A prospective cohort study is performed to test the effectiveness of a new chemotherapy drug,...

A prospective cohort study is performed to
test the effectiveness of a new chemotherapy drug, relative to the standard
chemotherapy drug, in reducing the chances of death within 5 years due to a
type of cancer. Suppose that the probability of death within 5 years due to the
cancer is 0.18 using the new chemotherapy drug (i.e., the five-year survival
probability is 0.82) and the five-year survival probability using the standard
chemotherapy is 0.78.

(a) Calculate the relative risk of death
from cancer within 5 years for patients using the new chemotherapy compared to
patients using the standard chemotherapy.

(b) Calculate the odds ratio for death within
5 years for cancer patients using the new chemotherapy relative to patients
using the standard chemotherapy.

(c) If the probability of death from cancer
within 5 years for patients using the new chemotherapy drug is 0.25 and the
odds ratio for death within 5 years for patients using the new chemotherapy
relative to patients using the standard chemotherapy is 0.25, what is the
probability of death within 5 years from cancer for patients using the standard
chemotherapy drug?