In a study of bladder cancer, tumors were removed from the bladders of 86 patients. Subsequently, the individuals were assigned to be treated either with a placebo or with the drug thiopeta. Time to the first recurrence of tumor in months is saved under the variable name time in the data set bladder (Appendix B, Table B.30) [9]. Treatment status is saved under the name group; the value 1 represents placebo. Indicators of censoring statuswhere 1 designates that a tumor did recur and 0 that it did not and that the observation was censoredare saved under the name censor.

(a) Use the product-limit method to estimate the survival function in each treatment group.

(b) Construct survival curves based on the product-limit estimates.

(c) Does it appear that the individuals in one group have a longer time to first recurrence of tumor than those in the other group?

(d) Test the null hypothesis that the distributions of recurrence times are identical in the two treatment groups. What do you conclude?

(e) The variable number is an indicator of the number of tumors initially removed from the bladder; 1 indicates that a patient had a single tumor, and 2 that the individual had two or more tumors. For patients treated with the placebo, test the null hypothesis that the distributions of recurrence times are identical for individuals who had one tumor and for those who had two or more tumors. What do you conclude?