Group Sequential Design for Proportions Calculator

Methodology

This calculator implements the canonical group-sequential framework used for a two-sample Z-test of two proportions. The maximum information is translated to sample size using the assumed alternative proportions. At each planned look, the alpha-spending function determines the cumulative Type I error available through that information fraction; the efficacy boundary is then calibrated so that the sequential crossing probability equals that cumulative spending.

Two-proportion information

For a fixed allocation ratio, the calculator searches over integer group sizes. Under the canonical joint-normal approximation, the standardized treatment effect at information fraction t is θ√(I_maxt). The sequential power is the probability of crossing at least one efficacy boundary under the alternative.

Alpha spending

The default O'Brien-Fleming spending function is the Lan-DeMets analogue of the O'Brien-Fleming design. Pocock, Power-family, and Hwang-Shih-DeCani spending functions are also provided. The final cumulative alpha equals the requested overall alpha.

Validation example

A published nQuery/Statistical Solutions example uses a two-sided α=0.05 design with placebo proportion 0.05, treatment proportion 0.10, 80% power, three looks at 25%, 50%, and 100% of information, and an O'Brien-Fleming alpha-spending function. The reported maximum sample size is 435 patients per group (870 total). This calculator reproduces 435 per group with the unpooled two-proportion Z approximation.

Important scope

• This is a planning calculator for the large-sample two-proportion Z framework represented by nQuery's GST2 procedure.
• The displayed sample size does not include continuity correction, dropout inflation, stratification, unequal information from differential follow-up, or simulation-based small-sample adjustments.
• For a regulatory trial with small expected counts or a design requiring exact reproduction of a vendor's continuity-corrected calculation, verify the final design in the validated statistical software used for the study.

References

Statistical Solutions / Statsols. (2025). nQuery 9.5.1 User Manual, Section 7.2.5.2, “Two Proportions (GST2).” The manual describes the information-to-sample-size translation for the inequality two-sample Z-test for two proportions and identifies GST2 as the group-sequential two-proportion design.

DeMets, D. L., & Lan, K. K. G. (1983). Interim analysis: The alpha spending function approach. Statistics in Medicine, 2, 1–16.

O'Brien, P. C., & Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics, 35(3), 549–556.

Statistical Solutions / Statsols. Unblinded Sample Size Re-estimation – Two Proportions. Published worked example using nQuery: α=0.05 two-sided, p_control=0.05, p_treatment=0.10, 80% power, three looks at 25%, 50%, and 100%, O'Brien-Fleming spending, with 435 patients per group reported.