Estimands for factorial trials

Brennan C Kahan* (Corresponding Author), Tim P Morris, Beatriz Goulão, James Carpenter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
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Factorial trials offer an efficient method to evaluate multiple interventions in a single trial, however the use of additional treatments can obscure research objectives, leading to inappropriate analytical methods and interpretation of results. We define a set of estimands for factorial trials, and describe a framework for applying these estimands, with the aim of clarifying trial objectives and ensuring appropriate primary and sensitivity analyses are chosen. This framework is intended for use in factorial trials where the intent is to conduct "two-trials-in-one" (ie, to separately evaluate the effects of treatments A and B), and is comprised of four steps: (i) specifying how additional treatment(s) (eg, treatment B) will be handled in the estimand, and how intercurrent events affecting the additional treatment(s) will be handled; (ii) designating the appropriate factorial estimator as the primary analysis strategy; (iii) evaluating the interaction to assess the plausibility of the assumptions underpinning the factorial estimator; and (iv) performing a sensitivity analysis using an appropriate multiarm estimator to evaluate to what extent departures from the underlying assumption of no interaction may affect results. We show that adjustment for other factors is necessary for non collapsible effect measures (such as odds ratio), and through a trial re-analysis we find that failure to consider the estimand could lead to inappropriate interpretation of results. We conclude that careful use of the estimands framework clarifies research objectives and reduces the risk of misinterpretation of trial results, and should become a standard part of both the protocol and reporting of factorial trials.

Original languageEnglish
Pages (from-to)4299-4310
Number of pages12
JournalStatistics in Medicine
Issue number22
Early online date25 Jun 2022
Publication statusPublished - 16 Sept 2022

Bibliographical note

Brennan C. Kahan, Tim P. Morris, and James Carpenter are funded by the UK MRC, Grants No. MC_UU_00004/07 and
No. MC_UU_00004/09.


  • 2 × 2
  • estimand
  • factorial trial
  • ICH-E9 addendum
  • Randomized controlled trial


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