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Stat Med. 2018 Nov 20;37(26):3709-3722. doi: 10.1002/sim.7836. Epub 2018 Jun 13.

Bayesian selective response-adaptive design using the historical control.

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UCSF Helen Diller Family Comprehensive Cancer Center, San Francisco, California, USA.
Department of Epidemiology and Biostatistics, University of California San Francisco, San Francisco, California, USA.
Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA.
Department of Neurology and Rehabilitation Medicine, University of Cincinnati College of Medicine, Cincinnati, Ohio, USA.


High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior-data conflict. Motivated by well-publicized two-arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior-data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors.


Bayesian design with commensurate priors; borrowing on the historical control data; doubly adaptive biased coin design; response-adaptive design

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