用神经网络建模健康状态转变概率,更好处理不规则随访数据。
A Longitudinal Attribute-Conditioned Neural Network for Modeling Health-State Transition Probabilities in Temporally Irregular Data: The LANTERN Framework

- 基于个体健康史和时间间隔,学习多状态转移概率
- 在测试集上对严重失能和死亡的判别能力优于传统模型
- 生成符合精算要求的转移矩阵,适合保险定价与风险评估
准确估计长期护理状态转移概率是残疾保险定价、准备金计提和偿付能力评估的核心。传统精算多状态模型常采用马尔可夫、半马尔可夫或比例风险设定,虽便于队列预测,但在非规则纵向健康数据、非线性老化模式及异质协变量历史面前存在局限。本文提出一种校准良好的多状态转移概率估计器——LANTERN框架,能从个体健康史中学习,纳入观测间时间间隔,并根据人口与社会经济特征条件化转移概率。模型输出下一观察状态的概率分布,共四种状态:健康、轻度失能、重度失能、死亡。个体概率按年龄组和起始状态聚合,形成与精算队列投影兼容的转移矩阵。利用美国健康与退休研究(HRS)数据,对比了该方法与逻辑回归、梯度提升树、循环神经网络及最后状态保持基准的表现。评估涵盖概率准确性、终点判别力与校准性(重度失能与死亡)、风险集中度及聚合后的转移矩阵误差。结果显示,该模型在重度失能判别上优于逻辑回归与梯度提升树,保持良好校准性,并在留出测试中取得最低转移矩阵误差。结果表明,结构化机器学习模型在以校准性和预测保真度为标准时,可有效支持长期护理转移建模。
原文摘要 · Abstract (English)
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.
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