优化细化分层,平衡协变量。

IF 1.4 4区 数学 Q3 BIOLOGY
Biometrics Pub Date : 2024-07-01 DOI:10.1093/biomtc/ujae061
Katherine Brumberg, Dylan S Small, Paul R Rosenbaum
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引用次数: 0

摘要

怎样才能最好地将一个分层一分为二,从而最大限度地减少许多协变量在分层内的不平衡?我们将其表述为一个整数程序,并通过线性程序的随机舍入来近似求解。线性程序可能会将一部分人分配到每个细化分层。随机四舍五入法将小数人视为概率,使用有偏差的硬币将完整的人分配到分层中。随机四舍五入是一种经过充分研究的理论技术,用于逼近某些无法解决的整数程序的最优解。当分层中的人数相对于协变量的数量较多时,我们证明了以下新结果:(i) 随机舍入分割分层的随机化程度很低,因此它非常类似于不分割完整人数的线性规划松弛法;(ii) 线性松弛法和随机舍入解为无法实现的整数规划解设定了下限和上限;由于(i)的原因,这些上限往往很接近,从而证明了随机舍入解的可用性。我们使用一项观察性研究进行说明,该研究通过使用倾向得分从 5735 名患者中选出 2016 名患者组成匹配对,平衡了许多协变量。而我们形成了 5 个倾向得分层,并将其细化为 10 个层,从而在保留所有患者的同时获得了极佳的协变量平衡。CRAN 上的 R 软件包 optrefine 实现了这一方法。补充材料可在线获取。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal refinement of strata to balance covariates.

What is the best way to split one stratum into two to maximally reduce the within-stratum imbalance in many covariates? We formulate this as an integer program and approximate the solution by randomized rounding of a linear program. A linear program may assign a fraction of a person to each refined stratum. Randomized rounding views fractional people as probabilities, assigning intact people to strata using biased coins. Randomized rounding is a well-studied theoretical technique for approximating the optimal solution of certain insoluble integer programs. When the number of people in a stratum is large relative to the number of covariates, we prove the following new results: (i) randomized rounding to split a stratum does very little randomizing, so it closely resembles the linear programming relaxation without splitting intact people; (ii) the linear relaxation and the randomly rounded solution place lower and upper bounds on the unattainable integer programming solution; and because of (i), these bounds are often close, thereby ratifying the usable randomly rounded solution. We illustrate using an observational study that balanced many covariates by forming matched pairs composed of 2016 patients selected from 5735 using a propensity score. Instead, we form 5 propensity score strata and refine them into 10 strata, obtaining excellent covariate balance while retaining all patients. An R package optrefine at CRAN implements the method. Supplementary materials are available online.

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来源期刊
Biometrics
Biometrics 生物-生物学
CiteScore
2.70
自引率
5.30%
发文量
178
审稿时长
4-8 weeks
期刊介绍: The International Biometric Society is an international society promoting the development and application of statistical and mathematical theory and methods in the biosciences, including agriculture, biomedical science and public health, ecology, environmental sciences, forestry, and allied disciplines. The Society welcomes as members statisticians, mathematicians, biological scientists, and others devoted to interdisciplinary efforts in advancing the collection and interpretation of information in the biosciences. The Society sponsors the biennial International Biometric Conference, held in sites throughout the world; through its National Groups and Regions, it also Society sponsors regional and local meetings.
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