Beyond this module

Adaptive designs, trial sequential meta-analysis and CUSUM charts; software, guidance and further reading.

Adaptive designs

Group sequential designs allow only one kind of change: stopping. Adaptive designs also allow data-driven changes to the sample size, the arms or the population, while still controlling the type I error.

Combination tests. The stage-wise p-values are combined with a pre-specified function — Fisher’s product (Bauer and Kohne 1994) or the weighted inverse normal (Lehmacher and Wassmer 1999; Cui et al. 1999). The second stage can then be redesigned freely.
Conditional error function. Any modification is allowed if the conditional type I error of the original design is preserved (Proschan and Hunsberger 1995; Müller and Schäfer 2001).
Sample-size re-estimation. Unblinded re-estimation, for example the “promising zone” (Mehta and Pocock 2011), and blinded re-estimation or internal pilots (Friede and Kieser 2006). Jennison and Turnbull (2006) show that a well-chosen non-adaptive group sequential design is often as efficient.
Multi-arm multi-stage (MAMS), seamless phase II/III and enrichment designs (Magirr et al. 2012).

Reviews and practical guides: Bretz et al. (2009), Pallmann et al. (2018), Burnett et al. (2020) and Wassmer and Brannath (2016). Estimation after adaptive designs is reviewed by Robertson et al. (2023a) and Robertson et al. (2023b).

Trial sequential analysis (sequential meta-analysis)

A cumulative meta-analysis repeats its test whenever a new trial is added, with the same type I error inflation as a monitored trial. Trial sequential analysis applies Lan–DeMets boundaries to the cumulative \(Z\). It uses a required information size adjusted for heterogeneity (Wetterslev et al. 2008, 2017). For statistical methods for updating meta-analyses in living reviews see Simmonds et al. (2017). For an e-value alternative see ALL-IN meta-analysis (Schure and Grünwald 2022).

CUSUM and quality-control charts

The cumulative sum (CUSUM) chart (Page 1954) and its risk-adjusted version for surgical outcomes (Steiner 2000) monitor a process for a change, restarting after each signal. Their error control is expressed as the average run length before a false alarm, not as the type I and II errors of a single test. Reviews: Grigg and Farewell (2004) and Woodall (2006).

Software

Tool	Type	Notes
rpact	R package	Group sequential and adaptive designs, simulation, full interim analysis
gsDesign, gsDesign2	R packages	Largest spending-function library; non-proportional hazards
ldbounds, lrstat, clinfun, Sequential, safestats, RTSA	R packages	Lan–DeMets bounds, weighted log-rank designs, Simon designs, MaxSPRT, e-values, trial sequential analysis
East Horizon, PASS, nQuery	commercial	Design and simulation
SAS PROC SEQDESIGN / SEQTEST	commercial	Design and interim analysis, including triangular tests
Stata `gsdesign` (version 18 or later)	commercial	Group sequential design with a graphical interface

Software reviews: Wassmer and Vandemeulebroecke (2006), Zhu et al. (2011), Tymofyeyev (2014), Grayling and Wheeler (2020) and Meyer et al. (2021).

Regulatory guidance and reporting

ICH E9 requires interim analyses and stopping rules to be pre-specified, with the type I error controlled (International Council for Harmonisation 1998).
FDA guidance on adaptive designs treats group sequential designs as a well-understood case (U.S. Food and Drug Administration 2019).
ICH E20 on adaptive designs was a Step 2 draft in 2025 (International Council for Harmonisation 2025). The EMA reflection paper remains relevant (European Medicines Agency, CHMP 2007).
Data monitoring committees: see DeMets and Ellenberg (2016).
Reporting: follow the CONSORT extension for adaptive designs (Dimairo et al. 2020).

References

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Bauer, P., and K. Kohne. 1994. “Evaluation of Experiments with Adaptive Interim Analyses.” Biometrics 50 (4): 1029. https://doi.org/10.2307/2533441.

Bretz, Frank, Franz Koenig, Werner Brannath, Ekkehard Glimm, and Martin Posch. 2009. “Adaptive Designs for Confirmatory Clinical Trials.” Statistics in Medicine 28 (8): 1181–217. https://doi.org/10.1002/sim.3538.

Burnett, Thomas, Pavel Mozgunov, Philip Pallmann, Sofia S. Villar, Graham M. Wheeler, and Thomas Jaki. 2020. “Adding Flexibility to Clinical Trial Designs: An Example-Based Guide to the Practical Use of Adaptive Designs.” BMC Medicine 18 (1). https://doi.org/10.1186/s12916-020-01808-2.

Cui, Lu, H. M. James Hung, and Sue‐Jane Wang. 1999. “Modification of Sample Size in Group Sequential Clinical Trials.” Biometrics 55 (3): 853–57. https://doi.org/10.1111/j.0006-341x.1999.00853.x.

DeMets, David L., and Susan S. Ellenberg. 2016. “Data Monitoring Committees — Expect the Unexpected.” New England Journal of Medicine 375 (14): 1365–71. https://doi.org/10.1056/nejmra1510066.

Dimairo, Munyaradzi, Philip Pallmann, James Wason, et al. 2020. “The Adaptive Designs CONSORT Extension (ACE) Statement: A Checklist with Explanation and Elaboration Guideline for Reporting Randomised Trials That Use an Adaptive Design.” BMJ, m115. https://doi.org/10.1136/bmj.m115.

European Medicines Agency, CHMP. 2007. Reflection Paper on Methodological Issues in Confirmatory Clinical Trials Planned with an Adaptive Design (CHMP/EWP/2459/02).

Friede, Tim, and Meinhard Kieser. 2006. “Sample Size Recalculation in Internal Pilot Study Designs: A Review.” Biometrical Journal 48 (4): 537–55. https://doi.org/10.1002/bimj.200510238.

Grayling, Michael John, and Graham Mark Wheeler. 2020. “A Review of Available Software for Adaptive Clinical Trial Design.” Clinical Trials 17 (3): 323–31. https://doi.org/10.1177/1740774520906398.

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International Council for Harmonisation. 2025. ICH E20: Adaptive Designs for Clinical Trials. Draft Guideline, Step 2b.

Jennison, Christopher, and Bruce Turnbull. 2000. Group Sequential Methods with Applications to Clinical Trials. In Chapman & Hall/CRC Interdisciplinary Statistics Series. Chapman & Hall/CRC. https://doi.org/10.1201/9781584888581.

Jennison, Christopher, and Bruce W. Turnbull. 2006. “Adaptive and Nonadaptive Group Sequential Tests.” Biometrika 93 (1): 1–21. https://doi.org/10.1093/biomet/93.1.1.

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Lakens, Daniël. 2014. “Performing High‐powered Studies Efficiently with Sequential Analyses.” European Journal of Social Psychology 44 (7): 701–10. https://doi.org/10.1002/ejsp.2023.

Lakens, Daniel, Friedrich Pahlke, and Gernot Wassmer. 2021. Group Sequential Designs: A Tutorial. January. https://doi.org/10.31234/osf.io/x4azm.

Lehmacher, Walter, and Gernot Wassmer. 1999. “Adaptive Sample Size Calculations in Group Sequential Trials.” Biometrics 55 (4): 1286–90. https://doi.org/10.1111/j.0006-341x.1999.01286.x.

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Mehta, Cyrus R., and Stuart J. Pocock. 2011. “Adaptive Increase in Sample Size When Interim Results Are Promising: A Practical Guide with Examples.” Statistics in Medicine 30 (28): 3267–84. https://doi.org/10.1002/sim.4102.

Meyer, Elias Laurin, Peter Mesenbrink, Tobias Mielke, Tom Parke, Daniel Evans, and Franz König. 2021. “Systematic Review of Available Software for Multi-Arm Multi-Stage and Platform Clinical Trial Design.” Trials 22 (1). https://doi.org/10.1186/s13063-021-05130-x.

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