With reference to a binary outcome and a binary mediator, we derive identification bounds for natural effects under a reduced set of assumptions. Specifically, no assumptions about confounding are made that involve the outcome; we only assume no unobserved exposure-mediator confounding as well as a condition termed partially constant cross-world dependence (PC-CWD), which poses fewer constraints on the counterfactual probabilities than the usual cross-world independence assumption. The proposed strategy can be used also to achieve interval identification of the total effect, which is no longer point identified under the considered set of assumptions. Our derivations are based on postulating a logistic regression model for the mediator as well as for the outcome. However, in both cases the functional form governing the dependence on the explanatory variables is allowed to be arbitrary, thereby resulting in a semi-parametric approach. To account for sampling variability, we provide delta-method approximations of standard errors in order to build uncertainty intervals from identification bounds. The proposed method is applied to a dataset gathered from a Spanish prospective cohort study. The aim is to evaluate whether the effect of smoking on lung cancer risk is mediated by the onset of pulmonary emphysema.

翻译：针对二元结局和二元中介变量，我们在简化假设集下推导了自然效应的识别边界。具体而言，不涉及结局的混杂假设均不作要求；我们仅假设不存在未观测的暴露-中介混杂，以及一个称为部分恒定跨世界依赖性（PC-CWD）的条件，该条件对反事实概率施加的约束少于通常的跨世界独立性假设。所提策略亦可用于实现总效应的区间识别，在所考虑的假设集下总效应不再能被点识别。我们的推导基于对中介变量和结局分别建立逻辑回归模型。然而，在这两种情况下，解释变量依赖关系的函数形式允许是任意的，从而形成半参数方法。为考虑抽样变异性，我们提供了标准误的Delta方法近似，以便从识别边界构建不确定性区间。所提方法应用于一项西班牙前瞻性队列研究收集的数据集，旨在评估吸烟对肺癌风险的影响是否通过肺气肿发病中介。