the measure of gun and nongun suicide (e.g., measurement error) may lead to purely spurious correlations between suicide and FS/S. Since suicide, S, is on both sides of the estimated equation, the implicit model is often a complicated, nonlinear relation between S and FS, not the linear model that is assumed in the literature. These issues may or may not be problematic when using FS/S to estimate the relationship between gun ownership and homicide.
Another important issue is how the proxy affects inference from specific models that may include other explanatory variables. This depends, among other things, on how true firearms prevalence and FS/S are related to the other observed and unobserved explanatory variables. These issues are complicated, and most of them have not been recognized, much less investigated, in the suicide and firearms literature.
All empirical studies face difficulties with making causal inferences, but ecological studies face special sources of bias in dealing with exposures and confounders. These difficulties arise because of the aggregation of observations and because the data on exposures, confounders, and outcomes are from different sources. At the most basic level, the data on firearms ownership in these studies may not come from the persons who committed suicide. Thus, ecological studies cannot establish whether there is a relation between gun ownership by an individual or household and suicide by that individual or member of the household. This may seem like a small problem in the case of gun suicide; after all, the victims of a gun suicide have undeniably achieved access to a gun. But community-level rates of gun ownership may not reflect the rates of gun ownership among highly suicidal persons. If, for example, the relationship between gun access and gun suicide varies by age and sex or by psychiatric disorder, then the aggregate association may reflect differences in the prevalence of suicidal states among persons of different age and sex or psychiatric disorder in the population, rather than differences in access to firearms. The geographical level of aggregation in state-level or regional ecological studies may be so high that there is no way of knowing whether the gun homicides or gun suicides occurred in the same areas with high levels of gun ownership.
Thus, even if FS/S is found to be a valid proxy for state-level gun prevalence, something that is not yet established, ecological studies may lead to biased inferences. The proxy is not a substitute for good data on household-level ownership or even ownership at a smaller level of aggregation by age, sex, or geography. Rather, better individual-level studies exploring the relationship between gun ownership and suicide may be needed in order to further understanding of the overall relationship between firearms and the risk of suicide.