dence ratepof severe side e¤ects as defined specifically for the trial: for exam-
ple, toxicity grade III or IV. As with any other statistical test of significant, the
decision is concerned with testing a null hypothesis
H 0 :p¼p 0against an alternative hypothesis
HA:p¼pAin whichp 0 is the investigator’s hypothesized value for the incidence ratepof
severe side e¤ects, often formulated based on knowledge from previous phase I
trial results. The other figure,pA, is themaximum tolerated levelfor the inci-
dence ratepof severe side e¤ects. The trial has to be stopped if the incidence
ratepof severe side e¤ects exceedspA. In addition to the null and alternative
parameters,p 0 andpA, a stopping rule also depends on the chosen level of sig-
nificancea(usually, 0.05) and the desired statistical powerð 1 bÞ;bis the size
of type II error associated with the alternativeHA:p¼pA. Power is usually
preset at 80 or 90%. With these specifications, we monitor for the side e¤ects
by sequentially counting the number of eventse(i.e., number of patients with
severe side e¤ects) and the number of evaluable patientsnðeÞat which theeth
event is observed. The trial is stopped when this condition is first met:
nðeÞ¼lnð 1 bÞlnaþe½lnð 1 pAÞlnð 1 p 0 ÞlnpAþlnp 0
lnð 1 pAÞlnð 1 p 0 ÞIn other words, the formula above gives us the maximum number of evaluable
patientsnðeÞat which the trial has to be stopped ifeevents have been observed.
Some phase II trials may be randomized; however, even in these randomized
trials, toxicity monitoring should be done separately for each study arm. That
is, if the side e¤ect can reasonably occur in only one of the arms of the study,
probably the arm treated by the new therapy, the incidence in that group alone
is considered. Otherwise, the sensitivity of the process to stop the trial would be
diluted by inclusion of the other group. Sometimes the goal is to compare two
treatments according to some composite hypothesis that the new treatment is
equally e¤ective but has less toxicity. In those cases, both e‰cacy and toxicity
are endpoints, and the analysis should be planned accordingly, but the sit-
uations are not that of monitoring in order to stop the trial as intended in the
rule above.
Example 12.6 Suppose that in the planning for a phase II trial, an investigator
(or clinicians in a study committee) decided thatp 0 ¼3% (0.03) based on some
prior knowlege and thatpA¼15% (0.15) should be the upper limit that can
be tolerated (as related to the risks of the disease itself). For this illustrative
example, we find thatnð 1 Þ¼7,nð 2 Þ¼5,nð 3 Þ¼18,nð 4 Þ¼31, and so on,
460 STUDY DESIGNS