Improving predictions when interest focuses on extreme random effects

Statistical models that generate predicted random effects are widely used to evaluate the performance of and rank patients, physicians, hospitals and health plans from longitudinal and clustered data. Predicted random effects have been proven to outperform treating clusters as fixed effects (essentially a categorical predictor variable) and using standard regression models, on average. These predicted random effects are often used to identify extreme or outlying values, such as poorly performing hospitals or patients with rapid declines in their health. When interest focuses on the extremes rather than performance on average, there has been no systematic investigation of best approaches. We develop novel methods for prediction of extreme values, evaluate their performance, and illustrate their application using data from the Osteoarthritis Initiative to predict walking speed in older adults. The new methods substantially outperform standard random and fixed effects approaches for extreme values.

生成预测随机效应的统计模型，被广泛应用于基于纵向数据与聚类数据的分析中，用于评估患者、医师、医院及健康保险计划的表现并进行排名。平均而言，预测随机效应的表现已被证实优于将聚类单元视为固定效应（本质为分类预测变量）以及采用标准回归模型的分析方法。此类预测随机效应常被用于识别极端值或异常值，例如运营不佳的医院，或是健康状况快速恶化的患者。当研究重点聚焦于极端值而非平均表现时，目前尚未有针对最优分析方法的系统性探究。本研究开发了用于极端值预测的新型方法，并对其性能开展评估；同时借助骨关节炎倡议（Osteoarthritis Initiative）的数据集，以老年人群步行速度预测为实例，演示了该方法的实际应用。相较于针对极端值分析的标准随机效应与固定效应方法，本研究提出的新型方法性能优势显著。