Nearly 300,000 older adults experience a hip fracture every year, the majority of which occur following a fall. Unfortunately, recovery after fall-related trauma such as hip fracture is poor, where older adults diagnosed with Alzheimer's Disease and Related Dementia (ADRD) spend a particularly long time in hospitals or rehabilitation facilities during the post-operative recuperation period. Because older adults value functional recovery and spending time at home versus facilities as key outcomes after hospitalization, identifying factors that influence days spent at home after hospitalization is imperative. While several individual-level factors have been identified, the characteristics of the treating hospital have recently been identified as contributors. However, few methodological rigorous approaches are available to help overcome potential sources of bias such as hospital-level unmeasured confounders, informative hospital size, and loss to follow-up due to death. This article develops a useful tool equipped with unsupervised learning to simultaneously handle statistical complexities that are often encountered in health services research, especially when using large administrative claims databases. The proposed estimator has a closed form, thus only requiring light computation load in a large-scale study. We further develop its asymptotic properties that can be used to make statistical inference in practice. Extensive simulation studies demonstrate superiority of the proposed estimator compared to existing estimators.

翻译：每年约有30万老年人发生髋部骨折，其中大多数由跌倒引发。遗憾的是，老年人在髋部骨折等跌倒相关创伤后的康复效果不佳，患有阿尔茨海默病及相关痴呆症（ADRD）的老年患者在术后恢复期间，在医院或康复机构停留的时间尤其漫长。由于老年人将功能恢复和居家时间（而非机构时间）视为住院后的关键结局指标，因此识别影响住院后居家天数的因素至关重要。虽已明确若干个体层面因素，但治疗医院的院级特征近期被发现是重要影响因素。然而，目前缺乏方法学严谨的工具来帮助克服潜在偏倚来源，例如医院层级的未测量混杂因素、信息性的医院规模以及因死亡导致的随访缺失。本文开发了一种结合无监督学习的实用工具，可同时处理卫生服务研究中常见的统计复杂性，尤其是在使用大型行政索赔数据库时。所提出的估计量具有封闭形式，因此在大规模研究中仅需轻量计算负荷。我们进一步推导了其渐近性质，可用于实践中的统计推断。广泛的模拟研究表明，该估计量相较现有估计量具有显著优越性。