Primary Submission Category: Machine Learning and Causal Inference
Doubly Robust Estimation of Treatment Effects with Missing Outcomes in Longitudinal Studies
Authors: Asteria Chilambo, Zach Branson,
Presenting Author: Asteria Chilambo*
Longitudinal studies are central to understanding dynamic treatment effects, but their analysis is complicated by within-unit temporal dependence and sequentially missing outcomes. Standard methods, such as outcome regression or inverse-probability weighting can address missingness, but may be biased under model misspecification or when nonparametric models are used. Although doubly robust estimators offer protection against such misspecification, existing theory largely focuses on cross-sectional data or single-time-point missingness. We develop a doubly robust framework for estimating mean potential outcomes under a sequential missing-at-random (SMAR) assumption. We derive the efficient influence function for the mean potential outcome under a fixed treatment regime and construct a doubly robust estimator that is root-n consistent and asymptotically normal, provided that cross-fitting is used and the nuisance functions are estimated at n^(-1/4) rates. The estimator allows flexible, data-adaptive estimation of nuisance components. Our method is motivated by and applied to a longitudinal randomized clinical trial of mindfulness-based interventions for irritable bowel syndrome, in which outcomes are collected via smartphone surveys and occasional nonresponse induces complex missingness structure. The method relies on a strong SMAR assumption using observed history (prior non-missing outcomes); future work will relax the assumption to account for unobserved past outcomes.