title: The use of randomisation-based efficacy estimators in non-inferiority trials.
abstract: In a non-inferiority (NI) trial, analysis based on the intention-to-treat (ITT) principle is anti-conservative, so current guidelines recommend analysing on a per-protocol (PP) population in addition. However, PP analysis relies on the often implausible assumption of no confounders. Randomisation-based efficacy estimators (RBEEs) allow for treatment non-adherence while maintaining a comparison of randomised groups. Fischer et al. have developed an approach for estimating RBEEs in randomised trials with two active treatments, a common feature of NI trials. The aim of this paper was to demonstrate the use of RBEEs in NI trials using this approach, and to appraise the feasibility of these estimators as the primary analysis in NI trials.
  
  
  
  Two NI trials were used. One comparing two different dosing regimens for the maintenance of remission in people with ulcerative colitis (CODA), and the other comparing an orally administered treatment to an intravenously administered treatment in preventing skeletal-related events in patients with bone metastases from breast cancer (ZICE). Variables that predicted adherence in each of the trial arms, and were also independent of outcome, were sought in each of the studies. Structural mean models (SMMs) were fitted that conditioned on these variables, and the point estimates and confidence intervals compared to that found in the corresponding ITT and PP analyses.
  
  
  
  In the CODA study, no variables were found that differentially predicted treatment adherence while remaining independent of outcome. The SMM, using standard methodology, moved the point estimate closer to 0 (no difference between arms) compared to the ITT and PP analyses, but the confidence interval was still within the NI margin, indicating that the conclusions drawn would remain the same. In the ZICE study, cognitive functioning as measured by the corresponding domain of the QLQ-C30, and use of chemotherapy at baseline were both differentially associated with adherence while remaining independent of outcome. However, while the SMM again moved the point estimate closer to 0, the confidence interval was wide, overlapping with any NI margin that could be justified.
  
  
  
  Deriving RBEEs in NI trials with two active treatments can provide a randomisation-respecting estimate of treatment efficacy that accounts for treatment adherence, is straightforward to implement, but requires thorough planning during the design stage of the study to ensure that strong baseline predictors of treatment are captured. Extension of the approach to handle nonlinear outcome variables is also required.
  
  
  
  The CODA study: ClinicalTrials.gov, identifier: NCT00708656 . Registered on 8 April 2008. The ZICE study trial: ClinicalTrials.gov, identifier: NCT00326820 . Registered on 16 May 2006.
authors.affiliation: South East Wales Trials Unit, Centre for Trials Research, College of Biomedical and Life Sciences, Cardiff University, Cardiff, UK. gillespied1@cardiff.ac.uk.
authors.forename: David
authors.identifier: 0000-0002-6934-2928
authors.initials: D
authors.lastname: Gillespie
authors.affiliation: Division of Population Medicine, School of Medicine, College of Biomedical and Life Sciences Cardiff University, Cardiff, UK.
authors.forename: Daniel
authors.initials: D
authors.lastname: Farewell
authors.affiliation: Velindre Cancer Centre, Velindre Rd., Whitchurch, Cardiff, UK.
authors.forename: Peter
authors.initials: P
authors.lastname: Barrett-Lee
authors.affiliation: Wales Cancer Trials Unit, Centre for Trials Research, College of Biomedical and Life Sciences, Cardiff University, Cardiff, UK.
authors.forename: Angela
authors.initials: A
authors.lastname: Casbard
authors.affiliation: Department of Medicine, University Hospital of Wales, Cardiff and Vale NHS Trust, Cardiff, UK.
authors.forename: Anthony Barney
authors.initials: AB
authors.lastname: Hawthorne
authors.affiliation: Wales Cancer Trials Unit, Centre for Trials Research, College of Biomedical and Life Sciences, Cardiff University, Cardiff, UK.
authors.forename: Chris
authors.initials: C
authors.lastname: Hurt
authors.affiliation: North Adelaide Oncology, Kimberley House, Calvary North Adelaide Hospital, 89 Strangways Terrace, North Adelaide, SA, Australia.
authors.forename: Nick
authors.initials: N
authors.lastname: Murray
authors.affiliation: Gastroenterology Research Unit, Department of Cellular and Molecular Physiology, Institute of Translational Medicine, University of Liverpool, Ashton Street, Liverpool, UK.
authors.forename: Chris
authors.initials: C
authors.lastname: Probert
authors.affiliation: Division of Infection and Immunity Research, School of Medicine, College of Biomedical and Life Sciences, Cardiff University, Cardiff, UK.
authors.forename: Rachel
authors.initials: R
authors.lastname: Stenson
authors.affiliation: Centre for Trials Research, College of Biomedical and Life Sciences, Cardiff University, Cardiff, UK.
authors.forename: Kerenza
authors.initials: K
authors.lastname: Hood
mesh_terms: D061605:Administration, Intravenous; D000284:Administration, Oral; D000893:Anti-Inflammatory Agents / Q000008:administration & dosage; D050071:Bone Density Conservation Agents / Q000008:administration & dosage; D001859:Bone Neoplasms / Q000517:prevention & control / Q000556:secondary; D001943:Breast Neoplasms / Q000188:drug therapy / Q000473:pathology; D003093:Colitis, Ulcerative / Q000175:diagnosis / Q000188:drug therapy; D003627:Data Interpretation, Statistical; D004164:Diphosphonates / Q000008:administration & dosage; D005260:Female; D005765:Gastrointestinal Agents / Q000008:administration & dosage; D006801:Humans; D000077557:Ibandronic Acid; D007093:Imidazoles / Q000008:administration & dosage; D057194:Intention to Treat Analysis; D008297:Male; D055118:Medication Adherence; D019804:Mesalamine / Q000008:administration & dosage; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D012074:Remission Induction; D012107:Research Design / Q000706:statistics & numerical data; D016896:Treatment Outcome; D000077211:Zoledronic Acid
chemical_list: D000893:Anti-Inflammatory Agents; D050071:Bone Density Conservation Agents; D004164:Diphosphonates; D005765:Gastrointestinal Agents; D007093:Imidazoles; D019804:Mesalamine; D000077211:Zoledronic Acid; D000077557:Ibandronic Acid
keywords: Efficacy; Intention-to-treat; Non-inferiority; Per-protocol; Structural mean models; Treatment non-adherence