Bayesian sample size determination for a Phase III clinical trial with diluted treatment effect

When Phase III treatment effect is diluted from what was observed from Phase II results, we propose to determine the Bayesian sample size for a Phase III clinical trial based on the normal, uniform, and truncated normal prior distributions of the treatment effects on an interval, which starts from an acceptable treatment effect to the observed treatment effect from Phase II. After incorporating the prior information of the treatment effects, the Bayesian sample size is the number of patients of the Phase III trial for a given Bayesian Predictive Power (BPP) or Bayesian Historical Predictive Power (BHPP). After that, the numerical simulations are carried out to determine the Bayesian sample size for the Phase III clinical trial. In particular, there exists a hook phenomenon for the BHPP when the number of patients of the Phase II trial equals 70 assuming the normal, uniform, or truncated normal treatment effect. Moreover, we add some sensitivity analysis of the Bayesian sample size about the parameters in the simulations. Finally, we determine the Bayesian sample size (number of events or deaths) of the Phase III trial for a fixed power, Bayesian Historical Power (BHP), and BHPP in the axitinib example.