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StatsToDo : Sample Size for Phase II Study (Gehan's Procedure) Explained and Tables
Introduction Sample Size Tables R Code
Gehan's procedure, and its comparison against other procedures available for the Phase II trial, are discussed in the Phase II Studies Explained Page . This page provides support for the use of the program in the Sample Size for Phase II Study (Gehan's Procedure) Program Page and the tables in this page.

Gehan's is 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.
The program in the Sample Size for Phase II Study (Gehan's Procedure) Program Page produces the results of Gehan's 2 stage procedures.
• The entry data is a single column of 3 rows, where
• Row 1 = ε, Probability of error for accepting the treatment for further study
• Row 2 = Power(1-β), where β is the probability of error for rejecting the treatment for further study
• Row 3 = p, the probability or proportion of successes required for accepting the treatment for further study
• The result are :
• The sample size for stage 1
• A table where each row is the parameters related to each value of k
• k = the number of successes in stage 1
• s2 = the sample size for stage 2
• n = the number of successes required (combine stage 1 and 2) for the treatment to be accepted.
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