Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of K asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of K candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the K proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study.

翻译：先前将半参数理论应用于因果推断的研究主要集中于推导在预设因果模型下具有统计稳健性的估计量，该模型允许识别所需的因果参数。然而，一个根本性挑战在于此类模型的正确设定，这通常涉及做出不可检验的假设。证据因子是一种在两种或更多候选因果模型下对共同因果零假设进行联合检验的方法。在一定条件下，这会产生一个检验，只要至少有一个底层模型正确，该检验便是有效的，这是一种因果稳健性的形式。我们提出了一种将半参数理论与证据因子相结合的方法。我们基于K个渐近线性半参数估计量的联合渐近正态性，开发了一种因果零假设检验，其中每个估计量均源自K个候选因果模型中每一个所推导出的不同识别泛函。我们证明，该检验同时提供了统计与因果稳健性，即只要所提出的K个因果模型中至少有一个正确，检验便是有效的，同时允许在估计干扰函数时以慢于参数模型的速率收敛。我们通过模拟实验以及对弗雷明汉心脏研究和威斯康星纵向研究的应用，展示了我们方法的有效性。