In the table below, 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).
c. What is S(1), the estimated probability of survival at one month? What is the estimated probability at 5 months? At 6 months?
d. Construct a survival curve based on the product-limit estimate.