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Group Sequential, Adaptive, and Interim Analysis

Unblinded Sample Size Re-estimation Calculator

Chen-DeMets-Lan unblinded sample size re-estimation using interim conditional power. Enter the interim Wald statistic and design information to determine whether the interim result is promising and, if so, the smallest final sample size needed to achieve the target conditional power.

Interim Analysis & SSR Rules

This implementation follows the Chen-DeMets-Lan approach described in the documentation for unblinded sample size re-estimation.
Use the signed statistic in the direction of the alternative hypothesis. For a two-look design, this is the cumulative test statistic at the interim look.

Re-estimation Result

Conditional power is evaluated from the observed interim Z statistic and the information fraction associated with each candidate final N.
Enter the interim information and click Re-estimate Sample Size.

Methodology

Unblinded sample size re-estimation uses the treatment effect information revealed at an interim analysis to determine whether the trial has enough conditional power to meet its prespecified objective. The documentation describes two principal approaches for unblinded sample size re-estimation: the Chen-DeMets-Lan method and the Cui-Hung-Wang method. This calculator implements the Chen-DeMets-Lan method.

Chen, DeMets, and Lan showed that a sample-size increase based on an unblinded interim result can be made without inflating the nominal type I error when the increase is restricted to a prespecified promising region. In their formulation, an interim result is promising when its conditional power exceeds a lower bound, typically 50%, while remaining below the prespecified target-power region.

Conditional Power

Let Z1 be the observed cumulative Wald statistic at the interim analysis, let t be the information fraction n1/N, and let c2 be the final-analysis efficacy boundary. Under the interim-effect estimate, conditional power for a candidate final sample size is

CP(N) = Φ[ { Z1 / √t − c2 } / √(1 − t) ]

where Φ is the standard normal cumulative distribution function. Because the information fraction changes when the final sample size is changed, the conditional power is recalculated for every candidate final sample size.

Chen-DeMets-Lan Re-estimation Rule

CP ≤ CP(L): stop for futility
CP(L) < CP < CP(T): increase N to the smallest N achieving CP(T)
CP ≥ CP(T): continue without a sample-size increase
N(re-estimated) ≤ N(max)

The calculator searches integer total sample sizes from the original planned sample size through the prespecified maximum. It selects the smallest candidate N whose conditional power reaches the target. If the target cannot be reached before the maximum sample size, the maximum N is reported together with the conditional power it achieves.

Information Fraction

For a two-stage design, the information fraction used in the conditional power calculation is the ratio of the information available at the interim analysis to the information corresponding to the proposed final sample size. With equal information per subject this is t = Ninterim/Nfinal.

Interpretation

The re-estimation is based on unblinded interim efficacy information. It should therefore be prespecified as part of the adaptive design, including the conditional-power limits, maximum sample size, and statistical testing procedure. This calculator is intended for the numerical sample-size decision itself; it does not replace a full operating-characteristic evaluation of the adaptive design.

References

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

Cui, L., Hung, H.M.J., & Wang, S.-J. (1999). Modification of sample size in group sequential clinical trials. Biometrics, 55(3), 853–857. doi:10.1111/j.0006-341X.1999.00853.x.

Statsols. Advanced User Manual, Section 4.3: Interim Monitoring and Unblinded Sample Size Re-estimation. The documentation identifies the Chen-DeMets-Lan and Cui-Hung-Wang methods as its two principal approaches to unblinded sample-size re-estimation.