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Firearms and Violence: A Critical Review 7 Firearms and Suicide While much attention surrounding the debate over firearms has focused on criminal violence in general, and homicide in particular, suicide is the most common cause of firearm-related death in the United States (National Center for Health Statistics, 2003; see Table 3-3). Do guns increase the lethality or frequency of suicide attempts? A large body of literature links the availability of firearms to the fraction of suicides committed with a gun. Yet, a central policy question is whether changes in the availability of firearms lead to changes in the overall risk of suicide. Despite the clear associations between firearms and gun suicide, answering this broader question is difficult. Box 7-1 sketches out a conceptual framework describing various mechanisms by which firearms may be associated with rates of suicide. The fundamental issue is the degree to which a suicidal person would simply switch to using other methods if firearms were less available. On one hand, if substitutes were easily enough available, then gun restrictions might change the typical method of suicide yet have no effect on the overall risk of suicide at all. On the other hand, there are at least two mechanisms by which guns might directly cause an increase in the risk of completed suicide. First, guns may provide a uniquely efficient method of self-destruction so that access to a gun could lead to a higher rate of completed suicide. It is often stated, for example, that easy access to firearms could increase the rate of completed suicide among persons with transient suicidal feelings because such access might increase the likelihood of an attempt with a lethal outcome. Second, the induction hypothesis proposes that the le-
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Firearms and Violence: A Critical Review BOX 7-1 Conceptual Framework Why might firearms access be associated with rates of suicide? Direct Causality: Firearms might directly increase the risk of suicide. The instrumentality hypothesis proposes that if guns were inherently more lethal than other methods, then access to a gun could lead to a higher rate of completed suicide. The method selection or induction hypothesis proposes that firearms might be preferred over other methods because their quickness and effectiveness might decrease some of the other “costs” of a suicide attempt. Spurious Correlation: Firearms might be associated with suicide but have no direct effect. Instead, there may be unmeasured confounders associated with both access to firearms and the propensity to commit suicide. In this case, if substitutes were easily enough available, gun access restrictions might reduce the incidence of gun suicide yet have no effect on the overall risk of suicide. Two examples highlight this possibility: Reverse Causality: The risk of suicide might increase or decrease the likelihood of gun ownership. On one hand, some persons who are planning to commit suicide may seek out a gun specifically for this purpose (Cummings et al., 1997b; Wintemute et al., 1999). On the other hand, family members might remove firearms from the home of someone who has made suicide attempts in the past. Other Confounders: Finally, there could be unmeasured and confounding “third factors” associated with both suicide risk and gun ownership, which could lead to an apparent (but noncausal) association between guns and suicide. Individual-level confounders might include propensities for social isolation and mistrust of others. For example, if persons who are prone to own guns because of their mistrust of others were also at greater risk for suicide, whether or not they owned guns, there could be a noncausal statistical association between gun ownership and suicide. Community-level confounders could also explain a link between gun ownership and suicide risk. For example, high levels of “social capital” might be associated with lower rates of defensive gun ownership, as well as with higher levels of social support for individuals at risk for suicide (Hemenway et al., 2001). Defensive gun use may also be correlated with particular cultural attitudes toward mental health services and individual problem-solving strategies; for accidental historical reasons or for specific cultural reasons, communities with higher levels of defensive gun ownership might also be communities that invest less heavily in “safety net” public services or with less access to mental health services. thality of a gun might itself increase the likelihood of a suicide attempt among gun owners: persons who would prefer the efficiency of a gun would be less likely to make an attempt if a gun were not available. Ultimately, it is an empirical question whether access restrictions lead to substantial reductions in the rates of suicide.
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Firearms and Violence: A Critical Review In this chapter we review studies of the relationship between household gun ownership and the risk of suicide.1 We review both studies that assess the relationships at aggregated geographic levels and those that look at the relationship between access and suicide at the level of the individual or household. Many studies conducted at aggregate levels rely on proxy measures of gun ownership; because these are so widely used, we devote special attention to discussing the pros and cons of using proxies for household gun ownership in ecological studies. Many individual-level studies of suicide use retrospective, case-control study designs; because the strengths and limitations of such a study design may be unfamiliar to some readers, we also discuss this methodology in some detail, with an explanation of the measures of association used in case-control studies presented in an appendix to the chapter. We then summarize the handful of studies that have evaluated the effects of specific gun laws on suicide. The final section presents the committee’s conclusions. ECOLOGICAL STUDIES OF GUN OWNERSHIP AND THE OVERALL RISK OF SUICIDE The great majority of research on suicide and gun ownership has been “ecological,” in which the unit of observation is the community rather than the individual, comparing measures of household gun ownership rates to the rates of completed suicide. In some cases, the comparisons are allowed to vary over time; in all cases, comparisons are made across several geographic regions. Ecological studies of gun ownership and suicide in the United States are summarized in Table 7-1. Cross-Sectional Associations Almost all ecological studies using cross-sectional data, both within the United States and across countries, have found that both gun suicide rates and the fraction of suicides committed with a gun are higher in geographic areas with a higher prevalence of household gun ownership. This association has been reported by investigators across the spectrum of the gun control debate. It has been found across cities, states, regions, and nations (Kleck and Patterson, 1993; Azrael et al., 2004; Killias, 2001), and it contrasts with the more variable association between gun ownership rates and the fraction of homicides committed with a gun. 1 Studies were identified using various search engines, by a search for book chapters and unpublished studies identified through personal communication with researchers in the field, and by review of the reference lists of previous publications. A particular effort was made to find studies in the firearms policy literature, reviewed for other chapters of this volume, which may have examined suicide as a secondary focus of the investigation.
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Firearms and Violence: A Critical Review However, the most important policy question is not whether gun access increases the risk of gun suicide, but whether gun access increases the overall risk of suicide. Many cross-sectional studies have reported a positive, bivariate association between gun ownership rates and overall suicide rates across cities, states, and regions of the United States, but the relationship is much smaller and less precise than the association between gun ownership rates and gun suicide rates. The association between gun ownership and overall suicide also appears to be sensitive to the details of the measures and the statistical models being used. U.S. Studies Several ecological studies by Birckmayer and Hemenway (2001) and by Miller et al. (2002a, 2002c) have focused on age-specific suicide rates by region and state. Their gun ownership measures include survey estimates of handgun and overall gun ownership from the GSS and, as a proxy measure, the fraction of suicides committed with a firearm. Before controlling for other social variables, Birckmayer and Hemenway find a positive association between regional GSS-reported rates of gun ownership and age-specific rates of suicide in every age group. After controlling for divorce, education, unemployment, urbanization, poverty, and alcohol consumption, they find a modest positive association between gun ownership and suicide risk for youth ages 15 to 24 (b = .35, 95% confidence interval .05 to .65) and for adults age 65 and over (b = .62, 95% C.I. .40-.84), but not for working-age adults between ages 25 and 64. Subsequent studies from the same research group use other model specifications, with varying results. For example, Miller et al. (2002a) do not incorporate control variables; they find a positive association between gun ownership and overall suicide rates in all age groups (incidence rate ratio 1.14; 95% CI 1.01-1.24) and a negative association between gun ownership and nongun suicide (IRR .87, 95% CI .77-.97) that is more pronounced for persons 45 years and older, suggesting greater substitution among methods in older age groups. Duggan (2003) undertook a similar age-specific analysis, using subscriptions to the gun magazine Guns & Ammo as his proxy for gun ownership. Like Miller et al., Duggan did not include other covariates in his regression models and, like Miller et al., he found a positive and significant bivariate association between gun ownership and suicide across states. But Duggan also found a significant positive association between gun magazine subscription and nongun suicide for youth ages 10 to 19. The association between the gun proxy and nongun suicide shifts from positive to negative between ages 20 and 69 and becomes negative and statistically significant for persons over age 69. He concludes that the positive association between gun magazine subscriptions and nongun suicide among youth is evidence
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Firearms and Violence: A Critical Review TABLE 7-1 Ecological Studies of Associations Between Firearms Prevalence and Suicide in the United States Source Unit of Analysis Gun Measure Subjects; Strata Duggan (2003) 50 states 1996 Proxy: Guns & Ammo 10 yr. age groups Hemenway and Miller (2002) 9 regions 1988-1997 Survey: GSS (household handgun ownership) Miller et al. (2002b) 9 regions 50 states 1988-1997 Survey: GSS, BRFSS Proxy: Cook index, FS/S (adult only) Children 5-14 Miller et al. (2002c) 9 regions 50 states 1988-1997 Survey: GSS, BRFSS Proxy: Cook index, FS/S Adult women Miller et al. (2002a) 9 regions 50 states 1988-1997 Survey: GSS, BRFSS Proxy: Cook index, FS/S 10-yr. age groups Birckmayer and Hemenway (2001) 9 regions 1979-1994 GSS 10-yr age groups Azrael et al. (2004) 9 regions 50 states 1994-1998 Survey: GSS, BRFSS, HICRC Proxies: FS/S, UFDR, Guns & Ammo, NRA membership
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Firearms and Violence: A Critical Review Control Variables Results: Guns and Gun Suicides Results: Guns and Nongun Suicides Results: Guns and Overall Suicides None all ages + 10-19: + 20-69:0 70+: – all ages + Major depression, suicidal thoughts, and urbanization, OR education, OR unemployment, OR alcohol consumption + – + Poverty, education, urbanization + 0 + Poverty, urbanization + BRFSS:+ Others: 0 + None all ages + <45:0 45+: – all ages + Divorce, education, unemployment, urbanization 15-24: + 25-44:0 45-84: + 0 15-24: + 25-64:0 65+: + None + n/a n/a
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Firearms and Violence: A Critical Review Source Unit of Analysis Gun Measure Subjects; Strata Kaplan and Geling (1998) 9 regions 1989-1991 Survey: GSS Sex × race Kleck and Patterson (1993) 170 U.S. cities OLS proxy: gun crimes IV proxy: gun sport Sloan et al. (1990) 2 cities 1985-1987 Registry: handguns Proxies: Cook index Strictness of gun laws Two age groups, race, sex Lester (1989) 48 states 1980 Proxy: gun magazines Lester (1988a) 6 (of 7) Australian states Survey-household gun ownership Lester (1988b) 9 regions 1970 Survey Proxy: gun laws Lester (1987a) 48 states 1970 Proxies: gun laws, UFDR Proxy: Cook index Duggan (2003) 50 states Proxy: guns ammo sales rate All ages
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Firearms and Violence: A Critical Review Control Variables Results: Guns and Gun Suicides Results: Guns and Nongun Suicides Results: Guns and Overall Suicides None + Male: Female: 0 n/a Community traits: race, sex, age unemployment rate, poverty, income, home ownership, college enrollment, transience, population change, divorce, place of worship, etc. + 0 OLS: + IV: 0 None + – 0 None + 0 + None 0 – 0 % black, median age, % urban, divorce rate + 0 0 None + UFDR:– Other: 0 0 State, year fixed effects 0 0 0
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Firearms and Violence: A Critical Review Source Unit of Analysis Gun Measure Subjects; Strata Mathur and Freeman (2002) 48 states Gun dealers per capita Adolescent suicide (15-19) Azrael et al. (2004) 9 regions 50 states Survey: GSS Proxy: FS/S Clarke and Jones (1989) Entire United States Survey: Gallup poll, GSS Type of gun NOTES: +, - indicate positive or negative effect (respectively), statistically significant at p < .05; 0 indicates not significant. BRFSS = Behavioral Risk Factor Surveillance System; GSS = General Social Survey; FS/S = ratio of firearm suicide/total suicides; Cook Index = mean of firearm suicide/total suicide and firearm homicide/total homicide; HICRC = Harvard Injury Control Research Center; UFDR = unintentional firearm death rate; FLFP = female labor force participation; OLS = ordinary least squares; IV = instrumental variable (two-stage least squares); NRA = National Rifle Association. When only one result is listed in column, all gun measures gave similar results. When reported results include models both with and without covariates, only results with covariates are presented. for an omitted variable, because any plausible causal effect of gun ownership should be independent of, or negatively associated with, the nongun suicide rate. There are several other possible explanations for Duggan’s results; most obviously, it may be that Guns & Ammo subscribers are not representative of all gun owners; his arguments about confounding would also have been strengthened by the inclusion of some observable covariates. All the same, both Miller’s and Duggan’s results support the view that different gun proxies may yield different results, and all of the age-stratified studies suggest that instrumentality effects, substitution, and omitted variables may be playing different roles at different ages. The most comprehensive effort to control for confounding factors was published a decade ago. Kleck and Patterson (1993) undertook a cross-sectional study of the effect of firearms prevalence on crime rates and firearm-related fatalities in 170 U.S. cities. Although the study did not consider differences by age, the models included a set of 38 control variables previously identified as predictors of violence rates. Like other investigators, these authors found that higher levels of the proxy for gun owner-
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Firearms and Violence: A Critical Review Control Variables Results: Guns and Gun Suicides Results: Guns and Nongun Suicides Results: Guns and Overall Suicides State, year fixed effects FLFP, divorce, alcohol consumption family & cohort size Not stated Not stated + Regional fixed effects + Not stated Not stated None Handgun + All guns: 0 n/a All guns: 0 Handgun: + ship predicted higher rates of suicide (b = .132, p < .05). Kleck and Patterson also found evidence that there might be a different association between suicide risk and sporting gun ownership and suicide risk and defensive gun ownership. In particular, they found no significant effect of sporting gun ownership on the risk of suicide. International Studies Like the U.S. studies, the existing cross-national surveys have looked for an association between rates of household gun ownership, overall suicide rates, and the fraction of suicides committed with a gun. And, like the U.S. studies, cross-national studies have found a consistent association between gun ownership and the fraction of suicides committed with a gun across countries; but in contrast to the U.S. studies, the cross-national surveys do not reveal a consistent association between gun ownership and overall suicide rates.
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Firearms and Violence: A Critical Review Although gun ownership rates in the United States are much higher than in most other developed countries, the rates of suicide in the United States rank in the middle. Killias (1993), Killias (2001), and Johnson et al. (2000) found that reported rates of household gun ownership were strongly correlated with the fraction of suicides committed with a gun in each country (Spearman’s rho = .79 to .92, p < .001). But the cross-country correlations between household gun ownership and overall rates of suicide have proven to be smaller and statistically imprecise (Spearman’s rho .25, p = .27) (Killias, 2001). Likewise, in an often-cited study, Sloan et al. (1990) compared the rates of gun and nongun suicides in Seattle, Washington, with suicide rates in Vancouver, British Columbia, between 1985 and 1987; they found higher rates of gun ownership are associated with higher rates of gun suicide, lower rates of nongun suicide, and no significant difference in the overall suicide rate between the two cities (relative risk .97, 95% CI .87 to 1.09). Associations Between Gun Ownership and Suicide Rates Across Time The fraction of suicides in the United States that are committed with a firearm has increased from just over 35 percent in the 1920s to about 60 percent in the 1990s. Four studies have attempted to link this change in the fraction of gun suicides with changes in gun ownership across time. Three of these four studies have found positive associations between proxies for gun ownership and the fraction of suicides committed with a gun, but only one study, focusing on youth suicide, found an association between gun ownership and overall suicide rates. Clarke and Jones (1989), examined the national prevalence of household gun ownership reported in polls by Gallup and the National Opinion Research Center between 1959 and 1984, comparing these reports with aggregate U.S. suicide rates over the same period. This study found a positive association between the fraction of households owning a handgun and the fraction of suicides committed with a gun (b = .68, p = .001), but no association between household gun ownership and overall risk of suicide (b = .04, p = .85). Azrael et al. (2004) also report a strong linear association between individual and household rates of gun ownership within regions and the fraction of suicides committed with a gun between 1980 and 1998, with cross-sectional beta coefficients ranging from .55 (for individual handgun ownership) to 1.02 (for household gun ownership of any kind), and an inter-temporal coefficient between FS/S and household gun ownership of .905 (s.e. = .355). They did not report the association between gun ownership and overall risk of suicide. Mathur and Freeman (2002) used state-level per capita gun dealership rates to predict adolescent suicide rates from 1970 to 1997. After controlling for state and year fixed effects and number of other observed
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Firearms and Violence: A Critical Review Source Areas Compared Time Periods Compared Gun Law Snowdon and Harris (1992) Australian states 1968-1979; 1980-1989 1980 gun law (South Australia) Thomsen and Albrektsen (1991) Denmark 1984-1985; 1986-1987 1986 law Loftin et al. (1991) DC vs. suburbs (a) mean monthly rates (b) ARIMA with age-standardized annual rates 1968-1976; 1977-1987 1976 handgun ban in DC Rich et al. (1990) Toronto 1973-1977; 1979-1983 1978 Bill C-51 Nicholson and Garner (1980) DC vs. nation Two selected years (1976; 1979) 1976 handgun ban in DC NOTE: ARIMA = autoregressive, integrated, moving-average time series models. In the first quasi-experimental study to examine effects of gun policy on adult suicide, Ludwig and Cook (2000) evaluated the impact of the 1994 Brady act in 32 “treatment” states that were directly affected by the act, compared with 19 “control” jurisdictions that had equivalent legislation already in place. The authors found a reduction in firearm suicides among persons age 55 and older of 0.92 per 100,000 (with a 95 percent confidence interval = –1.43 to –.042), representing about a 6 percent decline in firearm suicide in this age group. This decrease, however, was accompanied by an offsetting increase in nongun suicide, so that the net effect on overall suicide rates was not significant (–.54 per 100,000; with a 95 percent confidence interval = –1.27 to 0.19). Using a similar methodology, Reuter and Mouzos (2003) found no significant effect study of a large scale Australian gun buy-back program on total suicide rates.
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Firearms and Violence: A Critical Review Change in Gun Suicide After Gun Law Change in Nongun Suicide After Gun Law Change in Overall Suicide After Gun Law Decrease (SA males) Increase (S.A. males) No difference No change Not stated Decrease (not qualified) (a) Decrease (a) Not significant (a) Decrease (not quantified) (b) Not significant (b) Not stated (b) Not stated Decrease Increase-jumping Not significant Decrease Not significant Decrease Two other studies have evaluated the effects of safe storage laws on child and adolescent suicide (see Chapter 8). Cummings et al. (1997a) evaluated the possible effect of state safe storage gun laws on child mortality due to firearms; they found an insignificant decline in gun suicides (rate ratio 0.81, with a 95 percent confidence interval = 0.66-1.01) and overall suicides (rate ratio 0.95, with a 95 percent confidence interval = 0.75-1.20) for children under age 15 in states that had instituted such a law. In a similar study, Lott and Whitley (2000) investigated the effects of safe storage laws introduced in various states between 1979 and 1996. They compared gun and nongun suicides among children in the age group most likely to be affected by the law, as well as gun suicides in the next older age group, which should have been unaffected by the law. Their models also controlled for state and year fixed effects and 36 other demographic variables. They, too, found some reduction in gun suicides among children in states with stricter gun storage laws, but no reduction of overall suicide rates.
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Firearms and Violence: A Critical Review TABLE 7-6 Quasi-Experimental Studies of Gun Laws and Suicide Source Areas and Time Period Compared Gun Law Population Reuter and Mouzos Australian states, 1979-1998 1996 gun buy-back Whole population Ludwig and Cook (2001) 50 states + DC 1985-1997 1994 Brady act 21-54 years 55+ Lott and Whitley (2000) 50 states + DC 1979-1996 Safe storage laws Other gun laws Children and adolescents 0-19 Cummings, Grossman, Rivara, and Koepsell (1997a) 50 states + DC 1979-1994 Safe storage laws Children under 15 SUMMARY AND RECOMMENDATIONS The committee draws the following conclusions on the basis of the present evidence: States, regions, and countries with higher rates of household gun ownership have higher rates of gun suicide. There is also cross-sectional, ecological association between gun ownership and overall risk of suicide, but this association is more modest than the association between gun ownership and gun suicide; it is less consistently observed across time, place, and persons; and the causal relation remains unclear. The risk of suicide is highest immediately after the purchase of a handgun, suggesting that some firearms are specifically purchased for the purpose of committing suicide. Some gun control policies may reduce the number of gun suicides, but they have not yet been shown to reduce the overall risk of suicide in any population.
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Firearms and Violence: A Critical Review Change in Gun Suicide After Gun Law Change in Nongun Suicide After Gun Law Change in Overall Suicide After Gun Law Continuation of of decreasing trend Continuation of increasing trend Increase No significant difference No significant difference No significant difference Decrease No significant difference No significant difference Mixed: Decrease with higher age limits Not stated No significant difference mixed (see text) Not stated No significant differences No significant difference No significant difference No significant difference There are several substantive differences between the research literature linking guns and crime and the research literature linking guns and suicide. First, there is a cross-sectional association between rates of household gun ownership and the number and fraction of suicides committed with a gun that appears to be much more consistent than, for example, the cross-sectional association between gun ownership and gun homicide. There also appears to be a cross-sectional association between rates of household gun ownership and overall rates of suicide, reported by investigators on both sides of the gun policy debate. However, the association is small, the findings seem to vary by age and gender, and results have been sensitive to model specifications, covariates, and measures used; furthermore, the association is not found in comparisons across countries. In the absence of a simple association between household gun ownership and crime rates within the United States, the literature on guns and crime has been forced to attend to some of the methodological problems of omitted variables and endogenous relationships inherent in studying complex social processes. The presence of a simple bivariate association between gun ownership and suicide may have prevented suicide investigators from pursuing study designs hav-
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Firearms and Violence: A Critical Review ing a better hope of justifying a causal inference. The issue of substitution has been almost entirely ignored in the literature of guns and suicide. Some of the problems in the suicide literature may also be attributable to the intellectual traditions of the injury prevention field, which has been strongly shaped by successes in the prevention of car crashes and other unintentional injuries. An unintentional injury prevention model can lead to misunderstandings when it is applied to the study of intentional injury; the investigation of intentional injury should take account of the complexities of preference, motivation, constraint, and social interaction among the individuals involved. In addition to better addressing these fundamental problems associated with drawing causal inferences, this chapter has highlighted a number of other data and methodological obstacles. What sort of data and what sort of studies would be needed in order to improve the understanding of the association between firearms and suicide? Although some knowledge may be gained from further ecological studies, the most important priorities appear, to the committee, to be improved data systems, improved individual-level studies of the association between gun ownership and suicide, and a more systematic analysis of the effect of firearms laws and related interventions on the risk of suicide. Proxy Measures of Gun Ownership The association between gun ownership and gun suicide has led to recommendations for the use of the fraction of suicides committed with a firearm (FS/S) as a proxy for household gun ownership when direct measures are unavailable. This means that a better understanding of the relationship between firearms and suicide may also make a technical contribution to the study of firearms and crime. However, investigators should be aware of the biases that can be introduced by any proxy measures, and they are warned that particularly serious artifacts can be introduced if FS/S is used as a proxy for gun ownership when suicide is also the outcome of interest. Data Systems The absence of information about gun ownership has been a major stumbling block for ecological and individual-level studies of suicide as well as for studies of homicide and other gun-related crime. In order to better understand these associations, it would be useful to collect individual-level information about gun ownership in studies of suicidal behavior, as well as information about suicidal behavior in studies of legal and illegal gun use. Indeed, because FS/S should not be used as a proxy measure for gun owner-
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Firearms and Violence: A Critical Review ship in ecological studies of suicide, the further understanding of the association between firearms and suicide will be particularly dependent on the availability of direct information about gun ownership. Potentially valuable state-level information could be made available through the regular inclusion of gun ownership questions in the Behavioral Risk Factor Surveillance System, and a better understanding of the possible linkage between household gun ownership and adolescent risk-taking might come from the regular inclusion of household gun ownership questions, in addition to the existing adolescent gun use questions, in the Youth Risk Behavior Surveillance System. At the moment, the U.S. vital statistics system is the only source of nationally representative information about lethal self-injuries. This system sets important limitations on present knowledge. The proposed National Violent Death Reporting System, now being piloted in six states with funding from the Centers for Disease Control and Prevention, could provide more information about demographic background, intent, circumstances, precipitants, method of injury, and source of the firearm (in the case of gun suicides) than is presently available. In this regard, it may be a much more significant improvement for the study of suicide than for the study of homicide, for which similar national data systems are already available. But there are potential problems that should be considered in the planning of such a system, which might affect the overall usefulness of the final result (see Chapter 2 for further details). Data systems that collect information about a series of cases (such as the recording of injuries or deaths) cannot be used without an appropriate comparison group to make valid inferences about the association between exposures and outcomes. Will the data be collected in a way that would permit such comparisons? This might be accomplished by using the injury surveillance system in the way that cancer registries are now used, as a source of cases for case-control or record-linkage studies of the risk factors for the designated outcome. Will the data system collect sufficiently complete and reliable information about relevant exposures? It would be helpful to develop the NVDRS system with several specific research questions in mind, to ensure that the system will actually be usable, and will actually be used. Improved Individual-Level Studies The committee recommends further individual-level studies of the link between firearms and both lethal and nonlethal suicidal behavior. It would be useful to have an ongoing, longitudinal study that determines both predictors of gun ownership and other known risk factors for suicidal thoughts, nonlethal suicidal behaviors, and completed suicide. Added detail about method choice and correlates of gun ownership would help to clarify
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Firearms and Violence: A Critical Review the possible link between household gun ownership and intentional injury. In light of findings from previous case-control studies, sources of ascertainment bias, factors influencing impulsivity, and confounding and modifying factors other than psychiatric diagnosis should receive special attention. Several strategies might be used to overcome sources of reporting bias in psychological autopsy study designs. Administrative and medical records may be used to supplement individual interviews, and questionnaire designs and computer-assisted interview strategies developed to investigate sensitive topics, such as illegal drug use and adolescent sexual behavior, may serve as models. Further Policy Studies Suicide prevention has rarely been the basis for public support of the passage of specific gun laws, but effects on suicide rates could be an unintended by-product of such laws, and the effects of different firearms policy interventions on suicide remain poorly understood. Thus, the committee recommends further studies of the link between firearms policy and suicide. APPENDIX MEASURES OF ASSOCIATION IN CASE-CONTROL STUDIES The odds ratio is the principal measure of association in a case-control study. One of the most useful features of the odds ratio, and the reason for its use in case-control study designs, is that it can be estimated from a response-based sampling design, even if the incidence of the exposure and outcome in the underlying population remain unknown. Likelihood of Suicide and Gun Ownership Suppose, for example, that one wishes to learn how the likelihood of suicide varies with gun ownership in a population of 1,000,000 persons for whom there were the following number of suicides among gun owners and nongun owners in the course of one year: Suicide = yes Suicide = no Total Gun owner A = 60 B = 399,940 A + B = 400,000 Not gun owner C = 40 D = 599,960 C + D = 600.000 Total A + C = 100 B + D = 999,900 1,000,000 In this population, the incidence of suicide among gun owners is A/ (A+B), or 60 per 400,000 per year, and the incidence of suicide among
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Firearms and Violence: A Critical Review nongun owners is C/(C+D), or 40 per 600,000 per year. To compare these two probabilities, we could calculate the relative risk, which can be defined as the incidence of the outcome in the exposed group divided by the incidence of the outcome in the unexposed group, namely: In our example, the relative risk of suicide among gun owners compared with nongun owners would be (60/400,000)/(40/600,000), which equals 2.25. However, another relative measure of association is the odds ratio. The odds in favor of a particular event are defined as the frequency with which the event occurs, divided by the frequency with which it does not occur. In our sample population, the odds of suicide among gun owners were 60/ 399,940, and the odds of suicide among nongun owners were 40/599,960. The odds ratio can then be defined as the odds in favor of the outcome in the exposed group, divided by the odds in favor of the outcome in the In our example, the odds ratio of suicide for gun owners relative to nongun owners would be (60/399,940) / (40/599,960), which is about 2.2502. As the outcome becomes more rare, (B) approaches (A + B) and (D) approaches (C + D), and the odds ratio approaches the risk ratio. As a rule of thumb, the odds ratio can be used as a direct approximation for the risk ratio whenever the incidence of the outcome falls below about 10 percent. This “rare outcome assumption” holds true in most studies of completed suicide. Although the rare outcome assumption is not required for the odds ratio to be a valid measure of association in its own right (Miettinen, 1976; Hennekens and Buring, 1987), the odds ratio does diverge from the risk ratio as the outcome becomes more common. Of what use is this estimate? Why not just calculate the risk ratio directly? It turns out that the odds ratio has several attractive mathematical properties, but the most important property is that the ratio that we have just calculated as (a/b)/(c/d), is equivalent to (a/c)/(b/d). In our example, the odds ratio we calculated is therefore exactly equal to the ratio of gun owners to nonowners among the suicide victims (60/40) divided by the ratio of gun owners to nonowners among population members who have not committed suicide: (399,940/599,960). This sleight of hand means that the odds ratio of exposure, given the outcome, which is the measure of
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Firearms and Violence: A Critical Review association obtained from a case-control study, can be used to estimate the odds ratio of the outcome, given exposure, which is usually the question of interest. To see how this works, suppose that we now conduct a case-control study in the population in order to estimate the association between gun ownership and suicide. We might do this by selecting all 100 suicides that occurred during the study year, and by drawing a random sample of 100 control subjects who did not commit suicide during the study year. The results of the case-control study might be as follows: Even though the control group in the case-control study now contains only 100 subjects, we have selected these subjects so that they are representative of the frequency of exposure to firearms in the population of nonsuicides from which the control sample was drawn. So the odds ratio for our case-control study is: Prospective studies can measure the frequency of the outcome among persons with different levels of exposure; retrospective case-control studies measure the frequency of exposure among persons with different levels of the outcome. But the symmetry of the odds ratio allows us to estimate the risk of the outcome, given exposure, from information about the odds of exposure, given the outcome. Attributable Risk In fact, by themselves, neither the odds ratio nor the risk ratio can assist policy makers who need to compare the number of occurrences that could be altered through intervention with the costs of the intervention. Policy makers would prefer to know the attributable risk, which can be defined as the difference between the incidence of the outcome among the exposed and the incidence of the outcome among the unexposed:
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Firearms and Violence: A Critical Review To see the problem with the odds ratio and the relative risk, consider two populations, one in which the suicide probability conditional on owning a firearm is 0.02 per person per year and that conditional on not owning a firearm is 0.01 per person per year, and another in which these two probabilities are 0.0002 and 0.0001, respectively. The odds ratio and the relative risk are the same in both scenarios, but if guns are causal, then removal of guns from the population might avert 0.01 deaths per person per year in the first scenario, but only 0.0001 deaths per person per year in the second. In a case-control study, this limitation can be overcome by using information from other sources. When a case-control study is population based—that is, when all or a known fraction of cases in a particularly community are identified and a random sample of unaffected individuals are selected as controls—or when information about the incidence of outcome and exposure are available from other sources, it is possible to calculate the incidence rates and attributable risk from the information derived from the study (see, for example, Manski and Lerman, 1977; Hsieh et al., 1985). In our example, suppose that we already know that the cases represent all of the suicides occurring in the population in a given year, and suppose that we know the size of the population. We know, from the case-control study itself, that 40 percent of control households in random sample own firearms, and the study has revealed an odds ratio of (about) 2.25 to 1. The “rare outcome” assumption is satisfied, which simplifies the calculations; we can treat the odds ratio as a risk ratio and calculate incidence rates and attributable risks as follows: The total incidence of suicide in the population is equal to the incidence of suicide among gun owners, times the probability of being a gun owner, plus the incidence of suicide among nongun owners, times the probability of not being a gun owner, i.e.: A, B, C, and D are the unobserved “true” frequencies of events in the population. But from the risk ratio of 2.25 we also know that:
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Firearms and Violence: A Critical Review Therefore, the probability of suicide among nongun owners = C/(C+D) = (10/100,000)/(1.50) ≈ 6.67 per 100,000 persons per year; and the probability of suicide among gun owners = (2.25)(C/C+D) = 15 per 100,000 persons per year. The attributable risk is the difference between the probability of suicide among gun owners, and the probability of suicide among nongun owners: 15–6.67 ≈ 8.33 suicides per 100,000 attributable to gun ownership. The interpretation of this attributable risk depends on the actual causal mechanism linking exposure and outcome. In our example, there would be about 8.33 suicides per 100,000 that might be preventable by restricting access to guns, if guns were to play a causal role in the risk of suicide.
Representative terms from entire chapter: