A Bayesian Buckley–James–LightGBM framework for right-censored survival prediction: a methodological study using simulations and biomedical applications

Abstract

Prediction with right-censored survival outcomes is challenging because incomplete event-time observation degrades estimation prediction, and uncertainty quantification. Cox proportional-hazards and parametric accelerated-failure-time (AFT) models deteriorate when covariate effects are nonlinear, and risk profiles heterogeneous and deterministic Buckley–James imputation under-represents censoring uncertainty in downstream predictions. We propose Bayes–BJ–LGBM, a partially Bayesian (Bayesian–MAP hybrid), censoring-aware framework that recasts Buckley–James latent-time reconstruction as posterior sampling on the log time scale, coupling a regularized LightGBM ensemble to a nonlinear AFT structure. Latent event times, the residual variance and the linear coefficients are drawn by Gibbs sampling, whereas the tree ensemble is optimized by maximum a posteriori (MAP) updates rather than sampled; the reported posterior predictive survival functions and 95% credible bands are therefore conditional on that ensemble, not a full joint Bayesian posterior over all model components. An optional Bayesian proportional-hazards (Cox-Boost) block is fused by a validation-selected convex combination, then monotone rank-preserving recalibration. Evaluation used eleven Monte-Carlo scenarios and four cohorts (PBC, Veteran, MIMIC-III, SUPPORT) under a leakage-controlled repeated-split protocol, assessing concordance, time-dependent AUC, Brier scores, the integrated calibration index (ICI) and log-time mean squared error. Bayes–BJ–LGBM was strongest on calibration and time-scale accuracy. On PBC it attained the best ICI (0.0791), log-time mean squared error (0.5363) and Brier-at-horizon (0.1044) of all models, and stayed within the leading group on MIMIC-III and SUPPORT across all metric families, its MIMIC-III integrated Brier score (0.1959) effectively showing the best baseline. On discrimination it was competitive with, though not uniformly better than, penalized Cox models, which led on Veteran. In simulation it achieved the lowest or near-lowest probabilistic and point-prediction error under nonlinear and interaction structures, and stayed within a few thousandths of correctly specified Cox models under proportional-hazards misspecification and informative censoring. Ablation confirmed that proportional-hazards fusion drives discrimination while rank-preserving recalibration sharpens calibration without altering ranking. Bayes–BJ–LGBM integrates censoring-aware latent-time modelling, scalable nonlinear learning, and Tree-conditional uncertainty quantification into a predictor that returning calibrated survival probabilities and conditional credible bands not risk scores alone. Its advantages are clearest for calibration, probabilistic accuracy, and individualized uncertainty, quantified conditional on the MAP-optimized tree ensemble.