Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail in this manuscript. Our first key contribution is studying a commonly used strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption. We show that even if the joint distribution of principal strata is known, this strategy necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability leads to point identification in this setting, we discuss alternative, weaker assumptions and show how they can lead to informative partial identification regions. An additional contribution is that we provide theoretical support to strategies used in the literature for identifying association parameters that govern the joint distribution of principal strata. We prove that this is possible, but only if the principal ignorability assumption is violated. Additionally, due to partial identifiability of causal effects even when these association parameters are known, we show that these association parameters are only identifiable under strong parametric constraints. Lastly, we extend these results to more flexible semiparametric and nonparametric Bayesian models.

翻译：主层分析是研究涉及处理后变量的因果机制的一般框架。在估计主层因果效应时，通常需要假定主层可忽略性，本文对此进行了详细研究。我们的第一个关键贡献是：研究了一种常见策略，即在不要求主层可忽略性假设的情况下，使用参数模型对结果变量和主层进行联合建模。我们证明，即使已知主层的联合分布，该策略也必然只能导致因果效应的部分识别，即便在非常简单且正确指定的结果模型下也是如此。尽管主层可忽略性在此设定下能实现点识别，但我们讨论了替代性的、较弱的假设，并展示了这些假设如何能产生信息性部分识别区域。另一个贡献是：我们为文献中用于识别控制主层联合分布的关联参数的策略提供了理论支持。我们证明这是可能的，但仅在违背主层可忽略性假设时成立。此外，由于即使已知这些关联参数，因果效应仍可能仅被部分识别，我们证实在强参数约束条件下这些关联参数才能被识别。最后，我们将这些结果扩展至更灵活的半参数及非参数贝叶斯模型。