Summary Causal inference in a programme evaluation setting faces the problem of external validity when the treatment effect in the target population is different from the treatment effect identified from the population of which the sample is representative. This paper focuses on a situation where such discrepancy arises by a stratified sampling design based on the individual treatment status and other characteristics. In such settings, the design probability is known from the sampling design but the target population depends on the underlying population share vector, which is often unknown, and, except for special cases, the treatment effect parameters are not identified. In this paper we propose a method of constructing confidence sets that are valid for a given range of population shares. When a benchmark population share vector and a corresponding estimator of a treatment effect parameter are given, we develop a method to discover the scope of external validity with familywise error rate control. Finally, we derive an optimal sampling design that minimizes the semiparametric efficiency bound given a population share associated with a target population. We provide Monte Carlo simulation results and an empirical application to demonstrate the usefulness of our proposals.

中文翻译：

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基于治疗的抽样设计下治疗效果的估计和推断

总结 当目标人群中的治疗效果不同于从样本具有代表性的人群中确定的治疗效果时，项目评估设置中的因果推理面临外部有效性问题。本文重点讨论了这种差异是由基于个体治疗状态和其他特征的分层抽样设计引起的。在这种情况下，设计概率从抽样设计中是已知的，但目标人口取决于潜在的人口份额向量，这通常是未知的，并且除了特殊情况外，不会确定处理效果参数。在本文中，我们提出了一种构建对给定人口份额范围有效的置信度集的方法。当给定基准人口共享向量和相应的治疗效果参数估计量时，我们开发了一种方法来发现具有家庭错误率控制的外部有效性范围。最后，我们推导出一个最优抽样设计，该设计在给定与目标群体相关的群体份额的情况下最小化半参数效率界限。我们提供了蒙特卡洛模拟结果和一个实证应用来证明我们提议的有用性。