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

Confounding bias and selection bias bring 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 from confounding and attrition using sequential regressions, allowing for the inclusion of post-exposure and forbidden variables in the adjustment sets. We propose an estimator for the recovered Average Treatment Effect (ATE) based on Targeted Minimum-Loss Estimation (TMLE), which exhibits multiple robustness under certain technical conditions. This approach ensures consistency even in scenarios where the Double Inverse Probability Weighting (DIPW) and the naive 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.