For background information see the book by Green, Benedetti and Crowley:
Green SJ, Benedetti J., and Crowely J., Clinical Trials in Oncology, Chapman and Hall, 1997.
Green SJ and Dahlberg S. (1992). Planned Versus Attained Design in Phase II Clinical Trials. Statistics in Medicine 11:853-862.
Error Thresholds
Stage 1 Error Threshold
Probability threshold for failing to reject the null at stage 1 when alternative is true;
In other words, it is the probability threshold for erroneously accepting early futility defined as below:
P(X ≤ a1 | n1, p_{a})
Probability threshold for rejecting the null at stage 1 when the null is true; In other words, it is the
probability threshold for erroneously rejecting futility at stage 1 and is defined as below:
P(X ≥ r1 | n1, p_{0})
Stage 2 Error Threshold
Probability threshold for rejecting the null at stage 2 when the null is true;
In other words, it is the probability threshold for erroneously rejecting futility at stage 2 and is defined as below:
P(X ≥ r2 | n1 + n2, p_{0})
Definition of Variables
These are definitions of all variables referred to in the documentation:
p_{0}: The largest success probability which, if true, would imply that the treatment regimen does not warrant further investigation due to treatment futility.
p_{a}: The smallest success probability which, if true, would imply that the treatment regimen DOES warrant further investigation.
al: If the number of successes after completing the first stage is < al, we reject the alternative hypothesis that p > p_{a}.
rl: If the number of successes after completing the first stage is > rl, we reject the null hypothesis that p < p_{0} under the futility only design;
and in favor of the alternative: p > p_{1} that establishes treatment efficacy under the futility + efficacy design.
a2: If the number of successes after completing the trial is < a2 then we reject the alternative hypothesis.
r2: If the number of successes after completing the trial is > r2 then we reject the null hypothesis.
n1: Sample size for the first stage.
n2: Sample size for the second stage.
N: Total sample size.
p_{x}: The probability of accepting the null, given p_{a} is true, is < p_{x}.
Running the Program
The user is prompted for the type of calculation to be performed. There are 4
calculation steps. The first step determines the overall sample size for the design. The
second step calculates the sample sizes for each stage. The third step determines SWOG
critical values for the design (which can be modified by the user) and final step
calculates design probabilities for the given study.
1) N (Sample Size Needed for a Two Stage Study)
The user is prompted for values to the following items.
α, the significance level (.05) (unless already specified through another option).
1 - β, the power (.9 unless specified).
p_{0} (latest value).
p_{a} (latest value).
2) SWOG Rule for Finding the a1's and r1's
In this option both p_{0} and p_{a} are specified, along with the value
p_{x}; al and rl are calculated differently from in the
Fleming option. a1 is calculated to be the largest x such that the probability
of getting a smaller value than x (given p_{a} is true) is <= p_{x}.
The power is calculated for an array of p_{a} values.
The output also includes the probabilities for stopping early. Because of space
restriction there are rather terse abbreviations for these. An example is: PE(acc H_{0})/p_{0}.
This means the probability of stopping early because of accepting H_{0} given that
p_{0} is the true probability. The probability of accepting H_{A} given
that p_{0} is the true probability, PE(acc H_{A})/p_{0}, is also
given (and the analogous stuff for p_{a}).