## Box 51 A phase II trial in high risk stage I nonseminomatous germ cell tumours NSGCT using Flemings single stage design

Patients with high risk stage I NSGCT have a 40% risk of relapse within two years of diagnosis if receiving no post-surgical adjuvant treatment. Most high risk patients receive adjuvant chemotherapy, although for 60% of patients this is unnecessary. Interest surrounded the ability of an alternative scanning method, PET scanning, to identify a group of patients (those with a negative PET scan) with a sufficiently low risk of relapse that they could be spared adjuvant chemotherapy. Because of the expense, it is necessary to demonstrate that a PET scan provides a high level of discrimination between groups with a high (PET positive) and low (PET negative) risk of relapse. Amongst the PET —ve patients it was felt that a relapse-free rate of less than 80% would not provide sufficient discrimination, but that a relapse-free rate of 90% or more would. Using Fleming's single stage design, p1 = 0.8 and p2 = 0.9. Setting a to be 0.05 (so Z1-a = 1.6449) and p to be 0.1 (so Z1-p = 1.2816) 109 PET -ve patients are required.

### Suppose

£ = standard error of response rate r (the overall study response rate), ri(r2) = number of responses in the 1st (2nd) stage, and n1 (n2) = number of patients in the 1st (2nd) stage,

Then

£ = V[r(1 - r)/(n + «2)] where r = (n + r2)/(n + «2). This can be rearranged to calculate n2:

However, after the first stage we will know only r1 and thus the overall response rate r must be estimated. r1/n1 could be used, but to add a degree of conservatism, Gehan recommended using instead the upper 75 per cent confidence limit r1/n1. This can be calculated approximately as:

r1/n1 + Z0.75 x SE(r1/n1); where Z0.75 = 0.6745 and

Therefore the overall sample size depends critically on the response rate seen in the first stage of the study; the closer it is to 0.5, the larger the sample size necessary in the second stage to achieve the same precision. An example of a trial designed using Gehan's method is shown in Box 5.2.