We consider missingness in the context of causal inference when the outcome of interest may be missing. If the outcome directly affects its own missingness status, i.e., it is "self-censoring", this may lead to severely biased causal effect estimates. Miao et al. [2015] proposed the shadow variable method to correct for bias due to self-censoring; however, verifying the required model assumptions can be difficult. Here, we propose a test based on a randomized incentive variable offered to encourage reporting of the outcome that can be used to verify identification assumptions that are sufficient to correct for both self-censoring and confounding bias. Concretely, the test confirms whether a given set of pre-treatment covariates is sufficient to block all backdoor paths between the treatment and outcome as well as all paths between the treatment and missingness indicator after conditioning on the outcome. We show that under these conditions, the causal effect is identified by using the treatment as a shadow variable, and it leads to an intuitive inverse probability weighting estimator that uses a product of the treatment and response weights. We evaluate the efficacy of our test and downstream estimator via simulations.

翻译：我们考虑在因果推断中结果变量可能出现缺失的情况。若结果变量直接影响自身的缺失状态（即“自我审查”），可能导致严重偏误的因果效应估计。Miao等人[2015]提出影子变量法以校正自我审查带来的偏误，但验证所需的模型假设存在困难。本文基于随机激励变量（该变量用于鼓励结果报告）提出一种检验方法，可验证足以同时校正自我审查偏误与混杂偏误的识别假设。具体而言，该检验确认：给定协变量集是否能有效阻断处理与结果之间的所有后门路径，以及条件于结果后处理与缺失指示符之间的所有路径。我们证明在上述条件下，通过将处理变量作为影子变量可识别因果效应，进而采用处理权重与响应权重的乘积构建直观的逆概率加权估计量。通过仿真实验评估了所提检验方法及下游估计量的有效性。