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Fatal Firearm Incidents Before and After Australia's 1996 National Firearms Agreement Banning Semiautomatic Rifles
Annals of Internal Medicine ( IF 39.2 ) Pub Date : 2018-03-13 , DOI: 10.7326/m18-0503 Simon Chapman 1 , Michael Stewart 1 , Philip Alpers 1 , Michael Jones 2
中文翻译：
澳大利亚1996年《全国枪支协定》禁止半自动步枪之前和之后的致命枪支事件
更新日期：2018-03-13
Annals of Internal Medicine ( IF 39.2 ) Pub Date : 2018-03-13 , DOI: 10.7326/m18-0503 Simon Chapman 1 , Michael Stewart 1 , Philip Alpers 1 , Michael Jones 2
Affiliation
Background: In 1996, after the Port Arthur massacre in Tasmania, the National Firearms Agreement was enacted across Australia. Provisions included uniform gun registration, repudiation of self-defense as a legitimate reason to hold a firearm licence, locked storage, a ban on private gun sales and civilian ownership of semiautomatic rifles and pump-action shotguns, and standardized penalties (1). Two buyback programs and 26 uncompensated amnesties between 1996 and 2015 resulted in the surrender of 1 038 089 illicit firearms (2).
An analysis of firearm deaths between 1979 and 2013 showed that 13 mass shootings (homicides in which at least 5 persons died, not including the perpetrator) took place in the 18 years preceding and including the Port Arthur massacre; none has occurred in the 22 years since (3). Many believe that these data indicate that gun law reforms effectively stopped firearm massacres. However, others contend that this interpretation is unwise because of the rarity of these events compared with more common incidents in which fewer than 5 persons died (4).
Objective: To test the null hypothesis that the rate of mass shootings remained unchanged after introduction of the National Firearms Agreement.
Methods: We modeled the occurrence of mass shootings over time by using a rare events model in which occurrences in nonoverlapping intervals are independent Poisson random variables. Different intervals may have different intensities or rates. The expected value in each interval is the product of the rate and length of the interval.
The period before legislation was defined as January 1979 to June 1996 (210 months); the period after legislation was defined as July 1996 to February 2018 (260 months). We considered a constant rate model where the rate of mass shootings was assumed to remain constant over the entire period and a (2-period) changepoint model where the rate differed between these periods. A likelihood ratio test was used to compare the goodness of fit between the models.
We calculated the P value associated with the likelihood ratio test by using standard asymptotic theory and through simulation by using a parametric bootstrap method. As a sensitivity analysis, we recomputed the asymptotic P value to determine how it would change if another shooting had taken place in February 2018. An additional sensitivity analysis accounted for possible dependence over time (a mass shooting at 1 time may increase the chances of another in a subsequent short period) by using a test based on scan statistics (5). We obtained (unadjusted) P values for the maximal scan statistic at a range of window sizes between 1 and 18 and obtained a multiplicity-adjusted P value based on the smallest of these. Full details of this test and the simulation are available in the Supplement (available at Annals.org). The range of window sizes used was between 1 and 18 months, suggested by the 2 most significant sizes of 7 and 16 months (Supplement).
Results: Under the standard Poisson process model (Figure 1), strong evidence indicates a structural change in 1996. A (conservative, 2-sided) likelihood ratio test for a changepoint in a Poisson process model gives a P value of less than 0.001, which is strong evidence to reject the null hypothesis that the rate of mass shootings did not change after the legislation (Figure 2). Perturbing the data with an extra shooting again gives a P value of less than 0.001. A follow-up goodness-of-fit test designed to detect excessive clumping gives a P value of 0.095, which indicates that the Poisson model is a good fit in this sense; the degree of clumping in the data is not dramatic enough to reject the Poisson process model.
Figure 1.
Summary of statistics.
Reported P values are 2-sided. The constant model assumes that the rate of mass shootings remains constant across the full period; the changepoint model assumes that the rate differs between the before and after periods. LR = likelihood ratio.
* January 1979 to June 1996.
† July 1996 to February 2018.
‡ Based on 20 million simulations; R code (R Project for Statistical Computing) is provided in the Supplement.
Figure 2.
Mass shootings.
Open circles indicate mass shootings. Top. Occurrences of mass shootings, 1979–1996. Bottom. Estimated rate of mass shootings per year under 2 different models. Our statistical test compared the constant rate and changepoint models, rejecting the former in favor of the latter. The vertical dashed line indicates the change at June 1996.
Before 1996, approximately 3 mass shootings took place every 4 years. Had they continued at this rate, approximately 16 incidents (SD, 4) would have been expected since then by February 2018.
Discussion: Without a 22-year randomized controlled trial assigning only parts of a national population to live under the National Firearms Agreement, establishing a definitive causal connection between this legislation and the 22-year absence of mass firearm homicides is not possible. However, a standard rare events model provides strong evidence against the hypothesis that this prolonged absence simply reflects a continuation of a preexisting pattern of rare events.
References
- Australasian Police Ministers' Council. National Firearms Agreement. 10 May 1996. Accessed at www.documentcloud.org/documents/2796929-1996-National-Firearms-Agreement.html on 26 February 2018.
- Alpers P, Rossetti A. Australian firearm amnesty, buyback and destruction totals: official tallies and media-reported numbers, 1987-2015. GunPolicy.org. 3 May 2016. Accessed at www.gunpolicy.org/documents/5337-australia-firearm-amnesty-buyback-and-destruction-totals on 26 February 2018.
- Chapman S, Alpers P, Jones M. Association between gun law reforms and intentional firearm deaths in Australia, 1979-2013. JAMA. 2016;316:291-9. [PMID: 27332876] doi:10.1001/jama.2016.8752
- Kleck G. Did Australia's ban on semi auto firearms really reduce violence? A critique of Chapman et al (2016) study. 12 January 2018. Accessed at www.hoplofobia.info/wp-content/uploads/2015/08/2018-Kleck_Chapman_NFA_comments.pdf on 26 February 2018.
- Glaz J, Naus J, Wallenstein S. Scan Statistics. New York: Springer-Verlag; 2001.
中文翻译：
澳大利亚1996年《全国枪支协定》禁止半自动步枪之前和之后的致命枪支事件
背景： 1996年，塔斯马尼亚州发生亚瑟港大屠杀后，《全国枪支协定》在澳大利亚全国范围内颁布。规定包括统一枪支登记，拒绝自卫为持有枪支许可证的正当理由，锁定存储，禁止私人枪支销售以及半自动步枪和抽气shot弹枪的平民所有权以及标准化处罚（1）。1996年至2015年期间实施了两项回购计划和26项无偿大赦，结果交出了1 038 089支非法枪支（2）。
对1979年至2013年枪支死亡的分析表明，在亚瑟港大屠杀发生之前的18年内，发生了13起大规模枪击（凶杀，其中至少有5人死亡，不包括肇事者）；自（3）以来的22年中，没有发生任何事情。许多人认为，这些数据表明，枪支法律改革有效地制止了枪支大屠杀。但是，其他人则认为，这种解释是不明智的，因为这些事件与死于少于5人的更为常见的事件相比是罕见的（4）。
目的：检验引入《国家枪支协定》后集体射击率保持不变的零假设。
方法：我们使用罕见事件模型对大规模枪击事件的发生进行了建模，在该模型中，非重叠间隔中的事件是独立的Poisson随机变量。不同的间隔可能具有不同的强度或速率。每个间隔中的期望值是间隔的速率和长度的乘积。
立法之前的时期定为1979年1月至1996年6月（210个月）；立法后的期限为1996年7月至2018年2月（260个月）。我们考虑了一个恒定速率模型，在该模型中，假设整体枪击事件的发生率在整个时期内保持不变；而在两个时期之间，速率不同的一个（2周期）变化点模型被认为是恒定的。使用似然比检验比较模型之间的拟合优度。
我们使用标准渐近理论并通过使用参数自举方法进行仿真，计算了与似然比检验相关的P值。作为敏感性分析，我们重新计算了渐近P值，以确定如果在2018年2月进行另一次射击，它将如何变化。附加的敏感性分析说明了一段时间内可能的依赖性（一次大规模射击可能会增加一次二次射击的机会）在随后的短时间内），方法是使用基于扫描统计信息的测试（5）。我们在窗口大小介于1和18之间的范围内获得了（未调整的）最大扫描统计量的P值，并获得了经过多重调整的P值基于其中最小的一个。该测试和模拟的全部详细信息可在增补中找到（可在Annals.org上找到）。所使用的窗口大小范围介于1到18个月之间，这是由7个最大的窗口大小和16个月的两个最大大小所建议的（补充）。
结果：在标准的泊松过程模型（图1）下，有力的证据表明1996年结构发生了变化。泊松过程模型中变化点的（保守，两面）似然比检验得出的P值小于0.001，这是有力的证据，可以驳斥立法后集体射击率没有变化的零假设（图2）。再次拍摄额外的数据会干扰P值，使其小于0.001。设计用于检测过度结块的后续拟合优度测试得出的P值为0.095，这表明Poisson模型在这种意义上是很好的拟合。数据的聚集程度不足以拒绝Poisson过程模型。
图1。
统计摘要。
报告的P值为2面。恒定模型假设在整个时期内，大规模枪击事件的发生率保持恒定；变更点模型假设之前和之后期间的费率不同。LR =似然比。
* 1979年1月至1996年6月。
†1996年7月至2018年2月。
‡基于2000万次模拟；补编中提供了R代码（用于统计计算的R项目）。
图2。
大规模枪击事件。
空心圆圈表示大规模枪击事件。最佳。1979年至1996年发生大规模枪击事件。底部。在2种不同模式下，每年的大规模枪击事件估计发生率。我们的统计测试比较了恒定速率和变更点模型，拒绝了前者，而赞成后者。垂直虚线表示1996年6月的更改。
在1996年之前，每4年大约发生3次大规模枪击事件。如果以这样的速度继续下去，那么到2018年2月，预计将发生约16起事件（SD，4）。
讨论：如果没有一项为期22年的随机对照试验，根据国家枪支协定只分配一部分人口居住，就不可能在该立法与22年不存在大规模枪械凶杀案之间建立确定的因果关系。但是，标准的稀有事件模型提供了有力的证据，反对这种长期缺席仅反映了稀有事件先前存在的模式的延续这一假说。
参考
- 澳大利亚警察部长理事会。国家枪支协定。1996年5月10日.2018年2月26日访问www.documentcloud.org/documents/2796929-1996-National-Firearms-Agreement.html。
- Alpers P，Rossetti A.澳大利亚枪支大赦，回购和销毁总额：官方统计和媒体报道的数字，1987-2015年。GunPolicy.org。2016年5月3日。于2018年2月26日访问www.gunpolicy.org/documents/5337-australia-firearm-amnesty-buyback-and-destruction-totals。
- Chapman S，Alpers P，Jones M.枪法改革与澳大利亚故意枪支死亡之间的关联，1979-2013年。贾玛 2016; 316：291-9。[PMID：27332876] doi：10.1001 / jama.2016.8752
- Kleck G.澳大利亚对半自动枪支的禁令真的减少了暴力吗？对Chapman等人（2016）研究的批评。2018年1月12日.2018年2月26日访问www.hoplofobia.info/wp-content/uploads/2015/08/2018-Kleck_Chapman_NFA_comments.pdf。
- Glaz J，Naus J，Wallenstein S.扫描统计。纽约：施普林格出版社；2001年。
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