Identifying Optimal Methods for Addressing Confounding Bias When Estimating the Effects of State-Level Policies

TL;DR

This study compares four statistical methods for estimating policy effects in observational data, revealing that no single method is best across all confounding scenarios and providing guidance for method selection.

Contribution

It systematically evaluates the performance of four methods under various confounding conditions, offering practical recommendations and an R package for policy effect estimation.

Findings

AR and ASCM have lower root mean squared error than TWFE and CSA in most scenarios

Coverage rates are often overly high, indicating potential overconfidence in estimates

No single method outperforms others across all confounding scenarios

Abstract

Background: Policy evaluation studies that assess how state-level policies affect health-related outcomes are foundational to health and social policy research. The relative ability of newer analytic methods to address confounding, a key source of bias in observational studies, has not been closely examined. Methods: We conducted a simulation study to examine how differing magnitudes of confounding affected the performance of four methods used for policy evaluations: (1) the two-way fixed effects (TWFE) difference-in-differences (DID) model; (2) a one-period lagged autoregressive (AR) model; (3) augmented synthetic control method (ASCM); and (4) the doubly robust DID approach with multiple time periods from Callaway-Sant'Anna (CSA). We simulated our data to have staggered policy adoption and multiple confounding scenarios (i.e., varying the magnitude and nature of confounding relationships). Results: Bias increased for each method: (1) as confounding magnitude increases; (2) when confounding is generated with respect to prior outcome trends (rather than levels), and (3) when confounding associations are nonlinear (rather than linear). The AR and ASCM have notably lower root mean squared error than the TWFE model and CSA approach for all scenarios; the exception is nonlinear confounding by prior trends, where CSA excels. Coverage rates are unreasonably high for ASCM (e.g., 100%), reflecting large model-based standard errors and wide confidence intervals in practice. Conclusions: Our simulation study indicated that no single method consistently outperforms the others. But a researcher's toolkit should include all methodological options. Our simulations and associated R package can help researchers choose the most appropriate approach for their data.