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Dose-Finding & Phase I/II Design

Simon's Two-Stage Design Calculator

Computes the real Optimal and Minimax designs for a single-arm Phase II trial, searched directly in your browser — no external server, no third-party app.

Design Parameters

Response rate that would NOT justify further study
Response rate that WOULD justify further study
P(declare promising | true rate = p₀)
P(declare promising | true rate = p₁)
Runs entirely in your browser, typically in under a second even at the maximum.

Results

All designs shown satisfy your α and power constraints exactly — not approximated.
Enter parameters and click Compute Designs.

How This Calculator Works

Simon's two-stage design (Simon, 1989) tests whether a single-arm Phase II trial's true response rate exceeds an unacceptable level p₀ in favor of a desirable level p₁. Rather than enrolling all patients up front, the trial enrolls n₁ patients first: if r₁ or fewer respond, the trial stops for futility before any more patients are exposed to an ineffective treatment. Otherwise, it continues to the full sample size n, and rejects the null hypothesis if more than r total patients respond.

This calculator searches every feasible combination of (n₁, r₁, n, r) up to your specified maximum sample size, computes the actual Type I error and power of each design exactly via the binomial distribution (not an approximation), and returns two designs:

Optimal design: minimizes the expected sample size under p₀ — the design that on average exposes the fewest patients to an ineffective treatment.
Minimax design: minimizes the maximum possible sample size n — the design with the smallest worst-case trial size, at the cost of a somewhat higher expected sample size.
Admissible designs (Jung, Carey & Kim, 2001; formalized by Jung, Lee, Kim & George, 2004): the designs on the lower convex hull between Minimax and Optimal in the (n, expected N) plane — found by starting at Minimax and repeatedly jumping to whichever remaining design gives the steepest reduction in expected N per patient added, until reaching Optimal. This is stricter than simply "not dominated by any other design": a design can fail to be dominated by any single alternative and still not be admissible, if a mix of two other admissible designs would out-perform it under every possible weighting between minimizing n and minimizing expected N. When Optimal and Minimax differ substantially, these intermediate designs are often the actual best practical choice.

Validation

This implementation has been checked directly against a real published clinical trial protocol using identical parameters (p₀=0.10, p₁=0.30, α=0.05, β=0.20): both the Optimal design (n₁=10, r₁=1, n=29, r=5) and Minimax design (n₁=15, r₁=1, n=25, r=5) match exactly, including the actual achieved Type I error and power.

References

Simon, R. (1989). Optimal two-stage designs for phase II clinical trials. Controlled Clinical Trials, 10(1), 1–10.

Jung, S.H., Carey, M., & Kim, K.M. (2001). Graphical search for two-stage designs for phase II clinical trials. Controlled Clinical Trials, 22(4), 367–372.

Jung, S.H., Lee, T., Kim, K.M., & George, S.L. (2004). Admissible two-stage designs for phase II cancer clinical trials. Statistics in Medicine, 23(4), 561–569.