In the table in the textbook on page 511 you will find survival times in months since diagnosis for 10 AIDS patients suffering from concomitant esophageal candidiasis, an infection due to Candida yeast, and cytomegalovirus, a herpes infection that can cause serious illness. Censored observations are denoted by a plus sign.

Patient Number Survival (months)

1 0.5+

2 1

3 1

4 1

5 2

6 5+

7 8+

8 9

9 10+

10 12+

a. How many deaths were observed in this sample of patients?

b. Use the product-limit method to estimate the survival function S(t). Please show equations and work.

c. What is S(1), the estimated probability of survival at one month? What is the estimated probability at 5 months? At 6 months? Please show equations and work.

d. Construct a survival curve (do not submit) based on the product-limit estimate. Please show equations and work.