Dr Foster Unit at Imperial College, Department of Primary Care and Public Health, Imperial College London, London, UK.
J Am Coll Surg. 2011 Sep;213(3):392-401. doi: 10.1016/j.jamcollsurg.2011.06.423. Epub 2011 Jul 23.
Although logistic regression is traditionally used to calculate hospital standardized mortality ratio (HSMR), it ignores the hierarchical structure of the data that can exist within a given database. Hierarchical models allow examination of the effect of data clustering on outcomes.
Traditional logistic regression and random intercepts fixed slopes hierarchical models were fitted to a dataset of patients hospitalized between 2005 and 2007 in Massachusetts. We compared the observed to expected (O/E) in-hospital death ratios between the 2 modeling techniques, a restricted HSMR using only those diagnosis models that converged in both methods and a full hybrid HSMR using a combination of the hierarchical diagnosis models when they converge, plus the remaining diagnoses using standard logistic regression models.
We restricted the analysis to the 36 diagnoses accounting for 80% of in-hospital deaths nationally, based on 1,043,813 admissions (59 hospitals). A failure of the hierarchical models to converge in 15 of 36 diagnosis groups hindered full HSMR comparisons. A restricted HSMR, derived from a dataset based on the 21 diagnosis groups that converged (552,933 admissions) showed very high correlation (Pearson r = 0.99). Both traditional logistic regression and hierarchical model identified 12 statistical outliers in common, 7 with high O/E values and 5 with low O/E values. In addition, the multilevel analysis identified 5 additional unique high outliers and 1 additional unique low outlier, and the conventional model identified 2 additional unique low outliers.
Similar results were obtained from the 2 modeling techniques in terms of O/E ratios. However, because a hierarchical model is associated with convergence problems, traditional logistic regression remains our recommended procedure for computing HSMRs.
尽管传统上使用逻辑回归来计算医院标准化死亡率（HSMR），但它忽略了给定数据库中可能存在的分层数据结构。层次模型允许检查数据聚类对结果的影响。
将传统的逻辑回归和随机截距固定斜率层次模型拟合到 2005 年至 2007 年在马萨诸塞州住院的患者数据集。我们比较了两种建模技术的观察到的与预期的（O/E）院内死亡比，使用仅在两种方法中收敛的诊断模型的受限 HSMR，以及在它们收敛时使用层次诊断模型组合的完整混合 HSMR，加上使用标准逻辑回归模型的其余诊断。
我们根据全国范围内 80%的院内死亡归因于 36 种诊断，将分析限制在 36 种诊断中，基于 1043813 例住院（59 家医院）。由于 15 种诊断组中的层次模型无法收敛，因此无法进行完整的 HSMR 比较。基于 21 种诊断组收敛（552933 例住院）的数据得出的受限 HSMR 显示出非常高的相关性（Pearson r = 0.99）。传统的逻辑回归和层次模型都识别出了 12 个共同的统计异常值，其中 7 个具有高 O/E 值，5 个具有低 O/E 值。此外，多水平分析确定了 5 个额外的独特高异常值和 1 个额外的独特低异常值，而常规模型确定了 2 个额外的独特低异常值。
在 O/E 比率方面，两种建模技术得到了相似的结果。然而，由于层次模型与收敛问题相关，传统的逻辑回归仍然是我们计算 HSMR 的推荐方法。
