**Help Aids **Top

**Application: **Commonly, the central objective of Phase II clinical trials is the
assessment of the antitumor ‘therapeutic efficacy’ of a specific treatment regimen.
It is of interest to formulate test procedures which can be employed in these
trials to decide whether or not this therapeutic efficacy warrants further
investigation. One-sample multiple testing procedure
is proposed which employs the standard single-stage test procedure at the last
test.

**Procedure**:

- Enter

a) value of α, the probability of type I error

b) value of β, the probability of type II error, or (1-power) of the test

c) value of p_{0}, the largest response probability

d) value of p_{A}, the smallest response probability

e) value of Nmax, the maximum number of patients to be recruited

f) value of Numstage, the number of stages in Phase II **clinical trial.**

- Click the button “Calculate” to obtain

a) value
of n_{i}, the number of patients to be recruited in stage i

b) value
of a_{i}, the acceptance points in stage i

c) value of r_{i}, the rejection points in stage i**.**

**Assumption:**

1.
Assume
that a Phase I trial of the experimental treatment regimen has been completed,
from which the proper dosages yielding acceptable toxicity have been
established.

2.
Probability
of type I error is smaller or equal than that of type II error ().

3.
A
maximum of K=1,2 or 3 tests is adopted in the
calculator, since more frequent testing would not seem to be necessary in most
Phase II trials.

4.
Due
to the very limited number of patients who are eligible for a given Phase II
study, and also to the large number of treatment regimens generally awaiting
Phase II trials, the sample size *N*
for a given trial is frequently fixed in advance.

5.
A
certain number of Phase II trials are terminated due to extreme response
probability results, not due to other causes such as excessive toxicity or
unexpectedly inadequate patient accrual.

**Theory:**

Typically,
a Phase II trial is designed to have a single stage in which *N* evaluable patients accrue, are
treated, and are then observed, so that the number, *S*, who experience a regression is determined. In a multiple testing
procedure patients accrue in several stages, testing being performed at each
stage after appropriate patient accrual has been completed. This feature is
particularly appealing in a clinical setting where there are compelling ethical
reasons to terminate a Phase II trial early if the initial proportion of
patients experiencing a tumor regression is too low or too high.

Specify
largest response probability, *p _{0}*,
which if true clearly implies the treatment regimen does not warrant further
investigation and smallest response probability,

We
have one-sided hypotheses to be tested as

Suppose
that one decides to perform *K* stages
and to allow *n _{i}*
patients to accrue between the (

General
multiple testing procedures (proposed by Schultz *et al*. (1973)):

At
Stage g (),

if , terminate the trial and reject;

if , terminate the trial and reject;

if
, continue to Stage g+1.

(Proposed
by O’Brien and Fleming (1979)), at Stage g, would reject H_{0} whenever

where

Let , where z_{p} denotes the
p-quantile of the standard normal distribution.
Rejection of H_{A} at Stage g < K would occur whenever.

The
corresponding acceptance and rejection points are specified in the following
manner:

wheredenotes the nearest integer to x.

**Discussion:
**

1. Here is some introduction to single-stage procedure so that readers have a clear mind between the difference of single-stage procedure and multiple testing procedures.

The single-stage
procedure can be based upon the statistic, by rejecting H_{0} whenever is large or .

2. Fleming has shown that well-designed group sequential procedures are more efficient than single stage procedures in that they require fewer patients to achieve a predetermined size and power.

3. The multiple testing procedures will require, on the average, fewer patients than the single-stage procedure having similar power. It is more desirable to use a multiple-stage procedure over a single-stage procedure.

4. A choice
of either the Stage 1 or Stage K sample size should not be much less than *N/K* due to the resulting high degree of
conservatism which would be required at a very early first test, and, at Stage
K , to a resulting apparent small loss in efficiency.

5. To obtain useful and efficient designs, approximately equal sample sizes for each stage is recommended.

**Statistical
Notations:**

**α****:** The
probability of type I error (significance level) is the *probability of rejecting the true null
hypothesis. *

**β****:** The
probability of type II error (1 – power of the test) is the *probability of
not rejecting the false null hypothesis.*

**Example:**

Since Phase I
studies indicate that the experimental regimen is somewhat more toxic than the
standard, in phase II clinical trial, it is decided to set *p _{0}*=0.2 and

**Reference**: Fleming (1982) *Biometrics *38:
143-151