## Box 52 A phase II trial using Gehans twostage design

A phase II trial in recurrent malignant glioma aimed to assess the activity of human lymphoblastoid interferon [18]. The minimum useful response rate was considered to be 20%. The minimum number of failures (n) satisfying (1 - 0.2)n < 0.05 is 14. Therefore, the first stage of the trial aimed to include fourteen patients, and would stop after the first stage if no responses were seen, concluding that the probability that the true response rate was at least 20% was less than 5%.

The aim in the second stage was to estimate the response rate with a standard error of no more than 10% (i.e. £ = 0.1). The upper 75% confidence limit is calculated for a range of response rates in the first stage thus, for example:

If, say, five relapses were seen in the first fourteen patients (a response rate of 35.7%), the upper 75% confidence limit would be given by

0.357 + 0.6745 x ^[0.357 x (1 - 0.357)/14] = 0.4435.

Therefore, n2 = [0.4435 x (1 - 0.4435)/(0.10)2] - 14 = 10.7 (round up to 11).

Therefore, if five responses were seen in the first fourteen patients, an additional eleven patients would be needed to estimate the overall response rate with a standard error of no more than 10%.

The optimal/minimax Simon Design [19]

This design allows either the number of patients in the 1st stage, or the total number of patients to be minimized if the treatment has an inadequate response rate, subject to specification of the error rates. The former is known as the optimal design, the latter as the minimax design. As for the Fleming single-stage design, this requires specification of an unacceptable level of activity (p1) and an activity level above which there would be interest in taking the treatment forward for further testing (p2).

The sample size formulae for this design are not straightforward, and therefore we refer readers to tables such as those by Machin et al. [20] for further details. An example of how the Simon design was used in the design of a randomized phase II/III trial in metastatic germ cell cancer is shown in Box 5.3.

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