自联邦突击武器禁令解除，美国大规模枪击案的发生率和平均死亡人数呈肉眼可见的上升趋势，其中枪手使用突击武器和有明显预谋作案行为的大规模枪击案不仅发生更加频繁，而且自上世纪末以来最致命的几起案件中，枪手均使用了突击武器，且大多枪手有明显预谋作案行为。为解决这种持续甚久且影响甚远的公共卫生危机，重启联邦突击武器禁令一度成为重要立法话题，并需要证据证明，联邦突击武器禁令确实防止潜在大规模枪击案发生，或禁令解除后大规模枪击案，尤其是枪手使用突击武器并有预谋的大规模枪击案发生率和平均死亡人数有明显上升。

通过结合Andersen-Gill乘法强度模型和Fine-Gray子分布比例风险模型，本文提出了一种多类型复发事件分析模型适用于这样的场景。当全类型事件复发时，目标事件和其他事件会竞争发生，并且在其他事件作为复发事件被观测时，研究者无法再观测此时刻目标事件的潜在发生。本文通过基于计数过程的偏似然函数最大化估计方法和逆概率删失加权方法，给出了这种模型对外部时变协变量的一致且渐近正态估计，以及基线子分布强度和均值函数的估计，并通过数值模拟证实了其对于外部时变协变量影响的识别能力。

对于本文所研究的大规模枪击案复发事件，这种模型可以特别地考虑枪手对武器类型或预谋行为的选择，并基于竞争风险事件假设情况下，估计联邦突击武器禁令如何影响了枪手使用突击武器或预谋使用突击武器作案的大规模枪击案复发潜在强度和边际死亡人数。根据The Violence Project提供的第八版美国大规模枪击案数据集和其他数据源提供的协变量信息，本文证明了当枪手有充足成本准备突击武器或完成预谋作案情况下，联邦突击武器禁令的解除与枪手使用突击武器作案、枪手有预谋使用突击武器作案的大规模枪击案发生数和死亡人数增加有显著正相关关系。

The incidence and the average death of United States mass shootings have been on the rise ever since the repeal of the Federal Assault Weapons Ban. The use of assault weapons and significant plannings have not only become more frequent in mass shootings, but also in the deadliest cases since the last century. To address this longstanding and far-reaching public health crisis, reinstating the Federal Assault Weapons Ban has become an important legislative topic, while evidence is required to prove that the Ban has efficiently prevented potential mass shootings, or that the repeal of the Ban correlates with a significant increase in the incidence and the average death of mass shootings, especially of those involving with assault weapons and prior plannings.

This paper proposes a multitype recurrent event analysis model by combining the Andersen-Gill multiplicative intensity model and the Fine-Gray subdistribution proportional hazard model. This model is suitable for such scenarios that the type-of-interest event should recur but compete with other events once the all-cause event recurs., and its potential recurrence can never be observed once the competing risks events recurs at the moment. This paper provides with consistent and asymptotically normal estimation of external time-varying covariates, through maximizing the partial likelihood based on counting processes and the inverse probability of censorship weighting, as well as the baseline subdistribution intensity and mean function estimators. A numerical study of simulations confirms the identifiability of the impact from external time-varying covariates.

For the recurrent events of mass shootings studied in this paper, this model can specifically consider the shooter's choice of weapon type or planning behavior. Under the assumption of competing risks events, it estimates how the Federal Assault Weapons Ban affects the potential intensity and marginal death of mass shootings perpetrated with assault weapons or with plannings. Based on available data from The Violence Project's eighth edition dataset of the United States mass shootings and covariate information from other sources. The paper demonstrates a significant positive correlation between the repeal of the Federal Assault Weapons Ban and an increase in the incidence and death of mass shootings via assault weapons and significant plannings, where shooters should sufficiently acquire assault weapons or complete their assault plans.