Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure After Surgery
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用混合整数规划匹配研究术后肾损伤
- 研究问题
- 在观察性研究匹配中，如何直接控制处理组与对照组的协变量失衡，并兼顾配对距离和多个名义协变量的平衡要求？
- 方法与思路
- 作者使用混合整数规划，将失衡指标纳入加权目标函数或容差约束，同时允许精确、近似精确及精细平衡要求。
- 材料陈述的贡献
- 摘要称该方法可系统控制多种矩与分布差异，以Medicare患者术后急性肾损伤研究展示，并提供mipmatch包。
- 阅读关注点
- 应核对失衡权重与容差的选择、约束可行性、求解成本，以及匹配设计如何衔接研究目标、效应估计和敏感性分析。
- 阅读边界
- 索引摘要版本未注明；协变量平衡本身不能保证消除未观测混杂。摘要未说明因果识别条件、效应数值或软件当前可用性。
原文摘要
This article presents a new method for optimal matching in observational studies based on mixed integer programming. Unlike widely used matching methods based on network algorithms, which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls, this new method achieves covariate balance directly, either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance, or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances. The inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match. For example, the method minimizes or constrains differences in univariate moments, such as means, variances, and skewness; differences in multivariate moments, such as correlations between covariates; differences in quantiles; and differences in statistics, such as the Kolmogorov–Smirnov statistic, to minimize the differences in both location and shape of the empirical distributions of the treated units and matched controls. While balancing several of these measures, it is also possible to impose constraints for exact and near-exact matching, and fine and near-fine balance for more than one nominal covariate, whereas network algorithms can finely or near-finely balance only a single nominal covariate. From a practical standpoint, this method eliminates the guesswork involved in current optimal matching methods, and offers a controlled and systematic way of improving covariate balance by focusing the matching efforts on certain measures of covariate imbalance and their corresponding weights or tolerances. A matched case–control study of acute kidney injury after surgery among Medicare patients illustrates these features in detail. A new R package called mipmatch implements the method.