Comparing causal parameters with many treatments and positivity violations
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多处理与正值性违背下的因果参数比较
- 研究问题
- 处理取值较多且标准正值性难以成立时，如何构造可识别的因果参数，使其比较仍能反映目标处理之间的效果排序？
- 方法与思路
- 作者提出保留条件处理均值排序的可比性准则，研究较弱正值性下的截尾及平滑截尾处理均值，并构造双重稳健式估计量。
- 材料陈述的贡献
- 摘要称，许多常用参数不满足可比性准则，而两类截尾均值满足该准则；平滑版本的估计量在非参数条件下达到参数收敛速率。
- 阅读关注点
- 应核对可比性准则的量词与条件、较弱正值性的具体要求、截尾如何改变目标人群，以及参数速率所需的辅助估计条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未列出识别和收敛条件，不能理解为完全无需重叠或适用于任意截尾。
原文摘要
Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, with each targeting a different treatment. Treatment-specific means are commonly used, but their identification requires a positivity assumption, that every subject has a non-zero probability of receiving each treatment. This is often implausible, especially when treatment can take many values. Causal parameters based on dynamic stochastic interventions offer robustness to positivity violations. However, comparing these parameters may fail to reflect the effects of the underlying target treatments because the parameters can depend on outcomes under non-target treatments. To clarify when two parameters targeting different treatments yield a useful comparison of treatment efficacy, we propose a comparability criterion: if the conditional treatment-specific mean for one treatment is greater than that for another, then the corresponding causal parameter should also be greater. Many standard parameters fail to satisfy this criterion, but we show that only a mild positivity assumption is needed to identify parameters that yield useful comparisons. We then provide two simple examples that satisfy this criterion and are identifiable under the milder positivity assumption: trimmed and smooth trimmed treatment-specific means with multi-valued treatments. For smooth trimmed treatment-specific means, we develop doubly robust-style estimators that attain parametric convergence rates under nonparametric conditions. We illustrate our methods with an analysis of dialysis providers in New York State.