Abstract

Motivated by designing observational studies using matching methods subject to fine balance constraints, we introduce a new optimization problem. This problem consists of two phases. In the first phase, the goal is to cluster the values of a continuous covariate into a limited number of intervals. In the second phase, we find the optimal matching subject to fine balance constraints with respect to the new covariate we obtained in the first phase. We show that the resulting optimization problem is NP-hard. However, it admits an FPT algorithm with respect to a natural parameter. This FPT algorithm also translates into a polynomial time algorithm for the most natural special cases of the problem.

中文翻译：

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选择间隔以优化受精细平衡约束的观察研究的设计

摘要

通过使用受精细平衡约束的匹配方法设计观察研究，我们引入了一个新的优化问题。这个问题由两个阶段组成。在第一阶段，目标是将连续协变量的值聚类到有限数量的区间中。在第二阶段，我们找到相对于第一阶段获得的新协变量受到精细平衡约束的最佳匹配。我们证明了由此产生的优化问题是 NP 困难的。然而，它承认关于自然参数的 FPT 算法。该 FPT 算法还可以转换为多项式时间算法，用于解决问题的最自然的特殊情况。