Causal inference for treatment effects in partially nested designs.

artially nested designs (PNDs) are common in intervention studies in psychology and other social sciences. With this design, participants are assigned to treatment and control groups on an individual basis, but clustering occurs in some but not all groups (e.g., the treatment group). In recent years, there has been substantial development of methods for analyzing data from PNDs. However, little research has been done on causal inference for PNDs, especially for PNDs with nonrandomized treatment assignments. To reduce the research gap, in the current study, we used the expanded potential outcomes framework to define and identify the average causal treatment effects in PNDs. Based on the identification results, we formulated the outcome models that could produce treatment effect estimates with causal interpretation and evaluated how alternative model specifications affect the causal interpretation. We also developed an inverse propensity weighted (IPW) estimation approach and proposed a sandwich-type standard error estimator for the IPW-based estimate. Our simulation studies demonstrated that both the outcome modeling and the IPW methods specified following the identification results can yield satisfactory estimates and inferences of the average causal treatment effects. We applied the proposed approaches to data from a real-life pilot study of the Pregnant Moms' Empowerment Program for illustration. The current study provides guidance and insights on causal inference for PNDs and adds to researchers' toolbox of treatment effect estimation with PNDs. (PsycInfo Database Record (c) 2023 APA, all rights reserved).