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Group Sequential, Adaptive, and Interim Analysis

Promising Zone Design Sample Size Calculator

Calculates the original two-arm sample size and performs a Promising Zone sample-size reassessment at a single unblinded interim analysis using conditional power. Based on the adaptive framework of Mehta & Pocock (2011), as implemented for the continuous-outcome two-sample setting.

Trial Design

Two-arm parallel design, equal allocation, continuous endpoint, common known standard deviation, one-sided normal test.

Sample Size Recommendation

The reassessment uses the observed interim effect as the assumed treatment effect when calculating conditional power.
Enter the trial parameters and click Calculate Sample Size.

Methodology

This calculator implements the Promising Zone approach described by Mehta and Pocock (2011). The initial design is a two-arm parallel trial with equal allocation and a continuous endpoint. The original total sample size is chosen to achieve the specified power for the planned treatment difference under a common standard deviation.

Initial sample size

For total sample size N, with equal allocation, the standard error of the treatment difference is 2σ/√N. For a one-sided normal test, the continuous approximation is therefore:

N0 = 4σ2(zα + zβ)2 / δ2

The result is rounded up to the next even integer so that the two treatment groups remain equally sized.

Interim test statistic

At the interim analysis, the observed treatment difference δ̂1 is standardized using the interim information:

z1 = δ̂1√n1 / (2σ)

The calculator then evaluates conditional power under the observed interim treatment effect. For a candidate final total sample size N, the conditional power is:

CP(N) = Φ &left[ δ̂1√(N-n1)/(2σ) - {zα√N-z1√n1} /√(N-n1) &right]

Promising-zone classification

The interim result is divided into three regions using conditional power calculated at the original planned sample size:

Unfavorable: CP < CPmin
Promising: CPmin ≤ CP < target power
Favorable: CP ≥ target power

In the unfavorable and favorable zones, the original total sample size is retained. In the promising zone, the sample size is increased to the smallest feasible even total sample size for which the conditional power reaches the target, subject to the prespecified maximum total sample size.

N* = min{ smallest even N such that CP(N) ≥ target power, Nmax }

This is the continuous-outcome version of the adaptive promising-zone framework. The lower conditional-power cutoff is a design parameter and must be selected prospectively. It is not automatically safe to choose an arbitrary cutoff if conventional final inference is intended; the type-I-error properties depend on the prespecified promising-zone rule and the associated adaptive design.

Worked example

The following values reproduce the continuous-outcome example discussed by Mehta and Pocock: a one-sided α of 0.025, 80% target power, planned treatment difference δ = 2, common SD = 7.5, interim analysis at n1 = 208, original total sample size of 442, maximum total sample size of 884, and a promising-zone lower conditional power of 0.365.

For validation of this calculator, suppose the observed interim treatment difference is 1.5. The interim standardized statistic is approximately 1.4422 and the conditional power at the original N = 442 is approximately 0.5776. This places the result in the promising zone. Solving for the smallest even total sample size that reaches 80% conditional power gives N = 712; its conditional power is approximately 0.8001. Thus the calculator returns a recommended total sample size of 712.

Scope and interpretation

References

Mehta, C. R., & Pocock, S. J. (2011). Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine, 30(28), 3267–3284. DOI: 10.1002/sim.4102.

Chen, Y. H. J., DeMets, D. L., & Lan, K. K. G. (2004). Increasing the sample size when the unblinded interim result is promising. Statistics in Medicine, 23(7), 1023–1038. DOI: 10.1002/sim.1688.

Gao, P., Ware, J. H., & Mehta, C. (2008). Sample size re-estimation for adaptive sequential design in clinical trials. Journal of Biopharmaceutical Statistics, 18(6), 1184–1196.

Advanced User Manual, Section 4.3, “Interim Monitoring and Unblinded Sample Size Re-estimation.” Statsols/ documentation. The documentation describes the use of conditional power to identify promising interim results and increase sample size when the interim result is promising.