Matching for several nominal covariates with many levels has usually been thought to be difficult because these covariates combine to form an enormous number of interaction categories with few if any people in most such categories. Moreover, because nominal variables are not ordered, there is often no notion of a “close substitute” when an exact match is unavailable. In a case-control study of the risk factors for readmission within 30 days of surgery in the Medicare population, we wished to match for 47 hospitals, 15 surgical procedures grouped or nested within 5 procedure groups, two genders, or 47 × 15 × 2 = 1410 categories. In addition, we wished to match as closely as possible for the continuous variable age (65–80 years). There were 1380 readmitted patients or cases. A fractional factorial experiment may balance main effects and low-order interactions without achieving balance for high-order interactions. In an analogous fashion, we balance certain main effects and low-order interactions among the covariates; moreover, we use as many exactly matched pairs as possible. This is done by creating a match that is exact for several variables, with a close match for age, and both a “near-exact match” and a “finely balanced match” for another nominal variable, in this case a 47 × 5 = 235 category variable representing the interaction of the 47 hospitals and the five surgical procedure groups. The method is easily implemented in R.

中文翻译：

---

手术后再入院病例对照研究中几个稀疏名义变量的匹配

匹配具有多个级别的几个名义协变量通常被认为是困难的，因为这些协变量组合形成了大量的交互类别，在大多数此类类别中几乎没有人。此外，由于名义变量没有排序，因此当无法获得精确匹配时，通常没有“接近替代”的概念。在 Medicare 人群手术后 30 天内再入院风险因素的病例对照研究中，我们希望匹配 47 家医院、15 个手术程序分组或嵌套在 5 个程序组中、两种性别或 47 × 15 × 2 = 1410 个类别。此外，我们希望尽可能匹配连续可变年龄（65-80 岁）。有1380名患者或病例再次入院。部分析因实验可能会平衡主效应和低阶相互作用，而无法实现高阶相互作用的平衡。以类似的方式，我们平衡协变量之间的某些主效应和低阶相互作用；此外，我们使用尽可能多的完全匹配对。这是通过为多个变量创建一个精确匹配来完成的，与年龄接近匹配，以及另一个名义变量的“接近精确匹配”和“精细平衡匹配”，在这种情况下为 47 × 5 = 235 个类别变量代表 47 家医院和 5 个外科手术组之间的相互作用。该方法在 R 中很容易实现。我们使用尽可能多的完全匹配对。这是通过为多个变量创建一个精确匹配来完成的，与年龄接近匹配，以及另一个名义变量的“接近精确匹配”和“精细平衡匹配”，在这种情况下为 47 × 5 = 235 个类别变量代表 47 家医院和 5 个外科手术组之间的相互作用。该方法在 R 中很容易实现。我们使用尽可能多的完全匹配对。这是通过为多个变量创建一个精确匹配来完成的，与年龄接近匹配，以及另一个名义变量的“接近精确匹配”和“精细平衡匹配”，在这种情况下为 47 × 5 = 235 个类别变量代表 47 家医院和 5 个外科手术组之间的相互作用。该方法在 R 中很容易实现。