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Assessing the role of correlation between efficacy and toxicity endpoints in the performance of Bayesian optimal

Xun Xu1, Ying Yuan2, J Jack Lee2

  • 1Department of Biostatistics and Data Science, School of Public Health, University of Texas, Houston 77030, TX, United States; Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston 77030, TX, United States.

Contemporary Clinical Trials
|May 5, 2025
PubMed
Summary

Understanding the correlation between efficacy and toxicity is crucial for Bayesian optimal phase II (BOP2) designs. This study reveals how correlation influences statistical power and Type I error, offering guidance for accurate clinical trial planning.

Keywords:
Bayesian adaptive designData analysis stageDesign stageEfficacy-toxicity tradeoffPhi coefficientSensitivity analysis

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Area of Science:

  • Clinical Trials Methodology
  • Biostatistics
  • Pharmaceutical Research

Background:

  • Bayesian optimal phase II (BOP2) designs are essential for evaluating new treatments, balancing efficacy and toxicity.
  • The correlation between efficacy and toxicity significantly impacts BOP2 design performance, but this correlation is often unknown in practice.
  • Accurate estimation of this correlation is vital for maintaining statistical power and controlling Type I error.

Purpose of the Study:

  • To evaluate the influence of the efficacy-toxicity correlation (measured by the phi coefficient) on the performance of BOP2 designs.
  • To assess how this correlation impacts statistical power and Type I error at both the design and data analysis stages.
  • To provide recommendations for selecting appropriate correlation assumptions in BOP2 designs when the true correlation is unknown.

Main Methods:

  • Utilized the phi coefficient to quantify the correlation between treatment efficacy and toxicity.
  • Evaluated the impact of varying phi values on BOP2 design power during the design phase.
  • Conducted sensitivity analysis in the data analysis phase with pre-determined stopping boundaries to assess power.
  • Performed simulations to investigate discrepancies between assumed and true phi values.

Main Results:

  • In the design stage, statistical power increases with increasing phi.
  • In the data analysis stage, power decreases as phi increases, given fixed stopping boundaries.
  • Assuming a higher phi in design than in reality leads to overpowering and inflated Type I error.
  • Assuming a lower phi in design than in reality results in underpowering while controlling Type I error.

Conclusions:

  • The choice of assumed correlation (phi) in BOP2 design is critical and impacts trial outcomes.
  • For positive efficacy-toxicity correlation, assuming independence (phi=0) is recommended for robust power.
  • For negative correlation, using a phi value near the lower bound is advisable to ensure controlled Type I error.
  • Accurate assessment or conservative estimation of efficacy-toxicity correlation is necessary for reliable BOP2 trial design.