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In the comparative interrupted time series design (also called the method ofdifference-in-differences), the change in outcome in a group exposed totreatment in the periods before and after the exposure is compared to thechange in outcome in a control group not exposed to treatment in either period.The standard difference-in-difference estimator for a comparative interruptedtime series design will be biased for estimating the causal effect of thetreatment if there is an interaction between history in the after period andthe groups; for example, there is a historical event besides the start of thetreatment in the after period that benefits the treated group more than thecontrol group. We present a bracketing method for bounding the effect of aninteraction between history and the groups that arises from a time-invariantunmeasured confounder having a different effect in the after period than thebefore period. The method is applied to a study of the effect of the repeal ofMissouri's permit-to-purchase handgun law on its firearm homicide rate. Weestimate that the effect of the permit-to-purchase repeal on Missouri's firearmhomicide rate is bracketed between 0.9 and 1.3 homicides per 100,000 people,corresponding to a percentage increase of 17% to 27% (95% confidence interval:[0.6,1.7] or [11%,35%]). A placebo study provides additional support for thehypothesis that the repeal has a causal effect of increasing the rate ofstate-wide firearm homicides.

Bracketing in the Comparative Interrupted Time-Series Design to Address  Concerns about History Interacting with Group: Evaluating Missouri Handgun  Purchaser Law