In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects, i.e., the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.
翻译:在观察研究中,因果推断取决于若干关键的识别假设。一个可辨识性条件是假设性假设,这要求治疗的概率与0和1相隔开。也就是说,对于每一种共变组合,都应能够观察被治疗和受控的主体,即共变分布应重叠。如果违背假设性假设,人口水平因果推断必然涉及某种外推法。理想的情况是,在这种情况下应反映因果估计的更大程度的不确定性。为了这个目标,我们设计了一个高斯进程模型,以便在出现实际侵犯正态的情况下估计治疗效果。我们的方法的优点包括:最低分配假设、估算治疗效果的统一模型,以及与共变空间内重叠较少的地区有关的更多不确定性。我们利用模拟研究来评估我们在偏差和效率方面的做法的绩效。然后将这种方法应用于对严重患病的女性病人的研究,以研究发生右心心部畸形的效果。