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Unbiased estimation for response adaptive clinical trials.

Jack Bowden1,2, Lorenzo Trippa3

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Bayesian adaptive trials adjust treatment probabilities during studies. This research quantifies bias in response probability estimates, finding it small and negative, and explores methods to improve precision for better clinical trial design.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Bayesian adaptive trials dynamically alter treatment arm probabilities based on accumulating data.
  • A significant barrier to Bayesian adaptive trial adoption is the perceived poor or poorly understood frequentist operating characteristics.
  • Concerns exist regarding the accuracy of parameter estimates within these adaptive designs.

Purpose of the Study:

  • To investigate and quantify the bias in maximum likelihood estimates of response probability (p) for binary outcomes within Bayesian adaptive trials.
  • To develop and evaluate methods for obtaining precise and unbiased estimates of response probabilities in adaptive clinical trials.
  • To address concerns about the frequentist properties of Bayesian adaptive trial designs.

Main Methods:

  • Analysis of bias induced by adaptive randomization on the maximum likelihood estimate of a binary response probability parameter (p).
  • Derivation of a simple unbiased estimator for p.
  • Exploration of two precision-enhancing strategies: inverse probability weighting and Rao-Blackwellization.
  • Illustration of estimation strategies using established Bayesian adaptive trial designs.

Main Results:

  • The bias introduced by adaptive randomization in estimating response probability (p) is small in magnitude.
  • Under mild assumptions, this bias is consistently negative, leading to estimates closer to zero than the true value.
  • A simple unbiased estimator for p was derived but exhibited a large mean squared error.
  • Inverse probability weighting and Rao-Blackwellization showed promise in improving the precision of these estimates.

Conclusions:

  • The bias in maximum likelihood estimates of response probability in Bayesian adaptive trials is quantifiable and generally small.
  • While a simple unbiased estimator exists, its precision is limited, necessitating advanced techniques.
  • Inverse probability weighting and Rao-Blackwellization offer viable approaches to enhance the precision of parameter estimation in adaptive trial settings.
  • These findings contribute to a better understanding of the frequentist operating characteristics of Bayesian adaptive trials, potentially easing their clinical implementation.