Bracketing in the Comparative Interrupted Time-Series Design to Address Concerns about History Interacting with Group: Evaluating Missouri Handgun Purchaser Law (306609)Raiden Berte Hasegawa, unaffiliated
*Luke John Keele, University of Pennsylvania
Dylan Small, The Wharton School, University of Pennsylvania
Daniel Webster, Johns Hopkins University Bloomberg School of Public Health
Keywords: Causal inference, bracketing, difference-in-difference, comparative interrupted time series, permit-to-purchase, history-by-group interaction, unmeasured confounding, multiple control groups, gun violence, firearm policy
In the comparative interrupted time series design (also called the method of difference-in-differences), the change in outcome in a group exposed to treatment in the periods before and after the exposure is compared to the change in outcome in a control group not exposed to treatment in either period. The standard difference-in-difference estimator for a comparative interrupted time series design will be biased for estimating the causal effect of the treatment if there is an interaction between history in the after period and the groups; for example, there is a historical event besides the start of the treatment in the after period that benefits the treated group more than the control group. We present a bracketing method for bounding the effect of an interaction between history and the groups that arises from a time-invariant unmeasured confounder having a different effect in the after period than the before period. The method is applied to a study of the effect of the repeal of Missouri's permit-to-purchase handgun law on its firearm homicide rate.