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.

可生成预测随机效应的统计模型，被广泛应用于基于纵向聚类数据对患者、医师、医院及健康保险计划开展绩效评估与排名。平均而言，经实证验证，预测随机效应的性能优于将聚类视作固定效应（本质上为分类预测变量）并采用标准回归模型的分析方法。这类预测随机效应常被用于识别极端值或异常值，例如绩效不佳的医院，或是健康状况快速恶化的患者。当研究关注点聚焦于极端值而非平均绩效时，目前尚无针对最优分析方法的系统性调研。本研究开发了用于极端值预测的新型方法，对其性能进行了系统评估，并借助骨关节炎倡议（Osteoarthritis Initiative）的数据集，以老年人群步行速度预测为例，展示了该方法的实际应用。针对极端值预测任务，该新型方法的性能显著优于标准随机效应与固定效应分析方法。