 Content DisclaimerCopyright @2020.All Rights Reserved.
StatsToDo : Sample Size for Phase II Study (Simon's Procedure)
Explained, Calculations, and Tables

Introduction Calculations Sample Size Tables
Introduction Technical Considerations Example
This page provides explanations, calculations, and sample size tables for Phase II trials, where the sample size needed is determined by Simon's procedure.

Only Simon's two stage procedure will be discussed in this page. Readers are referred to the Phase II Studies Explained Page for Phase II studies generally and for comparison with other procedures available.

Simon's is a two stage procedure.

• The first stage requires a small sample size (n1), and sets a bench mark number of successes (r1) above which the trial enters the second stage. If that bench mark (r1) is not surpassed at the end of stage 1 (n1), then the trial ends with the treatment considered inadequate and abandoned (rejection).
• In the second stage, the total sample size, including those already collected in stage 1, is defined (nTot), and a second and final bench mark for the total number of successes, including those already collected in stage 1, is defined (rTot). once the number of successes surpassed rTot, the trial can terminate and the treatment considered worthy of further evaluation at the Phase III or control trial level (acceptance). If rTot is not surpassed after nTot cases, then the trial terminates, and the treatment considered inadequate and abandoned (rejection).
• Please note: In Simon's procedure, acceptance and rejection refers to whether the treatment being tested is successful enough for further evaluation, but not the acceptance or rejection of the null hypothesis
Simon's procedure therefore has advantages over Fleming's Procedures as in the Sample Size for Phase II Study (Fleming's Procedure) Page and Gehan's Procedure as in the Sample Size for Phase II Study (Gehan's Procedure) Page , in that the sample size is not fixed, and the trial can terminate early if the results are obvious. It is particularly effective in rejecting new treatments with below expectation proportion of successes.

Parameters : The following parameters are required

• The success rate below which the treatment is considered inadequate and rejected (π0)
• The success rate above which the treatment is accepted as worthy of further evaluatuion (π1)
• Probability of Type I Error (α), the probability of error for rejecting the null hypothesis, that of wrongly accepting the treatment as worthy of further evaluation. In most cases α of 0.1 or 0.05 is used
• Power (1-β) where β is the Probability of Type II Error. Power is therefore the probability of accepting the treatment as worthy of further evaluation, and in most cases power of 0.8 or 0.9 is used
Results : The programs produces the following results
• The maximum sample size for stage 1 (n1)
• The number of success required in stage 1, above which stage 2 is entered, and at or below which after n1 cases results in terminating the trial with rejection of the treatment
• The total maximum sample size (nTot), inclusive of both stages
• The total number of success required (rTot), inclusive of both stages, above which resulting in terminating the trial with acceptance of the treatment for further evaluation, and at or below which after nTot cases results in rejection of the treatment
• The average expected number of cases (EN) for a decision
• The probability of early termination of the study (PET) if the true success rate is below requirements
Models : Simon's Procedure produces two alternative results, based on different statistical assumptions.
• The Optimal model has a smaller sample size for stage 1 and is more likely to terminate early (PET) if the true success rate is below requirement (<π0), so is preferred for early screening of new treatments to exclude those without potentials from expensive further study.
• The minimax model requires a smaller overall sample size (EN), so is preferred if the researcher is optimistic about the treatment being tested, hoping to require a smaller overall sample size to validate the acceptance of the treatment for further trials

### References

Simon R (1989) Optimal two-stage designs for phase II clinical trials. Control Clin Trials 10:1-10

Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for Clinical Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 256-257