How to Use the BioStatHub Simon's Two-Stage Design Calculator

What This Tutorial Covers

This is a step-by-step guide to the BioStatHub calculator rather than a statistics primer. It takes one illustrative single-arm Phase II trial through the workspace: entering the assumptions, generating candidate Simon's two-stage designs, comparing them, selecting one, and documenting and exporting the decision. Every number shown comes from BioStatHub's exact calculations for the stated inputs.

The statistics behind each screen — the decision rule, how PET, expected sample size, Type I error and power are calculated, and how to choose between the designs — are worked through for the same example in the Simon's two-stage design example. For the design in general, see Simon's two-stage design explained.

Before you begin, gather four assumptions: an unacceptable response rate (p₀), a promising response rate (p₁), an acceptable type I error (α), and a target power (1 − β, entered in BioStatHub as β). You also need two operational facts: the largest number of patients your site network could realistically enroll, and whether the protocol can pause enrollment for an interim analysis. The tutorial closes with a documented, exportable design record.

Step 1: Define the Trial Assumptions

Create a study and open the Study Parameters panel. You enter the four assumptions; everything else follows from them.

Enter the null response rate (p₀) and the target response rate (p₁) under Response Assumptions; p₁ must be greater than p₀. Enter the Type I error (α) and the Type II error (β) under Statistical Criteria. BioStatHub asks for β directly and displays power = 1 − β beneath the field. The Generation Settings can usually be left at their defaults.

The assumptions used throughout this guide are illustrative — they demonstrate the workflow rather than recommend values for any particular indication:

Step 2: Generate Candidate Designs

Select Generate Designs at the top right of the workspace. BioStatHub searches every two-stage design that satisfies your α and power requirements up to the sample-size limit it is searching — 300 patients by default — and returns those on the admissible frontier rather than a single answer.

Three labels appear in the results. The Optimal design has the lowest expected sample size under p₀, the Minimax design has the lowest maximum sample size, and the Admissible designs sit between the two. All of them meet the same α and power criteria.

Read the columns as a single design rather than as independent numbers:

Step 3: Compare Designs and Interpret the Results

Tick the checkboxes beside the candidates in the Overview table and select Compare selected. The Compare view puts the chosen designs side by side against a benchmark design you nominate, and shows the trade-off rather than a verdict.

In Original mode, the comparison table shows the benchmark's values and every other selected design as a difference from it. Normalized mode instead places each design among all the admissible designs for the study, from 0 (best) to 1 (worst). The table includes expected sample size under p₁ as well as under p₀, so you can see how much each design enrolls when the treatment is promising, not only when it is inactive. Type I error and power are the exact rates each design achieves; all four stay at or below α = 0.05 and at or above 0.80 power.

The two numbers that usually drive the decision are expected sample size EN(p₀) and maximum sample size N. How they, PET(p₀), Type I error and power are calculated for these designs is shown step by step in the Simon's two-stage design example.

The complete output for the worked example, rounded from BioStatHub's exact calculation, is:

Step 4: Select and Finalize a Design

Selecting a design is a judgement about which constraint binds your study. If accrual is slow, the indication is rare, or the ethics committee will scrutinise total exposure, the Minimax design's cap of 25 patients is the strongest argument. If the priority is to expose as few patients as possible when the treatment is inactive, and 29 is deliverable, the Optimal design's expected 15.01 is the better case. If both matter, the intermediate admissible designs are the defensible middle, and Admissible(1) is where most of the expected saving is available for a single extra patient.

The Study Priority selector above the table (Balanced, Minimize Expected Sample Size, Minimize Maximum Sample Size) changes which candidate is highlighted as recommended; it does not change any calculation. Treat the recommendation as a starting point for the discussion rather than the decision itself.

Select a row in the Overview table to open Design Details. Check the six metrics against your assumptions, read the trade-off summary, and expand Operating curves if you want to see how the design behaves across the whole range of response rates before committing. When you are satisfied, select Set as Final Design.

Step 5: Document the Decision

Once a design is final, a Documented rationale field appears in Design Details. This is where you record why this design was chosen — the constraint that drove it, the alternatives you rejected, and any trade-off you accepted. Save rationale stores it with the study, and it is carried into the finalized protocol and the exported reports so that a reviewer can follow the reasoning without reconstructing it.

The Finalized Protocol view gathers the frozen inputs, the stopping rules, the operating curves, and the validation evidence for the selected design in one place. The Validation tab adds a Monte Carlo simulation check against the exact calculation, reporting the random seed, the maximum observed relative error, and a theoretical-versus-simulated table for type I error and power. Because the seed is recorded, the check can be repeated.

Keeping these two records together — the reason for the choice and the evidence that the design meets its criteria — is what turns a calculation into something a protocol author, a statistician, and a reviewer can all work from.

Exporting and Sharing the Record

The Export & Documentation tab is where the record leaves the workspace. Export all designs or a single design as JSON or CSV for the statistical analysis plan and any downstream analysis; export the operating characteristics to keep the exact power, expected sample size, and early-termination curves alongside the protocol; or create a read-only share link that shows co-investigators and reviewers the frozen results without an account.

Narrative PDF, Word, and LaTeX reports are available where the account has report access; where they are not, the report cards are shown as coming soon. Everything described here is the reproducible record of a design decision — the exact inputs, the boundaries, the achieved error rates, and the reason for the choice — which is what a protocol reviewer needs in order to check the design rather than take it on trust.

Key Takeaways

Simon's two-stage designs are chosen from a family, not looked up as a single answer: Optimal, Minimax, and the admissible designs between them all satisfy the same α and power criteria.

Read the interim rule and the final rule together. In this example all four candidates require six or more responses for a positive result; they differ in how many patients are exposed before the first decision and in the maximum enrollment.

Expected sample size and maximum sample size trade off directly. Lowering n₁ raises PET(p₀) and lowers the expected enrollment, but the larger stage-two cohort required to keep power increases the maximum.

Use the frontier and the operating curves to judge how sensitive the design is, then choose according to the constraint that binds your study rather than accepting a default.

Record the rationale and keep the validation evidence with the protocol. The design is only reproducible if the assumptions, boundaries, and reason for the choice travel together.

Frequently Asked Questions