Bayesian Methods in Nephrology: Applications in Adaptive Trials, Dynamic Risk Prediction, Pharmacokinetics, and Causal Inference

Abstract Bayesian statistics is gaining momentum in biomedical research, offering a flexible and intuitive framework for integrating prior knowledge, managing uncertainty, and informing decision-making. In nephrology, a field marked by complex pathophysiology, small patient populations, and evolving therapeutic landscapes, Bayesian approaches may provide critical advantages over traditional statistical methods. Bayesian methodologies may help reshape nephrology by improving trial efficiency, refining diagnostic and prognostic precision, and strengthening causal inference. We conducted a comprehensive narrative review of peer-reviewed literature on Bayesian applications in nephrology, highlighting studies in adaptive clinical trial designs, dynamic risk prediction models, network meta-analyses, pharmacokinetic modelling, and Bayesian Mendelian randomization approaches, including Bayesian model averaging frameworks. Bayesian adaptive designs enabled more efficient and ethically sound trials, such as the WIRE platform study in renal cell carcinoma. In diagnostics and prognostics, Bayesian models allowed individualized inference from dynamic data, as demonstrated in eGFR trajectory analyses and mortality prediction. Bayesian network meta-analyses improved comparative effectiveness research by incorporating probabilistic treatment rankings, while Bayesian frameworks strengthened causal inference through methods like MR-Bayesian Model Averaging and Bayesian Kernel Machine Regression. Bayesian approaches have emerging applications in nephrology, fostering a probabilistic mindset, enhancing the interpretability of complex data, and enabling more individualized clinical strategies. Their integration into research and practice requires investment in training, interdisciplinary collaboration, and development of user-friendly tools. Embracing Bayesian thinking will be key to advancing precision medicine and improving patient outcomes in nephrology.