12.27 A phase III double-blind randomized trial is planned to compare a new
drug versus placebo as adjuvant therapy for the treatment of women
with metastatic ovarian cancer who have had complete clinical response
to their primary treatment protocol, consisting of surgical debulking
and platium-based chemotherapy. Find the total sample size needed
using a two-sided test at the 0.05 level of significance and a statistical
power of 80% to detect the alternative hypothesis that the two-year
relapse rates in the placebo and the new drug arms are 60% and 40%,
respectively.
12.28 Suppose that an investigator considers conducting a case–control study
to evaluate the relationship between invasive epithelial ovarian cancer
and the history of infertility (yes/no). It is estimated that the proportion
of controls with a history of infertility is about 10% and the investigator
wishes to detect a relative risk of 2.0 with a power of 80% using a two-
sided level of significance of 0.05.
(a) Find the total sample size needed if the two groups, cases and con-
trols, are designed to have the same size.
(b)Find the total sample size needed if the investigator likes to have
the number of controls four times the number of cases.
(c) Find the number of cases needed if the design is 1:1 matched;
matching criteria are various menstrual characteristics, exogenous
estrogen use, and prior pelvic surgeries.
12.29 Suppose that an investigator considers conducting a case–control study
to evaluate the relationship between cesarean section delivery (C-
section) and the use of electronic fetal monitoring (EFM, also called
ultrasound) during labor. It is estimated that the proportion of controls
(vaginal deliveries) who were exposed to EFM is about 40% and the
investigator wishes to detect a relative risk of 2.0 with a power of 90%
using a two-sided level of significance of 0.05.
(a) Find the total sample size needed if the two groups, cases and con-
trols, are designed to have the same size.
(b)Find the total sample size needed if the investigator likes to have
the number of controls three times the number of cases.
(c) Find the number of cases needed if the design is 1:1 matched;
matching criteria are age, race, socioeconomic condition, educa-
tion, and type of health insurance.
12.30 When a patient is diagnosed as having cancer of the prostate, an
important question in deciding on treatment strategy for the patient is
whether or not the cancer has spread to the neighboring lymph nodes.
The question is so critical in prognosis and treatment that it is custom-
ary to operate on the patient (i.e., perform a laparotomy) for the sole
EXERCISES 481