Inverse propensity-score weighted (IPW) estimators are prevalent in causal inference for estimating average treatment effects in observational studies. Under unconfoundedness, given accurate propensity scores and $n$ samples, the size of confidence intervals of IPW estimators scales down with $n$, and, several of their variants improve the rate of scaling. However, neither IPW estimators nor their variants are robust to inaccuracies: even if a single covariate has an $\varepsilon>0$ additive error in the propensity score, the size of confidence intervals of these estimators can increase arbitrarily. Moreover, even without errors, the rate with which the confidence intervals of these estimators go to zero with $n$ can be arbitrarily slow in the presence of extreme propensity scores (those close to 0 or 1). We introduce a family of Coarse IPW (CIPW) estimators that captures existing IPW estimators and their variants. Each CIPW estimator is an IPW estimator on a coarsened covariate space, where certain covariates are merged. Under mild assumptions, e.g., Lipschitzness in expected outcomes and sparsity of extreme propensity scores, we give an efficient algorithm to find a robust estimator: given $\varepsilon$-inaccurate propensity scores and $n$ samples, its confidence interval size scales with $\varepsilon+1/\sqrt{n}$. In contrast, under the same assumptions, existing estimators' confidence interval sizes are $\Omega(1)$ irrespective of $\varepsilon$ and $n$. Crucially, our estimator is data-dependent and we show that no data-independent CIPW estimator can be robust to inaccuracies.

翻译：逆倾向得分加权（IPW）估计量在观测性研究中广泛用于估计平均处理效应。在无混淆性假设下，给定准确的倾向得分和 $n$ 个样本，IPW估计量的置信区间大小随 $n$ 缩放递减，且其若干变体改进了缩放速率。然而，IPW估计量及其变体均对不准确性缺乏稳健性：即使单个协变量的倾向得分存在 $\varepsilon>0$ 的加性误差，这些估计量的置信区间大小可能任意增大。此外，即使没有误差，在存在极端倾向得分（接近0或1）的情况下，这些估计量的置信区间随 $n$ 趋近于零的速率可能任意缓慢。我们引入了一类粗化IPW（CIPW）估计量，其涵盖了现有IPW估计量及其变体。每个CIPW估计量是在粗化协变量空间上的IPW估计量，其中某些协变量被合并。在温和假设下（例如期望结果的Lipschitz连续性和极端倾向得分的稀疏性），我们给出一种高效算法以寻找稳健估计量：给定 $\varepsilon$ 不准确的倾向得分和 $n$ 个样本，其置信区间大小以 $\varepsilon+1/\sqrt{n}$ 缩放。相比之下，在相同假设下，现有估计量的置信区间大小为 $\Omega(1)$，与 $\varepsilon$ 和 $n$ 无关。关键的是，我们的估计量具有数据依赖性，并且我们证明不存在数据无关的CIPW估计量能够对不准确性保持稳健。