Random Hazard Forests

Longitudinal studies often collect data at sparse, irregular, and unequally spaced time points. Such heterogeneity is often driven by subject-specific covariates, yet existing methods have been restricted to a scalar endpoint value, completely neglecting the underlying response trajectories. We propose a novel Longitudinal Random Forest (LRF) framework that leverages tree-based ensemble machine learning with adaptive node-wise longitudinal trajectory estimation. The LRF framework makes five methodological contributions. it captures each subject's individual response trajectory while simultaneously accommodating within-node correlation, between-node heterogeneity, and nonlinear and interactive covariate effects. It introduces a novel trajectory-based splitting criterion that maximizes trajectory separation while incorporating a size-weighted penalty; it provides two variants, Principal Analysis by Conditional Expectation (LRF-PACE) and adaptive linear mixed-effects models (LRF-adaptiveLMM), which employ nonparametric and semiparametric node-wise smoothers, respectively, while learning covariate effects in a data-driven manner. It provides a comprehensive interpretation of covariates using both the classical trajectory-based permutation variable importance measure (PVIM) and a newly proposed finite-way interaction frequency count, and it not only predicts entire trajectories for new subjects but also forecasts future trajectories for existing subjects. Extensive simulation studies demonstrate that LRF achieves superior performance over several competing methods, even under severe sparsity. The practical significance of the LRF framework lies in its ability to address five important clinical questions.

Numerical time-series models can effectively process irregular electronic health record (EHR) trajectories, but they do not naturally expose the measurements and temporal patterns supporting each risk estimate as readable evidence. Existing text-based interfaces improve readability, but typically rely on either raw serialization, which is lengthy and redundant, or patient-level free-form summaries, which are difficult to trace to source measurements and time windows. To bridge this gap, we introduce TreeText-CTS (Clinical Time-Series), which converts irregular EHR trajectories into human-readable, compact, source-traceable tree-path evidence units without patient-level summarization or inference-time autoregressive decoding. TreeText-CTS routes multi-scale window summaries through frozen XGBoost models and verbalizes activated tree paths as deterministic, source-traceable evidence units composed of threshold conditions. An evidence selector assembles an informative subset of these units, which a language-model encoder then integrates for prediction. Across PhysioNet 2012 mortality, MIMIC-III mortality, and PhysioNet 2019 sepsis-onset forecasting, TreeText-CTS achieves the best AUROC and AUPRC among evaluated text-based EHR time-series interfaces, improving AUPRC by 6.0 to 9.7 absolute percentage points over the strongest prior text-based interface while remaining competitive with numerical time-series models. Ablations show that tree-path evidence construction, evidence selection, and language-model composition each contribute to performance. Because every span passed to the language-model encoder is constructed from activated tree-path threshold conditions, TreeText-CTS makes the evidence supplied to the final predictor inspectable and source-traceable.

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.