# Two Stage

Program Code

Two Stage is available as a both a JavaScript and Server-side program. The JavaScript version may be downloaded as a Web page and run without an Internet connection. The Server-side version is provided in case your Web browser does not adequately support JavaScript (for example, Microsoft Pocket PC Phone browser). Both were coded by CRAB programmer Brent Hostetler. The original code was written in FORTRAN by an unidentified SWOG programmer.

Accessing the Program

The SWOG Web page under Stat Tools.

Sample Sizes for a Multi-stage Phase II Trial

Source

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.

Definition of Variables

These are definitions of all variables referred to in the documentation:

 P0 The largest success probability which, if true, would imply that the treatment regimen does not warrant further investigation. Pa 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 > Pa. Rl If the number of successes after completing the first stage is > Rl, we reject the null hypothesis that p < P0. 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. Za The probit of 1-a. (The Z value corresponding the alpha level: i.e., 1.6449 for a significance level of .05.) px The probability of accepting the null, given Pa is true, is < px. (See details in SWOG option.) Zx The probit of 1-px.

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.

• a, the significance level (.05) (unless already specified through another option).
• 1-b, the power (.9 unless specified).
• P0 (latest value).
• Pa (latest value).

2) SWOG Rule for Finding the A1's and R1's

In this option both P0 and Pa are specified, along with the value px; 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 Pa is true) is <= px.

The power is calculated for an array of Pa values, which are in an input file created by this program; you may edit this file. The editing feature is mainly intended for the Pa values, which have defaults ranging from P0+.1 to P0+.35. It may also be used to edit the A1 and R1. Warning: The program will only find the power for the values given in this file - it will not recalculate the A1 and R1, or any other 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 H0)/P0. This means the probability of stopping early because of accepting H0 given that P0 is the true probability. The probability of accepting Ha given that P0 is the true probability, PE(acc Ha)/P0, is also given (and the analogous stuff for Pa).

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