Inverse weighting with an estimated propensity score is widely used by estimation methods in causal inference to adjust for confounding bias. However, directly inverting propensity score estimates can lead to instability, bias, and excessive variability due to large inverse weights, especially when treatment overlap is limited. In this work, we propose a post-hoc calibration algorithm for inverse propensity weights that generates well-calibrated, stabilized weights from user-supplied, cross-fitted propensity score estimates. Our approach employs a variant of isotonic regression with a loss function specifically tailored to the inverse propensity weights. Through theoretical analysis and empirical studies, we demonstrate that isotonic calibration improves the performance of doubly robust estimators of the average treatment effect.

翻译：逆概率加权法通过估计倾向性得分，被广泛应用于因果推断中的估计方法以调整混杂偏倚。然而，直接对倾向性得分估计值取倒数可能导致不稳定、偏倚及因大逆权重引起的过度变异性，尤其在处理组重叠有限时更为明显。本研究提出一种用于逆倾向性权重的后验校准算法，该算法能够从用户提供的交叉拟合倾向性得分估计中生成校准良好且稳定的权重。我们的方法采用了一种等渗回归的变体，其损失函数专门针对逆倾向性权重进行定制。通过理论分析和实证研究，我们证明等渗校准能够提升平均处理效应的双重稳健估计器的性能。