Greenwood's Formula

#1
A clinical experiment is conducted to determine the effect of a new treatment, A, on remission times for laboratory rats with a first-stage specific type of cancer. A sample of
n = 21 rats is treated with A and the times of remission recorded (in weeks). In addition, 21 other rats were not given treatment A, as a control group, and their times of remission were recorded:

Treatment A Group: (Plus denotes censored time)
6 6 6 6+ 7 9+ 10 10+ 11+ 13 16 17+ 19+ 20+ 22 23 25+ 32+ 32+ 34+ 35+

Control Group (note ties, but no censoring):
1 1 2 2 3 4 4 5 5 8 8 8 8 11 11 12 12 15 17 22 23

(a) Plot the product-limit estimators of the survival function of the two groups of rats and compare. (You may use the computer to plot if you wish, after showing the calculation of the estimator at the first four observations in each group.)

(b) Using Greenwood's formula and the normal approximation, give a 95% confidence interval estimator for the survival probability (of remission) at 14 weeks for each group.