In a study of bladder cancer, tumors were removed from the bladders of 86 patients. Subsequently, the individuals were assigned to be treated with either a placebo or the drug thiopeta. Time to recurrence of tumor in months is saved under the variable name time in the data set bladder. Treatment status is saved under the name group; the 1 value represents placebo. Indicators of censoring status; where 0 indicates a tumor did not occur and the observation was censored, is saved under the name censor.

Data sheet link: https://docs.google.com/spreadsheets/d/1OY2mjC8ezk1jQoLnog9skFZkhqkzphQBBDNeXGfCTHM/edit?usp=sharing

This is on Survival Analysis. Please show your work if you are using a statistical calculator and please don't copy and past from other sources. Thanks.

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

We can estimate the product-limit estimates for each treatment for S(12) for the placebo group (1) is:

and for thiopeta group (2) is:

b. Plot a survival curve--do not submit.

c. Does it appear that the individuals in one group have a longer time to first recurrence than in the other group?

d. Test the null hypothesis that the distributions of recurrence times are identical. What do you conclude?

e. The variable number is an indicator of tumors initially removed from the bladder. Test the null hypothesis that the one tumor group has the same distribution as the more than one tumor group. What do you conclude?