Confounding bias and selection bias are two significant challenges to the validity of conclusions drawn from applied causal inference. The latter can arise through informative missingness, wherein relevant information about units in the target population is missing, censored, or coarsened due to factors related to the exposure, the outcome, or their consequences. We extend existing graphical criteria to address selection bias induced by missing outcome data by leveraging post-exposure variables. We introduce the Sequential Adjustment Criteria (SAC), which support recovering causal effects through sequential regressions. A refined estimator is further developed by applying Targeted Minimum-Loss Estimation (TMLE). Under certain regularity conditions, this estimator is multiply-robust, ensuring consistency even in scenarios where the Inverse Probability Weighting (IPW) and the sequential regressions approaches fall short. A simulation exercise featuring various toy scenarios compares the relative bias and robustness of the two proposed solutions against other estimators. As a motivating application case, we study the effects of pharmacological treatment for Attention-Deficit/Hyperactivity Disorder (ADHD) upon the scores obtained by diagnosed Norwegian schoolchildren in national tests using observational data ($n=9\,352$). Our findings support the accumulated clinical evidence affirming a positive but small effect of stimulant medication on school performance. A small positive selection bias was identified, indicating that the treatment effect may be even more modest for those exempted or abstained from the tests.

翻译：混淆偏差和选择偏差是应用因果推断结论有效性的两大挑战。后者可能通过信息性缺失产生，即目标总体中关于个体的相关信息因暴露、结果或其后果相关因素而缺失、删失或粗化。我们通过利用暴露后变量，扩展了现有图形准则以解决缺失结果数据导致的选择偏差。我们引入序贯调整准则，该准则通过序贯回归支持因果效应的恢复。进一步采用目标最小损失估计方法开发了改进的估计量。在特定正则条件下，该估计量为多重稳健的，即使在逆概率加权和序贯回归方法失效的场景中也能确保一致性。通过模拟实验（包含多种假设情景），我们比较了两种解决方案与其他估计量的相对偏差和稳健性。作为激励性应用案例，我们利用观测数据（n=9 352）研究注意缺陷/多动障碍药物治疗对挪威学龄儿童国家测试成绩的影响。研究结果支持累积的临床证据，确认兴奋剂药物对在校表现有正向但微小的效应。发现存在轻微的正向选择偏差，表明对于免试或放弃测试者，治疗效果可能更为微弱。