Bayesian Counterparts to the Frequentist Kaplan-Meier Estimate and Its Summary Measures for Comparative Heart Failure...

In comparative cardiovascular clinical studies, Bayesian analysis offers a valuable framework for integrating prior knowledge about treatment effects with observed data. This approach enables direct quantification of the likelihood that the true treatment difference falls within a clinically meaningful range, providing a more interpretable assessment of clinical significance than is achievable with traditional frequentist methods. Furthermore, Bayesian methods are often considered more flexible and intuitive than traditional frequentist approaches, even when prior information is limited. In survival or event-free time analysis, frequentist methods typically rely on analytical techniques that require minimal modeling assumptions, such as Kaplan-Meier estimation and hazard ratio estimates, making the development of an equally straightforward Bayesian alternative highly desirable. Although various model-assumption-free Bayesian methods for survival analysis have been proposed, their practical application remains limited, primarily as the result of challenges in understanding the methodology and its complex implementation for clinical researchers. In this article, we present a simple and intuitive Bayesian approach to survival analysis that avoids explicit modeling of the data-generating process. Instead, because time-to-event data in typical clinical studies are recorded daily, we assume that the unknown daily hazards vary over the entire study duration and derive their posterior distributions. We present this method heuristically to enhance accessibility for practitioners and provide open-source software to support its implementation. In addition, we discuss how this approach seamlessly facilitates the sequential incorporation of results from previous studies as priors for ongoing or future trials. We demonstrate the practical utility of our method using data from a cardiovascular heart failure clinical study.