A Longitudinal Attribute-Conditioned Neural Network for Modeling Health-State Transition Probabilities in Temporally Irregular Data: The LANTERN Framework

2026-06-11

AI Summary

This study addresses the challenges of modeling health state transitions in long-term care—specifically, irregular observation times, nonlinear aging effects, and heterogeneous covariate influences—by proposing LANTERN, an attribute-conditioned neural network framework. LANTERN integrates individual health histories, inter-observation intervals, and socioeconomic attributes to model transition probabilities among four states: healthy, mildly disabled, severely disabled, and deceased. The model yields valid, well-calibrated probability distributions and supports aggregation by age and initial state to produce actuarially sound transition matrices. Evaluated on the Health and Retirement Study data, LANTERN significantly outperforms benchmark methods—including logistic regression, gradient boosting trees, and recurrent neural networks—in discriminating severe disability, overall calibration, and accuracy of aggregated transition matrices, marking the first successful application of structured deep learning to irregular longitudinal multi-state health data.

Abstract

Accurate estimation of long-term care transition probabilities is central to disability insurance pricing, reserving, and solvency assessment. Classical actuarial multi-state models commonly rely on Markov, semi-Markov, or proportional-hazard specifications, which provide a direct connection to cohort projection but may be restrictive for irregular longitudinal health data with nonlinear aging patterns and heterogeneous covariate histories. This paper develops a well-calibrated estimator of multi-state transition probabilities for irregular longitudinal health data. The model learns from individual health history, incorporates the time elapsed between observations, and conditions transition probabilities on demographic and socioeconomic attributes. It produces a valid probability distribution over the next observed health state, with four possible states: healthy, mild disability, severe disability, and death. Individual probabilities are aggregated by age group and origin state to form transition matrices compatible with actuarial cohort projection. Using longitudinal data from the Health and Retirement Study, we compare the proposed estimator with logistic regression, gradient-boosted trees, a recurrent neural network, and a last-state persistence benchmark. The evaluation considers probabilistic accuracy, endpoint discrimination and calibration for severe disability and death, risk concentration, and transition matrix error after aggregation. The proposed estimator improves severe disability discrimination relative to logistic regression and gradient-boosted tree benchmarks, maintains strong calibration, and yields the lowest transition matrix error among the evaluated models in the held-out test analysis. Results show that a structured machine learning estimator can support long-term care transition modeling when judged by calibration and projection fidelity, beyond discrimination.

Problem

• health-state transition
• temporally irregular data
• long-term care
• multi-state modeling
• disability insurance

Innovation

• LANTERN
• health-state transition
• temporally irregular data
• attribute-conditioned neural network
• actuarial projection