Optimal Covariate Balancing Conditions in Propensity Score Estimation
Optimal Covariate Balancing Conditions in Propensity Score Estimation
复制标题
DOI：
10.1080/07350015.2021.2002159
复制
发表时间：
2021-12-17
影响因子：
3
通讯作者：
Yang, Xiaolin
中科院分区：
文献类型：
--
作者：
Fan, Jianqing;Imai, Kosuke;Yang, Xiaolin
处理加权逆概率（IPTW）是估计平均处理效果（ATE）的常用方法。然而，实证研究表明，IPTW估计器可能对倾向得分模型的错误规范很敏感。为了解决这一问题，研究人员提出通过直接优化预处理协变量的平衡来估计倾向得分。虽然这些方法在经验上表现良好，但人们对平衡条件的选择如何影响其理论性质知之甚少。为了填补这一空白，我们首先对局部模型错配下基于协变量平衡倾向得分（CBPS）方法的IPTW估计器的渐近偏差和效率进行了表征。在此基础上，我们展示了如何优化选择协变量平衡函数，并提出了一个最优的基于cbps的IPTW估计器。该估计器具有双重鲁棒性；如果倾向得分模型或结果模型中的任何一个是正确的，则ATE是一致的。此外，当两个模型都正确指定时，所提出的估计器是局部半参数有效的。为了进一步放宽参数假设，我们使用筛选估计方法扩展了我们的方法。我们证明了所得到的估计量在一组更弱的假设下是全局有效的，并且比现有的估计量具有更小的渐近偏差。最后，我们通过模拟和实证研究来评估所提出的估计器的有限样本性能。一个开源软件包可用于实现所提出的方法。
Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pretreatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asymptotic bias and efficiency of the IPTW estimator based on the covariate balancing propensity score (CBPS) methodology under local model misspecification. Based on this analysis, we show how to optimally choose the covariate balancing functions and propose an optimal CBPS-based IPTW estimator. This estimator is doubly robust; it is consistent for the ATE if either the propensity score model or the outcome model is correct. In addition, the proposed estimator is locally semiparametric efficient when both models are correctly specified. To further relax the parametric assumptions, we extend our method by using a sieve estimation approach. We show that the resulting estimator is globally efficient under a set of much weaker assumptions and has a smaller asymptotic bias than the existing estimators. Finally, we evaluate the finite sample performance of the proposed estimators via simulation and empirical studies. An open-source software package is available for implementing the proposed methods.