# Graphical Criteria for Efficient Total Effect Estimation via Adjustment in Causal Linear Models

## TL;DR

This paper introduces graphical criteria for selecting covariate adjustment sets that optimize the accuracy of total effect estimates in causal linear models, applicable to various graph types.

## Contribution

It develops a graphical criterion to compare asymptotic variances of adjustment sets and introduces tools for variance reduction and optimal adjustment set identification.

## Key findings

- Graphical criteria effectively compare adjustment set variances.
- Pruning procedure reduces variance in adjustment sets.
- Optimal adjustment sets minimize asymptotic variance.

## Abstract

Covariate adjustment is a commonly used method for total causal effect estimation. In recent years, graphical criteria have been developed to identify all valid adjustment sets, that is, all covariate sets that can be used for this purpose. Different valid adjustment sets typically provide total effect estimates of varying accuracies. Restricting ourselves to causal linear models, we introduce a graphical criterion to compare the asymptotic variances provided by certain valid adjustment sets. We employ this result to develop two further graphical tools. First, we introduce a simple variance reducing pruning procedure for any given valid adjustment set. Second, we give a graphical characterization of a valid adjustment set that provides the optimal asymptotic variance among all valid adjustment sets. Our results depend only on the graphical structure and not on the specific error variances or edge coefficients of the underlying causal linear model. They can be applied to directed acyclic graphs (DAGs), completed partially directed acyclic graphs (CPDAGs) and maximally oriented partially directed acyclic graphs (maximal PDAGs). We present simulations and a real data example to support our results and show their practical applicability.