Group Sequential, Adaptive, and Interim Analysis
Planning calculations for a two-stage seamless Phase II/III trial in which several treatments are evaluated in Stage 1, a promising treatment is selected at the interim analysis, and Stage 1 and Stage 2 evidence are combined using the weighted inverse-normal framework. The calculator provides the corresponding planning power and the Stage 2 sample size needed to reach a specified target power.
For K = 5, m1 = 28, m2 = 140, sigma = 5 and one-sided alpha = 0.025, Hampson & Jennison report a BK inverse-normal Dunnett critical value of 1.958.
An adaptive seamless Phase II/III design combines a learning stage and a confirmatory stage into one trial. In a typical two-stage design, several active treatments are studied against a common control in Stage 1. At the interim analysis, one or more promising treatments can be selected for continued evaluation in Stage 2. The final analysis then combines evidence from the two stages while accounting for the treatment-selection step.
The planning calculation implemented here uses the weighted inverse-normal combination framework. For independent stage-wise standardized test statistics, the combined statistic is
The weights are proportional to the square root of the planned information contribution from each stage. This is the standard weighted inverse-normal combination rule used in seamless Phase II/III methodology.
For a two-arm comparison with equal allocation and a normally distributed endpoint with common standard deviation σ, the expected standardized treatment-effect contribution from a stage containing m patients per treatment group is
Consequently, the noncentral mean of the weighted combination statistic is
If c is the prespecified critical value, the corresponding planning power is calculated as
The Stage 2 sample-size calculation searches upward over integer values of m2 until the target power is reached. The resulting total enrollment is
The first term is the complete Stage 1 enrollment across K active treatments plus the common control. The second term represents the selected treatment and control continued into Stage 2.
Treatment selection creates a multiple-testing problem. The published confirmatory seamless-design procedures therefore use methods such as Dunnett-based closed testing combined with an inverse-normal or inverse-χ2 combination function to maintain familywise type I error. The critical value is design-specific rather than a universal 1.96 cutoff.
This calculator deliberately separates the published critical value from the normal-endpoint planning equation. It is therefore appropriate as a transparent planning calculator when the validated critical value for the selected seamless design is supplied. It should not be interpreted as a replacement for the full simulation-based operating-characteristic evaluation required for a regulatory trial with complex treatment selection, different endpoints, multiple selections, or adaptive sample size modifications.
Hampson and Jennison provide a published seamless Phase II/III example involving five active treatments and a common control. The Stage 1 sample size is 28 patients per group and the Stage 2 sample size is 140 patients per selected treatment/control group. The assumed standard deviation is 5, the clinically meaningful treatment effect is 2, and the one-sided familywise significance level is 0.025. For the BK inverse-normal Dunnett procedure, the published critical value is 1.958.
With these values, the calculator reproduces the published critical-value target of 1.958. The power displayed by this page is the corresponding weighted-normal planning approximation; the paper's reported operating characteristics were obtained by large-scale simulation of the complete treatment-selection procedure.
Bretz, F., Schmidli, H., König, F., Racine, A., & Maurer, W. (2006). Confirmatory seamless Phase II/III clinical trials with hypotheses selection at interim: General concepts. Biometrical Journal, 48(4), 623–634.
Hampson, L. V., & Jennison, C. (2015). Optimizing the data combination rule for seamless phase II/III clinical trials. Statistics in Medicine, 34, 39–58.
Stallard, N., & Todd, S. (2011). Seamless Phase II/III designs. Statistical Methods in Medical Research, 20(6), 623–634.
/ Statsols. Adaptive Clinical Trial Design Software. Adapt documentation and product information covering group sequential, sample-size re-estimation, and seamless Phase II/III designs.