Distribution-free predictive inference in health sciences: a review of conformal prediction methods for biostatistics and epidemiology

Conformal prediction (CP) provides a flexible, distribution-free framework for uncertainty quantification with guaranteed finite-sample validity under minimal assumptions. This review presents recent developments and biomedical applications of CP across four major domains: survival analysis, causal inference, diagnostic classification, and dynamic biological modeling. We summarize foundational algorithms, including split, weighted, and quantile conformal methods, and highlight how these extensions address challenges such as censoring, covariate shift, and unmeasured confounding. Applications range from constructing calibrated survival bounds and individual treatment effect intervals to improving reliability in AI-assisted diagnostics and quantifying uncertainty in nonlinear dynamic systems. We also discuss implementation strategies, empirical findings, and emerging directions involving fairness, semi-supervised inference, federated learning, and privacy preservation. By bridging statistical methodology and biomedical practice, this review aims to provide researchers with a principled framework for leveraging CP to enhance reliability, interpretability, and equity in modern biostatistical inference.