Proportions: One and Two Groups
Plan or evaluate a two-arm group sequential Z-test for a difference in proportions. The calculator uses information-based alpha-spending boundaries, supports equal or user-specified information times, and computes maximum sample size or attainable power entirely in your browser.
A group sequential trial evaluates the treatment effect at several planned information times rather than only once at the end. The overall type I error is preserved by spending the cumulative alpha budget over information time and solving for correlated sequential Z boundaries. nQuery describes its GST2 procedure as an inequality two-sample Z-test for two proportions, with pooled or unpooled variance, and translates the maximum information to sample size through the two group proportions and allocation ratio.
At information fraction t, the sequential Z-statistic has mean drift × √t under the planning alternative. The calculator evaluates the joint normal process recursively, retaining only probability mass that has not crossed a stopping boundary at an earlier look.
The calculator implements four standard cumulative spending functions. Pocock uses the Lan-DeMets form α(t) = α log[1 + (e - 1)t]. O'Brien-Fleming uses the Lan-DeMets form based on the fixed-final-analysis normal critical value. The power family uses α(t) = αtρ. Hwang-Shih-DeCani uses the gamma family α(t) = α[1 - exp(-γt)]/[1 - exp(-γ)]. At each look, the critical boundary is solved numerically so the cumulative crossing probability under H0 equals the cumulative alpha spent through that information time.
For sample-size calculations, the program searches for the smallest integer maximum n1 whose computed power reaches the requested target, with n2 determined by the allocation ratio. For power calculations, it reports the attainable probability of crossing an efficacy boundary at one of the planned looks. This is a planning calculation based on the normal approximation; no continuity correction is applied.
The Statistical Solutions manual gives a historical two-proportion group-sequential example with p1 = 0.40, p2 = 0.60, α = 0.05, one-sided testing, five equally spaced looks, no continuity correction, a Pocock spending function, and a 90% power target. Its reported result is 129 participants per group and 90.12% power. The present implementation independently evaluates the same planning setup using numerical joint-normal integration; with the pooled variance parameterization used here it gives 130 participants per group and approximately 90.14% power. The one-participant difference reflects the numerical/variance implementation difference from the historical software calculation rather than changing the underlying group-sequential design.
Statistical Solutions Ltd. (2010). nTerim 2.0 User Manual: Power and Sample Size for Group Sequential Trials, Section 3.2, Two Proportions. The manual states that the two-proportion group-sequential calculations use the Lan-DeMets alpha-spending approach and procedures described by Reboussin et al. (1992) and Jennison & Turnbull (2000).
nQuery / Statsols. (2026). nQuery Advanced User Manual, Section 7.2.5.2, Two Proportions (GST2). The current documentation describes GST2 as an inequality two-sample Z-test for two proportions and gives pooled and unpooled information translations.
Reboussin, D. M., DeMets, D. L., Kim, K. M., & Lan, K. K. (1992). Computation of group sequential boundaries in clinical trials. Statistics in Medicine, 11, 1083–1096.
Jennison, C. & Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC.