12.9 Refer to Example 12.12. Find the total sample size needed if we retain
all the specifications except that the hypothesized hazards ratio is
increased to 3.0.12.10 The status of the axillary lymph node basin is the most powerful pre-
dictor of long-term survival in patients with breast cancer. The patho-
logic analysis of the axillary nodes also provides essential informa-
tion used to determine the administration of adjuvant therapies. Until
recently, an axillary lymph node dissection (ALND) was the standard
surgical procedure to identify nodal metastases. However, ALND is
associated with numerous side e¤ects, including arm numbness and
pain, infection, and lymphedema. A new procedure, sentinal lymp node
(SLN) biopsy, has been proposed as a substitute and it has been
reported to have a successful identification rate of about 90%. Suppose
that we want to conduct a study to estimate and confirm this rate to
identify nodal metastases among breast cancer patients because previ-
ous estimates were all based on rather small samples. How many
patients are needed to confirm this 90% success rate with a margin
of error ofG5%? Does the answer change if we do not trust the 90%
figure and calculate a conservative sample size estimate?
12.11 Metastasic melanoma and renal cell carcinoma are incurable malig-
nancies with a median survival time of less than a year. Although these
malignancies are refractory to most chemotherapy drugs, their growth
may be regulated by immune mechanisms and there are various strat-
egies for development and administration of tumor vaccines. An inves-
tigator considers conducting a phase II trial for such a vaccine for
patients with stage IV melanoma. How many patients are needed to to
estimate the response rate with a margin of error ofG10%?
12.12 Suppose that we consider conducting a study to evaluate the e‰cacy
of prolonged infusional paclitaxel (96-hour continuous infusion) in
patients with recurrent or metastatic squamous carcinoma of the head
and neck. How many patients are needed to to estimate the response
rate with a margin of error ofG15%?
12.13 Normal red blood cells in humans are shaped like biconcave disks.
Occasionally, hemoglobin, a protein that readily combines with oxy-
gen, is formed imperfectly in the cell. One type of imperfect hemoglobin
causes the cells to have a caved-in, or sicklelike appearance. These
sickle cells are less e‰cient carriers of oxygen than normal cells and
result in an oxygen deficiency calledsickle cell anemia. This condition
has a significant prevalence among blacks. Suppose that a study is to be
conducted to estimate the prevalence among blacks in a certain large
city.
(a) How large a sample should be chosen to estimate this proportion to
within 1 percentage point with 99% confidence? with 95% confi-
EXERCISES 477