Gehan Two Stage Design

This page provides an assessment of the sample sizes for the two stages of the Gehan (1961) phase II clinical trial. This design provides for stopping due to futulity after Stage I, when, even a user specified minimal response seems unlikely. Should the minimal response be plausible, the second stage provides estimates of the response rate with user specified Standard Errors (SE). The futility assessment at Stage I followed by the confidence interval estimation softens the hypothesis testing approach used in similar contexts such as the Simon two-stage design and the Fleming Designs. The Gehan appraoch may be helpful in moving a therapy forward in contexts with high disease burden, in salvage settings where even minimal response may be attractive, or where the therapy is being considered for subsequent combination with other agents.

Assessment of Futility

The futility decision in stage I is based on the occurrance of a large successive string of non-responders. The size of the string of patients is determined by the first box of the calculator. In the default example we consider a minimal response rate of 20% and a single-sided significance level of 0.05. The 5% or 10%, 1-sided level is often used in early phase designs but the calculator permits other choices of the significance level. For these choices, a 14 patient first stage is recommended.

Continuation into Second Stage

The second stage sample size can be determined at the start of the trial should resource committments for this stage need to be made prior to the start of the first stage. This can be done through the use of a 50% response rate when computing the second stage sample size, as this yields the worst case margin of error (standard error) in estimation. Alternately the second stage sample size can be computed using data in the first stage to get a narrower, yet somewhat conservative, margin of error. Here instead of 50%, Gehan uses an SE estimator obtained using the Wald Normal Approximation based 75% Upper Confidence Limit of the stage I response rate. For details see documentation in this note. The user can choose either method to assess the second stage sample size through the drop-down for the ‘Method for Computing Second Stage Size’. When ‘Conservative Using Stage I Data’ is chosen (as we have) the fields for the actual Stage I size and the number of responders allow entry of data. They are blacked out otherwise.

We have N1 = 15 and 2 responders entered. The planned number may sometimes differ from actuals (15 here instead of 14) and the data field allows for the entry of a different sample size from that planned. As an aid to the user, the calculator computes the SE corresponding to a trivial second stage of 1 patient. The user should enter, in the next field, an SE less than this when specifying a maximum margin of error. A further aid is the width of the 90% Confidence Interval (CI) associated with this SE in estimation. In the default setting of this calculator we have a standard error of 6%, which is less than the SE we obtain for the trivial second stage of 10.6%. The 90% CI width corresponding to the maximum 6% margin of error is 9.9%. The second stage sample size computes as 35, with a total sample size of 50.

Analysis on Trial Completion

The third box of the calculator allows for the determination of the CI estimate of the proportion responding once the trial terminates. You can enter the final sample size and the final number of responders to obtain either a Wald Normal Approximation Interval or a Wilson Score Interval at the required confidence level. The Wilson score interval estimate has similar improved optimality properties like some of the CI estimation procedures that analysts would use, for smaller samples, instead of the Normal Approximation estimate. The optimality of the latter improves with larger sample sizes. Further, the confidence limits for the Wilson method are bounded between 0% and 100%. For the Wald limits, we reset limits to this range should smaller proportions/sample sizes lead to confidence limits outside this plausible range. A total sample size of 51 with 6 responders, corresponds to a 90% Wilson’s Score based CI of (6.21%, 21.17%), around an estimate of 11.76%.

Edit the blue cells in the spreadsheet and enter your data and the calculations in the spreadsheet will refresh. Ensure that the blue cells entries in each box reflect your context rather than default values.