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 efficacy of our method via simulations and an application to the Framingham Heart Study.

翻译：先前将半参数理论应用于因果推断的研究主要关注在预设因果模型下推导具有统计稳健性的估计量，该模型允许识别目标因果参数。然而，这类模型的正确设定（通常涉及不可检验的假设）是一个根本性挑战。证据因子法是一种在两种或多种候选因果模型下对共同因果零假设进行联合假设检验的方法。在一定条件下，该方法能够保证只要至少一个基础模型正确，检验即有效——这构成了一种因果稳健性。我们提出将半参数理论与证据因子相结合的方法。通过构建基于K个候选因果模型导出的不同识别泛函所对应的K个渐近线性半参数估计量的联合渐近正态性，我们开发了一种因果零假设检验方法。研究表明，该检验同时具备统计稳健性与因果稳健性：只要至少一个候选因果模型正确，检验即有效，同时允许在估计 nuisance 函数时达到比参数速率更慢的收敛速度。我们通过模拟实验和弗雷明汉心脏研究的应用验证了该方法的有效性。