Lawless (1982), Gehan (1965) and others have discussed data from a clinical trial examining steroid-induced remission...

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Lawless (1982), Gehan (1965) and others have discussed data from a clinical trial examining steroid-induced remission times (weeks) for leukemia patients. One group of 21 patients were given 6-mercaptopurine (6-MP); a second group of 21 patients were given a placebo. Since the trial lasted 1 year and patients were admitted to the trial during the year, some of the data could not be gathered by the cut-off date when some of the patients were still in remission. Observations on remission time were as follows: a. b. C. 6-MP Placebo 6 6 6 6+ 7 9+ 10 10+ 11+ 13 16 17+ 19+ 20+ 22 1 1 2 2 3 4 4 5 5 8 8 8 8 23 25+ 32+ 32+ 34+ 35+ 11 11 12 12 15 17 22 23 Construct an empirical survivor plot for the placebo group. Give a general comparison of the survival prospects of the two groups based on the graphs of the K-M estimators. Read off the graphs estimates of the probability of survival beyond 3 months. 2. A complete data set of n = 23 ball bearing failure times to test the endurance of deepgroove ball bearings has been extensively studied. The ordered set of failure times measured in 10 revolution is 17.88 28.92 33.00 41.52 42.12 45.60 48.48 51.84 51.96 54.12 55.56 67.80 68.64 68.64 68.88 84.12 93.12 98.64 105.12 105.84 127.92 128.04 173.40. Find a nonparametric survivor function estimator and a 95% confidence interval for the probability that a ball bearing will last 50,000,000 cycles. 3. An experiment is conducted to determine the effect of a drug named 6-mercaptopurine (6-MP) on leukemia remission times. A sample of n = 21 leukemia patient is treated with 6-MP and the times of remission are recorded. There are r =9 individuals for whom the remission time is observed, and the remission times for the remaining 12 individuals are randomly censored on the right. Letting an asterisk denote a censored observation, the remission times (in weeks) are 6 6* 7 9* 10 10* 17* 19* 20* 22 23 25* 11* 32* 6 6 13 16 32* 34* 35*. a. Find an estimate for S(14) for the treatment group in the 6-MP experiment. b. Determine a 95% confidence interval for the probability of survival to time 14. Lawless (1982), Gehan (1965) and others have discussed data from a clinical trial examining steroid-induced remission times (weeks) for leukemia patients. One group of 21 patients were given 6-mercaptopurine (6-MP); a second group of 21 patients were given a placebo. Since the trial lasted 1 year and patients were admitted to the trial during the year, some of the data could not be gathered by the cut-off date when some of the patients were still in remission. Observations on remission time were as follows: a. b. C. 6-MP Placebo 6 6 6 6+ 7 9+ 10 10+ 11+ 13 16 17+ 19+ 20+ 22 1 1 2 2 3 4 4 5 5 8 8 8 8 23 25+ 32+ 32+ 34+ 35+ 11 11 12 12 15 17 22 23 Construct an empirical survivor plot for the placebo group. Give a general comparison of the survival prospects of the two groups based on the graphs of the K-M estimators. Read off the graphs estimates of the probability of survival beyond 3 months. 2. A complete data set of n = 23 ball bearing failure times to test the endurance of deepgroove ball bearings has been extensively studied. The ordered set of failure times measured in 10 revolution is 17.88 28.92 33.00 41.52 42.12 45.60 48.48 51.84 51.96 54.12 55.56 67.80 68.64 68.64 68.88 84.12 93.12 98.64 105.12 105.84 127.92 128.04 173.40. Find a nonparametric survivor function estimator and a 95% confidence interval for the probability that a ball bearing will last 50,000,000 cycles. 3. An experiment is conducted to determine the effect of a drug named 6-mercaptopurine (6-MP) on leukemia remission times. A sample of n = 21 leukemia patient is treated with 6-MP and the times of remission are recorded. There are r =9 individuals for whom the remission time is observed, and the remission times for the remaining 12 individuals are randomly censored on the right. Letting an asterisk denote a censored observation, the remission times (in weeks) are 6 6* 7 9* 10 10* 17* 19* 20* 22 23 25* 11* 32* 6 6 13 16 32* 34* 35*. a. Find an estimate for S(14) for the treatment group in the 6-MP experiment. b. Determine a 95% confidence interval for the probability of survival to time 14.

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