when we preset the level of significance at 0.05 and statistical power at 80%. In
other words, we stop the trial if there are two events among the first five
evaluable patients, three events among the first 18 patients, four events among
the first 31 patients, and so on. Here we use only positive solutions and the
integer proportion of each solution from the equation above. The negative
solutionnð 1 Þ¼7 indicates that the first event will not result in stopping the
trial (because it is judged as not excessive yet).
Example 12.7 The stopping rule would be more stringent if we want higher
(statistical) power or if incidence rates are higher. For example:
(a) Withp 0 ¼ 3 %andpA¼ 15 %as set previously, but if we preset the level
of significance at 0.05 and statistical power at 90%, the results become
nð 1 Þ¼8,nð 2 Þ¼4,nð 3 Þ¼17,nð 4 Þ¼30, and so on. That is, we would
stop the trial if there are two events among the first four evaluable
patients, three events among the first 17 patients, four events among the
first 30 patients, and so on.
(b) On the other hand, if we keep the level of significance at 0.05 and sta-
tistical power at 80%, but if we decide onp 0 ¼ 5 %andpA¼20%, the
results becomenð 1 Þ¼7,nð 2 Þ¼2,nð 3 Þ¼11,nð 4 Þ¼20, and so on.
That is, we would stop the trial if there are two events among the first
two evaluable patients, three events among the first 11 patients, four
events among the first 20 patients, and so on.It can be seen that the rule accelerates faster with higher rates than with
higher power.
12.9 SAMPLE SIZE DETERMINATION FOR PHASE III TRIALS
The determination of the size of a sample is a crucial element in the design of a
study, whether it is a survey or a clinical trial. In designing any study, one of
the first questions that must be answered is: How large must a sample be to
accomplish the goals of the study? Depending on the study goals, the planning
of sample size can be approached in two di¤erent ways: either in terms of con-
trolling the width of a desired confidence interval for the parameter of interest,
or in terms of controlling the risk of making type II errors. In Section 12.3, the
planning of sample size was approached in terms of controlling the width of a
desired confidence interval for the parameter of interest, the response rate in a
phase II trial. However, phase III and IV clinical trials are conducted not for
parameter estimation but for the comparison of two treatments (e.g., a new
therapy versus a placebo or a standard therapy). Therefore, it is more suitable
to approach the planning of sample size in terms of controlling the risk of
making type II errors. Since phase I and II trials, especially phase I trials, are
specific for cancer research but phase III and IV trials are applicable in any
SAMPLE SIZE DETERMINATION FOR PHASE III TRIALS 461