Risk Set Matched Difference-in-Differences for the Analysis of Effect Modification in an Observational Study on the Impact of Gun Violence on Health Outcomes

Gun violence is a major problem in contemporary American society. However, relatively little is known about the effects of firearm injuries on survivors and their family members and how these effects vary across subpopulations. To study these questions and, more generally, to address a gap in the causal inference literature, we present a framework for the study of effect modification or heterogeneous treatment effects in difference-in-differences designs. We implement a new matching technique, which combines profile matching and risk set matching, to (i) preserve the time alignment of covariates, exposure, and outcomes, avoiding pitfalls of other common approaches for difference-in-differences, and (ii) explicitly control biases due to imbalances in observed covariates in subgroups discovered from the data. Our case study shows significant and persistent effects of nonfatal firearm injuries on several health outcomes for those injured and on the mental health of their family members. Sensitivity analyses reveal that these results are moderately robust to unmeasured confounding bias. Finally, while the effects for those injured are modified largely by the severity of the injury and its documented intent, for families, effects are strongest for those whose relative's injury is documented as resulting from an assault, self-harm, or law enforcement intervention.