Survival analysis (Statistics)

5.1 For the survival times given in Table 3.1, compare the survival distributions of

the two treatment groups using:

(a) Gehan's generalized Wilcoxon test

(b) The Cox-Mantel test

5.2 For the remission data given in Table 3.1, compare the remission time

distributions of the two treatment groups using

(a) The logrank test

(b) The Peto and Peto's generalized Wilcoxon test

Exercise 4.5 the following remission times of 42 patients with acute leukemia reported by Freireich et al. (1963)* in a clinical trial to assess the efficacy of 6-mercaptopurine (6-MP) to maintain remission. The patients were randomized to receive 6-MP or a placebo. The study was terminated after 1 year and the following remission times, in weeks, were recorded: 6- MP(21 patients) : 6, 6, 6, 7, 10, 13, 16, 22, 23, 6+, 94, 10+, 11+, 17+, 19+, 20+, 25+, 32+, 32+, 34+, 35+ Placebo (21 patients) : 1, 1, 2, 2, 3, 4, 4, 5, 5, 8, 8, 8, 8, 11, 11, 12, 12, 15, 17, 22, 23

5.5 Consider the remission time in Exercise 4.5. Use the logrank test and the generalized Wilcoxon test to test the equality of the two treatments.

5.6 For the first four skin tests given in Exercise Table 3.1, use the Cox-Mantel test and the logrank test to see if there is a significant difference in survival between patients with positive (25x5 mm for mumps, ≥10 x 10 mm for others) and negative (<5×5 mm for mumps, <10 x 10 mm for others) reactions.

5.7 Using the data in Table 3.1, compare the age distributions of the two treatment groups using Cox's F-test.