Causal inference amid missingness-specific independencies and mechanism shifts

TL;DR

This paper introduces extended causal models that incorporate context-specific independencies to better estimate causal effects in the presence of mechanism shifts caused by missing data, providing new estimands and estimators.

Contribution

It develops $lm$-SCMs and $lm$-graphs to account for missingness-induced mechanism shifts, defining new causal effects and proposing robust estimation methods.

Findings

Simulations show differences between FATE and NATE estimands.

Application indicates a small effect of ADHD treatment on test achievement.

Missing data can slightly shift causal effect estimates.

Abstract

The recovery of causal effects in structural models with missing data often relies on $m$-graphs, which assume that missingness mechanisms do not directly influence substantive variables. Yet, in many real-world settings, missing data can alter decision-making processes, as the absence of key information may affect downstream actions and states. To overcome this limitation, we introduce $lm$-SCMs and $lm$-graphs, which extend $m$-graphs by integrating a label set that represents relevant context-specific independencies (CSI), accounting for mechanism shifts induced by missingness. We define two causal effects within these systems: the Full Average Treatment Effect (FATE), which reflects the effect in a hypothetical scenario had no data been missing, and the Natural Average Treatment Effect (NATE), which captures the effect under the unaltered CSIs in the system. We propose recovery criteria for these queries and present doubly-robust estimators for a graphical model inspired by a real-world application. Simulations highlight key differences between these estimands and estimation methods. Findings from the application case suggest a small effect of ADHD treatment upon test achievement among Norwegian children, with a slight effect shift due to missing pre-tests scores.