  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.
