How large should a total sample size be if we decide to preseta¼ 0 : 01
and that it is important to detect an LDL cholesterol level reduction of
1.0 mmol/L with a power of 95%?12.19 Depression is one of the most commonly diagnosed conditions among
hospitalized patients in mental institutions. The primary measure of
depression is the CES-D scale developed by the Center for Epidemio-
logic Studies, in which each person is scored on a scale of 0 to 60. The
following results were found for a group of randomly selected women:
n¼200,x¼ 10 :4, ands¼ 10 :3. A study is now considered to investi-
gate the e¤ect of a new drug aimed at lowering anxiety among hos-
pitalized patients in similar mental institutions. Subjects would be
randomized to receive either the new drug or placebo, then averages of
CES-D scores will be compared using the two-sided two-samplettest at
the 5% level. How large should the total sample size be if it is important
to detect a CES-D score reduction of 3.0 with a power of 90%?
12.20 A study will be conducted to compare the proportions of unplanned
pregnancy between condom users and pill users. Preliminary data show
that these proportions are approximately 10% and 5%, respectively.
How large should the total sample size be so that it would be able to
detect such a di¤erence of 5% with a power of 90% using a statistical
test at the two-sided level of significance of 0.01?
12.21 Suppose that we want to compare the use of medical care by black and
white teenagers. The aim is to compare the proportions of teenagers
without physical checkups within the last two years. Some recent survey
shows that these rates for blacks and whites are 17% and 7%, respec-
tively. How large should the total sample be so that it would be able to
detect such a 10% di¤erence with a power of 90% using a statistical test
at the two-sided level of significance of 0.01?
12.22 Among ovarian cancer patients treated with cisplatin, it is anticipated
that 20% will experience either partial or complete response. If adding
paclitaxel to this regimen can increase the response by 15% without
undue toxicity, that would be considered as clinically significant. Cal-
culate the total sample size needed for a randomized trial that would
have a 80% chance of detecting this magnitude of treatment di¤erence
while the probability of type I error for a two-sided test is preset at
0.05.
12.23 Metastatic breast cancer is a leading cause of cancer-related mortality
and there has been no major change in the mortality rate over the past
few decades. Therapeutic options are available with active drugs such
as paclitaxel. However, the promising response rate is also accom-
panied by a high incidence of toxicities, especially neurotoxicity. An
investigator considers testing a new agent that may provide significant
EXERCISES 479