Defining and Estimating Causal Effects in Randomized Single-Case Alternating Treatment Design: A Counterfactual Approach

• In Event: Effect Estimation for Causality and Prediction: Multilevel and Single-case Designs, Machine Learning, and Distributional Assumptions

Abstract

Single-case alternating treatment designs (ATDs) are effective for establishing internal validity, yet quantifying causal effects remains a significant challenge. Traditional estimators like the mean difference (MD) and percentage of nonoverlapping data (PND) lack a formal causal definition, leading to ambiguity. This study addresses the issue by defining a causal estimand for the average immediate effect in randomized ATDs using a counterfactual framework and introducing inverse probability weighting (IPW) and augmented IPW (AIPW) estimators. A Monte Carlo simulation compared these estimators to traditional methods. Results show the AIPW estimator is consistently unbiased and efficient, especially with time trends or lag-1 effects, where traditional estimators become severely biased. AIPW also demonstrated superior statistical power when a lag-1 effect was present.

Authors

• Wen Luo, Texas A&M University

• Chendong Li, Texas A&M University