Recovery and inference of causal effects with sequential adjustment for confounding and attrition

Confounding bias and selection bias are two significant challenges to the validity of conclusions drawn from applied causal inference. The latter can stem from informative missingness, such as in cases of attrition. We introduce the Sequential Adjustment Criteria (SAC), which extend available graphical conditions for recovering causal effects using sequential regressions, allowing for the inclusion of post-exposure and forbidden variables in the admissible adjustment sets. We propose an estimator for the recovered Average Treatment Effect (ATE) based on Targeted Minimum-Loss Estimation (TMLE), which enjoys multiple robustness under certain conditions. This approach ensures consistency even in scenarios where the Double Inverse Probability Weighting (DIPW) and the na\"ive plug-in sequential regressions approaches fall short. Through a simulation study, we assess the performance of the proposed estimator against alternative methods across different graph setups and model specification scenarios. As a motivating application, we examine the effect 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 align with the accumulated clinical evidence, affirming a positive but small impact of medication on academic achievement.