When constructing a model to estimate the causal effect of a treatment, it is necessary to control for other factors which may have confounding effects. Because the ignorability assumption is not testable, however, it is usually unclear which minimal set of controls is appropriate -- as is their appropriate functional form in the model -- and effect estimation can be sensitive to these choices. A common approach in this case is to fit several models, each with a different control specification (under the assumption that the available controls are sufficient but possibly not all necessary to deconfound the treatment effect), but it is difficult to reconcile inference for the treatment effect under the multiple resulting posterior distributions. Therefore we propose a two-stage approach to measure the sensitivity of effect estimation with respect to control specification. In the first stage, a model is fit with all available controls using a prior carefully selected to adjust for confounding. In the second stage, posterior distributions are calculated for the treatment effect under submodels of nested sets of controls using projected posteriors under the full model, providing valid Bayesian inference. We demonstrate how our approach can be used to detect influential confounders in a dataset, and apply it in a sensitivity analysis of an observational study measuring the effect of legalized abortion on crime rates.
翻译:在设计一种模型来估计治疗的因果关系时,有必要控制可能造成混乱影响的其他因素。然而,由于忽略的假设是无法测试的,因此通常不清楚哪一套最起码的控制是适当的 -- -- 和模型中的适当功能形式一样 -- -- 并且效果估计可能对这些选择很敏感。在这种情况下,一个共同的方法是适合几种模型,每个模型都有不同的控制规格(假设现有的控制足够,但可能并非全部必要,以解析治疗效果),但难以调和在多种结果的后部分布下治疗效果的推断。因此,我们建议采用两阶段方法衡量影响估计在控制规格方面的敏感度。在第一阶段,模型适合所有现有的控制,使用事先经过仔细选择的调整以调和的调和。在第二阶段,利用全模型预测的后部控制组合,利用预测的后部效应来计算后部分布的治疗效果,提供有效的贝耶斯语推论。我们证明,我们的方法可以用来测量对堕胎率的敏感度。在法律观测中如何测量堕胎率进行法律研究,应用后部分布。