Regression-Based Estimation of Causal Effects in the Presence of Selection Bias and Confounding
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存在选择偏差与混杂时的因果效应回归估计
- 研究问题
- 连续处理与结果受到系统性缺失和混杂影响时，能否借助外部无偏观测数据中的代理变量，恢复干预下的期望结果？
- 方法与思路
- 作者推导利用代理变量纠正选择机制与混杂的识别及恢复条件，并提出线性两步回归估计量，可通过加入非线性基函数扩展。
- 材料陈述的贡献
- 摘要称给出因果效应可识别与可恢复的理论条件；无混杂时，两步回归与既有估计量相容且方差更低，并以模拟检验混杂情形。
- 阅读关注点
- 应核对代理变量与选择、处理及结果的关系，外部数据与目标总体的连接条件，以及低方差比较和非线性扩展各自适用的范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核实；摘要未列出完整识别约束，也未说明代理变量不足或外部数据失配的后果。
原文摘要
We consider the problem of estimating the expected causal effect $E[Y|do(X)]$ for a target variable $Y$ when treatment $X$ is set by intervention, focusing on continuous random variables. In settings without selection bias or confounding, $E[Y|do(X)] = E[Y|X]$, which can be estimated using standard regression methods. However, regression fails when systematic missingness induced by selection bias, or confounding distorts the data. Proxy variables unaffected by the selection process can, under certain constraints, be used to correct for selection bias to recover $E[Y|X]$, and hence $E[Y|do(X)]$, reliably. When data is additionally affected by confounding, recovering the causal effect from selection-biased data is more challenging and requires access to proxies to both correct for confounding and for the selection mechanism. Assuming access to such proxies from external unbiased observational data, we derive theoretical conditions ensuring identifiability and recoverability of causal effects. We further introduce a linear two-step regression estimator (TSR), which can be extended through adding non-linear basis functions, capable of exploiting proxy variables to adjust for selection bias while accounting for confounding. We show that TSR is consistent with previous estimators when confounding is absent, but achieves a lower variance. Extensive simulation studies validate TSR's correctness for scenarios that include both selection bias and confounding with proxy variables.