Variations of Power Priors in Time‐to‐Event Analysis With Piecewise Constant Hazards Through Baseline and Outcome Similarity Driven Bounded Weighting

Patient recruitment in clinical trials, particularly in rare diseases or pediatric populations, remains a significant challenge. Leveraging external data to supplement trial information offers a promising solution, reducing placebo allocation, and enhancing recruitment feasibility while increasing the number of patients receiving active treatment, thus improving safety evaluations. However, the success of this method depends on the alignment of external data with target data from a population characteristics perspective and scientific translation perspective. Bayesian statistical methods, including power priors, commensurate priors, and mixture priors, facilitate the dynamic adjustment of borrowed information based on outcome data when this alignment is not perfect. Such outcome‐dependent approaches ensure robust and accurate inference by recalibrating the posterior distribution when empirical results deviate from prior assumptions. In the context of time to event analysis with piecewise constant hazards, we propose a variation of the power prior through a novel bounded weighting function, which balances population similarity and/or scientific translatability with the outcome‐based criteria. Both of these innovations address the scientific principle that underpins borrowing, the scarcity of studies on population and outcome‐dependent borrowing, and the limited literature on power priors for survival data. The practical implementation of the proposed method is demonstrated through simulations and real‐world case studies, highlighting its potential to improve the accuracy of inference in clinical trials.