StatsToDo : Sample Size for Phase II Study (Gehan's Procedure)
Explaination, Calculations and Tables

Introduction Calculations Sample Size Tables
This page provides explanations, calculations, and sample size tables for Phase II trials using Gehan's procedure. Comparison with other Phase II procedures are discussed in the Phase II Studies Explained Page .

Gehan's is for a preliminary study of a new treatment, to test whether the proportion of success from the treatment satisfies the level required to warrant further detailed study in a Phase II trial.

• Stage 1 :
• Sample size for stage 1 (s1) is the number of cases to be used in stage 1. This depends on
• The proportion of success required (p) is defined, a value between 0 (0%) and 1 (100%)
• The power required, the ability to detect that proportion if it is there. Mathematically power = 1-β, where β is the probability of error in rejecting the new treatment
• At the end of stage 1, after s1 cases are included, k = the number of successes found
• If k=0 or k< a critical value where reaching the required proportion of success is unlikely, the treatment is rejected without proceeding to stage 2
• If k> a critical value where reaching the required proportion of success is likely, the treatment is accepted without proceeding to stage 2
• Otherwise, stage 2 of the procedure is required for decision making.
• Stage 2 :
• The sample size in stage 2 is the number of additional cases to be used in stage 2 This depends on
• The number of cases alr3eady used in stage 1 (s1)
• The number of successes (k) found in stage 1
• The acceptable probability of error for a decision to acceot the treatment (ε)
• The total number of successes is the number of successes in stage 1 (k) + number of successes in stage 2 .
• The required total number of successes for a decision to accept the treatment is n = p(s1+s2)
• if the total number of successes reached n, then the trial can be terminated, with a decision to accept the treatment
• If at the end of stage 2, the total number of successes had not reached n, then a decision to reject the treatment is made.
Calculations are provided in to modes
• A Javascript program allows the user to estimate sample size requirement immediately on the web page, without the need to set up other applications.
• R codes to detail the calculations, and to allow the algorithm to be copid and incorporated into other applications.
The tables on this page provides the results of calculations for Gehan's 2 stage prod=cdures
• Three levels of power (1-β) at 0.8, 0.9, and 0.95
• Two level of error (ε) at 0.05 and 0.1
• Required proportion of successes :
• From 0.03 (3%) to 0.2 (20%) at 0.01 (1%) intervals
• From 0.2 (20%) to 0.3 (30%) at 0.02 (2%) intervals
• From 0.3 (30%) to 0.5 (50%) at 0.05 (5%) intervals
• From 0.5 (50%) to 0.9 (90%) at 0.1 (10%) intervals
• The cells contains results
• Blanks for impossible situations, where k>s1
• R is the combination of s1 and k that allows the treatment to be rejected at the end of stage 1
• A is the combination of s1 and k that allows the treatment to be accepted at the end of stage 1
• Cells with numbers are combinations of s1 and k that From 0.3 (30%) to 0.5 (50%) at 0.05 (5%) intervals
• From 0.5 (50%) to 0.9 (90%) at 0.1 (10%) intervals

### References

Gehan E A (1961) The determination of the number of patients required in a preliminary and a follow-up trial of a new chemotherapeutic agent Journal of Chronic Diseases. 13:4, Pages 346-353

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. 255-256