Introductory Biostatistics

Example 12.4 Perhaps it is simpler to see the sample size determination con-
cerning a continuous endpoint in the context of a survey. Suppose that a study
is to be conducted to estimate the average birth weight of babies born to
mothers addicted to cocaine. Suppose also that we want to estimate this aver-
age to within^12 lb with 95% confidence. This goal specifies two quantities:

d¼ 0 : 5

coe‰cient¼ 1 : 96

What value should be used for the variance? Information from normal babies
may be used to estimates. The rationale here is that the addiction a¤ects every
baby almost uniformly; this may result in a smaller average, but the variance is
unchanged. Suppose that the estimate from normal babies issF 2 :5 lb, then
the required sample size is

n¼

ð 1 : 96 Þ^2 ð 2 : 5 Þ^2

ð 0 : 5 Þ^2

¼97 approximately

12.6 ABOUT SIMON’S TWO-STAGE PHASE II DESIGN

Phase I trials treat only three to six patients per dose level according to the
standard design. In addition, those patients may be diverse with regard to their
cancer diagnosis; consequently, phase I trials provide little or no information
about e‰cacy. A phase II trial is the first step in the study of antitumor e¤ects
of an investigational drug. The aim of a phase II trial of a new anticancer drug
is to determine whether the drug has su‰cient antitumor activity to warrant
further development. Further development may mean combining the drug
with other drugs, or initiation of a phase III trial. However, these patients are
often at high risk of dying from cancers if not treated e¤ectively. Therefore,
it is desirable to use as few patients as possible in a phase II trialifthe regi-
men under investigation is, in fact, low antitumor activity. When suchethical
concernsare of high priority, investigators often choose theSimon two-stage
design:

1. A group ofn 1 patients are enrolled in the first stage. Ifr 1 or fewer of these
   n 1 patients respond to the drug, the drug is rejected and the trial is ter-
   minated; if more thanr 1 responses are observed, investigators proceed to
   stage II and enrolln 2 more patients.


2. After stage II, ifror fewer responses are observed, including those in
   stage I, the drug is rejected; If more thanrresponses are observed, the
   drug is recommended for further evaluation.

456 STUDY DESIGNS