Optimizing subgroup selection in two-stage adaptive enrichment and umbrella designs

Nicolás M. Ballarini, Thomas Burnett, Thomas Jaki, Christoper Jennison, Franz König, Martin Posch

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)


We design two-stage confirmatory clinical trials that use adaptation to find the subgroup of patients who will benefit from a new treatment, testing for a treatment effect in each of two disjoint subgroups. Our proposal allows aspects of the trial, such as recruitment probabilities of each group, to be altered at an interim analysis. We use the conditional error rate approach to implement these adaptations with protection of overall error rates. Applying a Bayesian decision-theoretic framework, we optimize design parameters by maximizing a utility function that takes the population prevalence of the subgroups into account. We show results for traditional trials with familywise error rate control (using a closed testing procedure) as well as for umbrella trials in which only the per-comparison type 1 error rate is controlled. We present numerical examples to illustrate the optimization process and the effectiveness of the proposed designs.

Original languageEnglish
Pages (from-to)2939-2956
Number of pages18
JournalStatistics in Medicine
Issue number12
Early online date29 Mar 2021
Publication statusPublished - 30 May 2021

Bibliographical note

Funding Information:
information H2020 Marie Sk?odowska-Curie Actions, 633567; Innovative Medicines Initiative, 853966; Medical Research Council, MR/M005755/1; National Institute for Health Research, NIHR-SRF-2015-08-001Nicol?s Ballarini is supported by the EU Horizon 2020 Research and Innovation Programme, Marie Sklodowska-Curie grant No 633567. Thomas Jaki is supported by the National Institute for Health (NIHR-SRF-2015-08-001) and the Medical Research Council (MR/M005755/1). Franz K?nig and Martin Posch are members of the EU Patient-Centric Clinical Trial Platform (EU-PEARL) which has received funding from the Innovative Medicines Initiative 2 Joint Undertaking, grant No 853966. This Joint Undertaking receives support from the EU Horizon 2020 Research and Innovation Programme, EFPIA, Children's Tumor Foundation, Global Alliance for TB Drug Development, and SpringWorks Therapeutics. The views expressed in this publication are those of the authors. The funders and associated partners are not responsible for any use that may be made of the information contained herein.



  • Bayesian optimization
  • conditional error function
  • subgroup analysis
  • utility function

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


Dive into the research topics of 'Optimizing subgroup selection in two-stage adaptive enrichment and umbrella designs'. Together they form a unique fingerprint.

Cite this