Variable-ratio matching is a flexible alternative to conventional $1$-to-$k$ matching for designing observational studies that emulate a target randomized controlled trial (RCT). To achieve fine balance -- that is, matching treated and control groups to have the same marginal distribution on selected covariates -- conventional approaches typically partition the data into strata based on estimated entire numbers and then perform a series of $1$-to-$k$ matches within each stratum, with $k$ determined by the stratum-specific entire number. This ``divide-and-conquer" strategy has notable limitations: (1) fine balance typically does not hold in the final pooled sample, and (2) more controls may be discarded than necessary. To address these limitations, we propose a one-shot variable-ratio matching algorithm. Our method produces designs with exact fine balance on selected covariates in the matched sample, mimicking a hypothetical RCT where units are first grouped into sets of different sizes and one unit within each set is assigned to treatment while others to control. Moreover, our method achieves comparable or superior balance across many covariates and retains more controls in the final matched design, compared to the ``divide-and-conquer" approach. We demonstrate the advantages of the proposed design over the conventional approach via simulations and using a dataset studying the effect of right heart catheterization on mortality among critically ill patients. The algorithm is implemented in the R package match2C.

翻译：变量比率匹配是设计模拟目标随机对照试验（RCT）的观察性研究时，对传统$1$对$k$匹配的一种灵活替代方案。为实现精细平衡——即匹配处理组与对照组，使其在选定协变量上具有相同的边际分布——传统方法通常基于估计的整数将数据划分为若干层，然后在每层内执行一系列$1$对$k$匹配，其中$k$由该层特定的整数决定。这种“分而治之”策略存在显著局限性：（1）精细平衡通常在最终合并样本中不成立；（2）可能丢弃比必要更多的对照个体。为解决这些局限性，我们提出了一种一次性变量比率匹配算法。我们的方法能够在匹配样本中对选定协变量实现精确的精细平衡，模拟一个假设的RCT，其中单元首先被分组为不同大小的集合，每个集合内一个单元被分配至处理组，其余分配至对照组。此外，与“分而治之”方法相比，我们的方法在众多协变量上实现了相当或更优的平衡，并在最终匹配设计中保留了更多的对照个体。我们通过模拟研究以及使用一个研究右心导管插入术对危重患者死亡率影响的数据集，展示了所提出设计相对于传统方法的优势。该算法已在R包match2C中实现。