Introductory Biostatistics

toxicity, thereby reducing the number of patients treated at the lowest toxicity
selected in single-patient cohorts. On the other hand, the fast-track design may
allow a higher percentage of patients to be treated at very high toxic doses; and
the fact that it uses a single-patient cohort until the first DLT is observed seems
too risky for some investigators. For more experienced investigators, the fast-
track design presents an improved use of patient resources with a moderate
compromise of patient safety; but safety could be a problem with inexperienced
investigators who might select high doses to start with. The common problem
for both designs is the lack of robustness: that the expected rate of MTD
selected is strongly influenced by the doses used, and these doses may be
selected arbitrarily by investigators, which makes their experience a crucial
factor.

12.4 SAMPLE SIZE DETERMINATION FOR PHASE II TRIALS

AND SURVEYS

The determination of the size of a sample is a crucial element in the design of a
survey or a clinical trial. In designing any study, one of the first questions that
must be answered is: How large must the sample be to accomplish the goals of
the study? Depending on the study goals, the planning of sample size can be
approached accordingly.
Phase II trials are the simplest. The drug, at the optimal dose (MTD) found
from a previous phase I trial, is given to a small group of patients who meet
predetermined inclusion criteria. The focus is often on the response rate.
Because of this focus, the planning of sample size can be approached in terms
of controlling the width of a desired confidence interval for the parameter of
interest, the response rate.
Suppose that the goal of a study is to estimate an unknown response ratep.
For the confidence interval to be useful, it must be short enough to pinpoint the
value of the parameter reasonably well with a high degree of confidence. If a
study is unplanned or poorly planned, there is a real possibility that the result-
ing confidence interval will be too long to be of any use to the researcher. In
this case, we may decide to have an estimate error not exceedingd, an upper
bound for the margin of error since the 95% confidence interval for the re-
sponse ratep, a population proportion, is

pG 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

pð 1 pÞ

n

r

wherepis the sample proportion. Therefore, our goal is expressed as

1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

pð 1 pÞ

n

r

ad

SAMPLE SIZE DETERMINATION FOR PHASE II TRIALS 451