Group Sequential, Adaptive, and Interim Analysis
Plan a two-group group-sequential study comparing means. Compute Lan-DeMets efficacy boundaries, required maximum sample size for a target power, or attainable power for a specified sample size using O’Brien-Fleming or Pocock spending functions.
The calculator implements the two-sample mean framework described for the nQuery Group Sequential Design for Two Means procedure. The underlying test statistic is the standardized difference in two independent means. At interim looks, the accumulating standardized statistics have the canonical joint-normal correlation structure determined by the information fractions. The design uses Lan-DeMets alpha spending to obtain efficacy boundaries while preserving the prespecified overall Type I error.
Let Δ = μ1 − μ2, let r = N2/N1, and let N1 denote the maximum sample size in group 1. The final standardized drift is
For a specified drift, the corresponding continuous sample size is obtained algebraically. The calculator then rounds the group sample sizes upward when solving for maximum sample size so the requested power is attained or exceeded.
For a two-sided design, the O’Brien-Fleming-type spending function used here is
For a one-sided design it is
The Pocock-type spending function is α*(t) = α log[1 + (e − 1)t]. At each look, the critical Z boundary is solved recursively from the cumulative probability of crossing an efficacy boundary through that look. This is the Lan-DeMets construction rather than simply converting each incremental alpha allocation to an independent-test critical value.
Power is the probability, under the specified treatment difference, that the canonical sequence of Z statistics crosses an efficacy boundary at any scheduled look. For two looks the calculation uses direct numerical integration of the bivariate normal distribution. For three to five looks, the page uses deterministic numerical integration of the corresponding sequential normal transition densities. This avoids a simulation-based result and keeps the calculator self-contained in the browser.
A published nQuery example uses a two-sided Z-test with α = 0.05, means −2.3 and −1.5, common SD = 2.1, one interim analysis plus the final analysis (2 looks), an O’Brien-Fleming spending function, equal allocation, and a target power of 80%. nQuery reports 109 patients per group, 80.16% achieved power, and a drift of 2.813.
With the same inputs, this implementation returns 109 per group, approximately 80.15% power, and drift approximately 2.812. The displayed drift differs only in the final decimal because the nQuery example reports a rounded drift value while the calculator derives it directly from the integer maximum sample size.
The worked example is documented by Statistical Solutions/nQuery in its published hypothesis-testing example for the Group Sequential Test of Two Means.
Statistical Solutions / nQuery. nQuery Advanced User Manual, Section 4, “Group Sequential Designs, Interim Monitoring & Unblinded Sample Size Re-estimation,” describing group sequential planning for two means and the nQuery Group Sequential Design for Two Means table. nQuery Advanced User Manual.
O’Brien, P. C., & Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics, 35(3), 549–556.
Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika, 64(2), 191–199.
Lan, K. K. G., & DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika, 70(3), 659–663.
DeMets, D. L., & Lan, K. K. G. (1994). Interim analysis: The alpha spending function approach. Statistics in Medicine, 13(13–14), 1341–1352.
Reboussin, D. M., DeMets, D. L., Kim, K., & Lan, K. K. G. (2000). Computations for group sequential boundaries using the Lan-DeMets spending function method. Controlled Clinical Trials, 21(3), 190–207.
Jennison, C., & Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC.