Methods/Statistics
Comparing cohort and self-controlled designs for studying Extreme Risk Protection Orders Nicole Asa* Nicole Asa Stephen Mooney Ali Rowhani-Rahbar
When studying treatments that apply to individuals for a fixed period of time, we learn differently from a cohort design and a self-controlled risk interval design. Whereas a cohort design compares treated and untreated individuals, the self-controlled risk interval design compares treated individuals during treated and untreated time. We compare these designs to study the impact of Extreme Risk Protection Orders (ERPOs) on arrests and convictions. ERPOs are a civil protection order which remove and restrict firearm access to individuals who demonstrate high-risk behavior until the order is expired, typically around one-year. A judge will either grant or deny (“non-granted”) an ERPO to the individual demonstrating high-risk behavior (also known as the “respondent”) based on the availability of evidence on whether the respondent poses substantial harm to themselves or others. In a traditional prospective cohort design, we can compare arrests and convictions among granted and non-granted ERPO respondents. Because the evidence used to inform the decision to grant an ERPO is linked to outcomes, we use propensity scores to increase conditional exchangeability. By contrast, in a self-controlled risk interval design, we compare arrests and convictions in the ERPO period (“control interval”) with arrests and convictions after the ERPO has expired and firearm rights are restored (“risk interval”), among granted ERPO respondents. Whereas the self-controlled risk interval designs may better ensure exchangeability, it also limits sample size and is vulnerable to misclassification of “risk” and “control” time. Nonetheless, the self-controlled risk interval design may be used more broadly in epidemiology, particularly to analyze policies that affect people temporarily or to analyze individuals temporarily treated.
