomization to the two groups). Table 9.7 contains quantities related to the construction of the Kaplan-Meier estimates for survival probabilities of patients with AML who received maintenance chemotherapy.
a. Fill in the remaining quantities in Table 9.7.
b. Examine the table. How many patients in the study who received maintenance chemotherapy had censored event times?
c. Estimate the probability that a randomly selected patient who received maintenance chemotherapy remains in remission (does not relapse) for more than 40 weeks.
Table 9.7 Quantities associated with patients with AML who received maintenance chemotherapy.

d. Calculate the estimated mean time until relapse for those patients receiving maintenance chemo-therapy. (Be sure to include the time metric in your answer.)
e. Compute and interpret the estimated hazard rate (t) for the time interval 13 ‰¤ t ‰¤ 18.
f. Figure 9.18 displays the Kaplan-Meier curves for the maintained and nonmaintained groups. Does it appear that maintenance chemotherapy has an effect on time until AML relapse? Briefly explain.

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