Understanding Difference-in-differences methods to evaluate policy effects with staggered adoption: an application to Medicaid and HIV

Abstract: While a randomized control trial is considered the gold standard for estimating causal treatment effects, there are many research settings in which randomization is infeasible or unethical. In such cases, researchers rely on analytical methods for observational data to explore causal relationships. Difference-in-differences (DID) is one such method that, most commonly, estimates a difference in some mean outcome in a group before and after the implementation of an intervention or policy and compares this with a control group followed over the same time (i.e., a group that did not implement the intervention or policy). Although DID modeling approaches have been gaining popularity in public health research, the majority of these approaches and their extensions are developed and shared within the economics literature. While extensions of DID modeling approaches may be straightforward to apply to observational data in any field, the complexities and assumptions involved in newer approaches are often misunderstood. In this paper, we focus on recent extensions of the DID method and their relationships to linear models in the setting of staggered treatment adoption over multiple years. We detail the identification and estimation of the average treatment effect among the treated using potential outcomes notation, highlighting the assumptions necessary to produce valid estimates. These concepts are described within the context of Medicaid expansion and retention in care among people living with HIV (PWH) in the United States. While each DID approach is potentially valid, understanding their different assumptions and choosing an appropriate method can have important implications for policy-makers, funders, and public health as a whole.