Group Sequential, Adaptive, and Interim Analysis
Calculates conditional power and the futility index at an interim analysis using the stochastic-curtailment approach. The calculation asks how likely the final analysis is to reject the null hypothesis, given the information observed so far and a specified alternative treatment effect. Runs entirely in your browser.
Stochastic curtailment uses conditional power to determine whether continuing an ongoing study is unlikely to produce a statistically significant final result. The conditional power is calculated using the observed interim test statistic, the information available at the interim analysis, the planned final information, the significance level, and a specified alternative treatment effect.
For an upper one-sided test, the general conditional-power calculation used here is the normal-information formulation documented in the statistical literature/the software. Let Ik denote information at the interim analysis and IK the information at the planned final analysis. Then:
Here, θ = δ1 − δ0 is the assumed treatment effect under the alternative hypothesis. For the paired-mean information formulation used in the this method worked example, Ik = nk/σd2 and IK = N/σd2.
The futility index is one minus conditional power:
A stochastic-curtailment rule stops the study for futility when conditional power falls at or below the prespecified threshold. A common example is CP ≤ 0.20, although the threshold must be specified as part of the trial's monitoring plan. This calculator therefore reports both the conditional power and the corresponding futility index rather than treating the 20% threshold as universally required.
For a fixed information level and alternative effect, the calculator also reports the interim Z value at which conditional power equals the selected futility threshold. Observed Z values at or below this boundary produce a futility recommendation for an upper one-sided test.
where γ is the futility conditional-power threshold and zγ = Φ−1(γ).
Conditional power depends on an assumption about the future treatment effect. In the primary stochastic-curtailment calculation, that effect should generally be the prespecified effect for which the study was designed. A low conditional power means that, under that assumed future effect, the probability of ultimately rejecting the null hypothesis is low given the information already observed. Stochastic curtailment is therefore a futility-monitoring rule, not a replacement for the primary final analysis.
Jennison, C. & Turnbull, B.W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC, New York.
Lan, K.K.G., Simon, R., & Halperin, M. (1982). An aid to data monitoring in long-term clinical trials. Controlled Clinical Trials, 3(4), 311–323.
Proschan, M.A., Lan, K.K.G., & Wittes, J.T. (2006). Statistical Monitoring of Clinical Trials: A Unified Approach. Springer, New York.
this method/the software, Chapter 403: Conditional Power and Sample Size Reestimation of Paired T-Tests. the relevant methodological literature gives the general one-sided conditional-power formula, defines the futility index as 1 minus conditional power, and provides a numerical validation example.