title: Adaptive adjustment of the randomization ratio using historical control data.
abstract: BACKGROUND
  Prospective trial design often occurs in the presence of 'acceptable' historical control data. Typically, these data are only utilized for treatment comparison in a posteriori retrospective analysis to estimate population-averaged effects in a random-effects meta-analysis.
  
  
  OBJECTIVE
  We propose and investigate an adaptive trial design in the context of an actual randomized controlled colorectal cancer trial. This trial, originally reported by Goldberg et al., succeeded a similar trial reported by Saltz et al., and used a control therapy identical to that tested (and found beneficial) in the Saltz trial.
  
  
  METHODS
  The proposed trial implements an adaptive randomization procedure for allocating patients aimed at balancing total information (concurrent and historical) among the study arms. This is accomplished by assigning more patients to receive the novel therapy in the absence of strong evidence for heterogeneity among the concurrent and historical controls. Allocation probabilities adapt as a function of the effective historical sample size (EHSS), characterizing relative informativeness defined in the context of a piecewise exponential model for evaluating time to disease progression. Commensurate priors are utilized to assess historical and concurrent heterogeneity at interim analyses and to borrow strength from the historical data in the final analysis. The adaptive trial's frequentist properties are simulated using the actual patient-level historical control data from the Saltz trial and the actual enrollment dates for patients enrolled into the Goldberg trial.
  
  
  RESULTS
  Assessing concurrent and historical heterogeneity at interim analyses and balancing total information with the adaptive randomization procedure lead to trials that on average assign more new patients to the novel treatment when the historical controls are unbiased or slightly biased compared to the concurrent controls. Large magnitudes of bias lead to approximately equal allocation of patients among the treatment arms. Using the proposed commensurate prior model to borrow strength from the historical data, after balancing total information with the adaptive randomization procedure, provides admissible estimators of the novel treatment effect with desirable bias-variance trade-offs.
  
  
  CONCLUSIONS
  Adaptive randomization methods in general are sensitive to population drift and more suitable for trials that initiate with gradual enrollment. Balancing information among study arms in time-to-event analyses is difficult in the presence of informative right-censoring.
  
  
  CONCLUSIONS
  The proposed design could prove important in trials that follow recent evaluations of a control therapy. Efficient use of the historical controls is especially important in contexts where reliance on preexisting information is unavoidable because the control therapy is exceptionally hazardous, expensive, or the disease is rare.
authors.affiliation: Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA. bphobbs@mdanderson.org
authors.forename: Brian P
authors.initials: BP
authors.lastname: Hobbs
authors.forename: Bradley P
authors.initials: BP
authors.lastname: Carlin
authors.forename: Daniel J
authors.initials: DJ
authors.lastname: Sargent
mesh_terms: D003110:Colonic Neoplasms; D006801:Humans; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D012107:Research Design; D018401:Sample Size; D015983:Selection Bias