Abstract:
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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, e.g., 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.
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