EXERCISES
12.1 Some opponents of the randomized, double-blinded clinical trial, espe-
cially in the field of psychiatry, have argued that a necessary or at least
important component in the e‰cacy of a psychoactive drug, for exam-
ple a tranquilizer, is the confidence that the physician and the patient
have in this e‰cacy. This factor is lost if one of the drugs in the trial is a
placebo and the active drug and placebo cannot be identified. Hence
active drug that would be e‰cacious if identified appears no better than
placebo, and therefore is lost to medical practice. Do you agree with
this position? Explain.
12.2 Suppose that we consider conducting a phase I trial using the standard
design with only three prespecified doses. Suppose further that the tox-
icity rates of these three doses are 10%, 20%, and 30%, respectively.
What is the probability that the middle dose will be selected as the
MTD? (Hint:Use the binomial probability calculations of Chapter 3.)12.3 We can refer to the standard design as a three-and-three design because
at each new dose, it enrolls a cohort of three patients with the option
of enrolling an additional three patients evaluated at the same dose.
Describe the dose-escalation plan for a three-and-two design and de-
scribe its possible e¤ects on the toxicity rate of the resulting maximum
tolerated dose (MTD).12.4 Repeat Exercise 12.2 but assuming that the toxicity rates of the three
doses used are 40%, 50%, and 60%, respectively.12.5 Refer to Example 12.9, where we found that 234 subjects are needed for
a predetermined power of 90% and that the power would be 81% if
the study enrolls only 180 subjects. What would be the power if
the study was substantially underenrolled and conducted with only 120
patients?12.6 Refer to Example 12.10, where we found that 378 subjects are needed
for a predetermined power of 90%. What would be the power if the
study was actually conducted with only 300 patients, 150 in each
group?12.7 Refer to Example 12.14, where we found that 73 cases and 73 controls
are needed for a predetermined power of 90%. What would be the
power if the study was actually conducted with only 100 subjects, 50 in
each group?12.8 Refer to Example 12.18, where we found that 21 cases and 63 controls
are needed for a predetermined power of 90%. What would be the
power if the study was actually conducted with only 15 cases but 105
controls?476 STUDY DESIGNS