Rosenbaum P R, Rubin D B
Biometrics. 1985 Mar;41(1):103-16.
Observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments. Matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group. In practice, there is a trade-off between the desires to find matches for all treated units and to obtain matched treated-control pairs that are extremely similar to each other. We derive expressions for the bias in the average matched pair difference due to the failure to match all treated units--incomplete matching, and the failure to obtain exact matches--inexact matching. A practical example shows that the bias due to incomplete matching can be severe, and moreover, can be avoided entirely by using an appropriate multivariate nearest available matching algorithm, which, in the example, leaves only a small residual bias due to inexact matching.
比较治疗组和对照组的观察性研究常用于估计治疗所产生的效果。匹配是一种从大量潜在对照中进行抽样的方法，以产生一个规模适中且表面上与治疗组相似的对照组。在实际操作中，要为所有治疗单位找到匹配对象以及获得彼此极为相似的匹配治疗-对照配对这两个目标之间存在权衡。我们推导了由于未能匹配所有治疗单位（不完全匹配）以及未能获得精确匹配（不精确匹配）而导致的平均匹配对差异偏差的表达式。一个实际例子表明，不完全匹配导致的偏差可能很严重，而且通过使用适当的多变量最近可用匹配算法可以完全避免这种偏差，在该例子中，由于不精确匹配仅留下很小的残余偏差。
