We consider mediated effects of an exposure, X on an outcome, Y, via a mediator, M, under no unmeasured confounding assumptions in the setting where models for the conditional expectation of the mediator and outcome are partially linear. We propose G-estimators for the direct and indirect effects and demonstrate consistent asymptotic normality for indirect effects when models for the conditional means of M, or X and Y are correctly specified, and for direct effects, when models for the conditional means of Y, or X and M are correct. This marks an improvement, in this particular setting, over previous ‘triple’ robust methods, which do not assume partially linear mean models. Testing of the no-mediation hypothesis is inherently problematic due to the composite nature of the test (either X has no effect on M or M no effect on Y), leading to low power when both effect sizes are small. We use generalized methods of moments (GMM) results to construct a new score testing framework, which includes as special cases the no-mediation and the no-direct-effect hypotheses. The proposed tests rely on an orthogonal estimation strategy for estimating nuisance parameters. Simulations show that the GMM-based tests perform better in terms of power and small sample performance compared with traditional tests in the partially linear setting, with drastic improvement under model misspecification. New methods are illustrated in a mediation analysis of data from the COPERS trial, a randomized trial investigating the effect of a non-pharmacological intervention of patients suffering from chronic pain. An accompanying R package implementing these methods can be found at github.com/ohines/plmed.

我们考虑介导的曝光，影响X上的结果，ÿ，通过调解，中号，下的设置没有不可测混杂的假设，其中型号为调解员和成果的条件期望是部分线性。我们提出了直接和间接效应的 G 估计量，并证明了当M或X和Y的条件均值的模型正确指定时间接效应的一致渐近正态性，而对于直接效应，当Y的条件均值的模型时，或X和M是正确的。在此特定设置中，这标志着对先前不假设部分线性均值模型的“三重”稳健方法的改进。无调解假说的测试是在测试的复合性质固有问题的，因为（无论是X有没有影响中号或中号没有影响ÿ)，当两个效应量都很小时导致低功效。我们使用广义矩方法 (GMM) 结果来构建新的分数测试框架，其中包括作为特殊情况的无中介和无直接影响假设。建议的测试依赖于用于估计干扰参数的正交估计策略。仿真表明，与部分线性设置中的传统测试相比，基于 GMM 的测试在功效和小样本性能方面表现更好，在模型错误指定的情况下有显着改善。COPERS 试验数据的中介分析说明了新方法，这是一项随机试验，研究非药物干预对慢性疼痛患者的影响。可以在以下位置找到实现这些方法的随附 R 包github.com/ohines/plmed。