From the Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA.
Department of Health Policy and Management, Johns Hopkins Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD.
Epidemiology. 2019 May;30(3):371-379. doi: 10.1097/EDE.0000000000000989.
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 with 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. We estimate that the effect of the permit-to-purchase repeal on Missouri's firearm homicide 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 the hypothesis that the repeal has a causal effect of increasing the rate of state-wide firearm homicides.
在比较中断时间序列设计（也称为差异中的差异方法）中，暴露于治疗的组在暴露前后时期的结果变化与未暴露于任何时期治疗的对照组的结果变化进行比较。如果在后时期中存在历史与组之间的相互作用，则比较中断时间序列设计的标准差异中的差异估计量将偏向于估计治疗的因果效应；例如，在后时期中除了治疗开始之外还有一个历史事件，该事件使治疗组比对照组受益更多。我们提出了一种方法来限制历史与组之间相互作用的影响，这种相互作用源于一个在时期不变的未测量混杂因素在后时期的效果与前时期不同。该方法应用于研究密苏里州取消手枪购买许可证对其枪支凶杀率的影响。我们估计，取消手枪购买许可证对密苏里州枪支凶杀率的影响在每 10 万人 0.9 至 1.3 起凶杀案之间，相当于百分比增加 17%至 27%（95%置信区间：0.6，1.7 或 11%，35%）。一项安慰剂研究为假设该取消具有增加全州范围内枪支凶杀率的因果效应提供了额外支持。
