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

Bayesian optimal phase II (BOP2) design serves to screen the efficacy and/or toxicity of a new treatment, determining whether it warrants further development. When employing the BOP2 design to jointly monitor the efficacy-toxicity tradeoff, the correlation between them plays an important role in achieving good performance on the statistical power while controlling Type I error. However, in practice, this correlation is usually unknown, posing challenges in the trial design and data analysis. In this study, the phi coefficient is chosen to measure the correlation. The influence of the efficacy-toxicity tradeoff on the power of BOP2 designs is first evaluated in the design stage and the data analysis stage, separately, then, overall considerations are given. In the design stage, we observe that the power increases as phi increases. Upon performing the sensitivity analysis in the data analysis stage, we find that the power decreases as phi increases given the pre-determined stopping boundaries. Simulations demonstrate instances of overpowering with inflated Type I error when the assumed phi in the design stage exceeds the true phi in the data analysis stage. Conversely, underpowering occurs with controlled Type I error when the assumed phi is lower than the true phi in the data analysis stage. To obtain the power under controlled Type I error in design, we recommend the use of independent correlation when the efficacy and toxicity are likely to be positively correlated. Conversely, for cases of likely negative correlation, taking a phi value close to the lower bound is advisable.