Association Between Acute Alcohol Use and Firearm-Involved Suicide in the United States

 Here is a link to an article in the Journal of the American Medical Association (JAMA) by Lange, Jiang, Kaplan, et al.

 https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2802848

 As John Lott of the Center for Crime Prevention Research has shown, JAMA papers involving firearms often have fatal statistical flaws. This appears to be an example – although I must caution readers that, at 86 years old, I have forgotten most of my statistics.

 An excerpt from the paper follows.

 My comments are in italics. I address only some basic issues of probability that suggest that the authors misinterpret their results. I ignore other major statistical issues, such as control variables in the regression models.

Key Points

Question Does the probability of using a firearm as the method of suicide increase as the amount of alcohol consumed increases?

This statement is of the form: Probability that a firearm was used given a suicide is a function of alcohol consumption, P(firearm | suicide)=f(alcohol) and, at least over some relevant range, f(alcohol) is an increasing function. Call this kind of statement S1.

You can visualize such a relationship by grouping suicides into classes of alcohol consumption and then plotting class percentage of firearm use vs class alcohol consumption. Essentially, the authors did this and found an inverted U shape.

Findings In this cross-sectional study of 58 095 suicide decedents, the probability of a firearm-involved suicide increased as blood alcohol concentration increased until the blood alcohol level reached approximately 0.40 g/dL for male decedents and approximately 0.30 g/dL for female decedents, at which point the probability started to decrease.

This is the inverted U shape referred to above.

Meaning This study suggests that interventions targeting heavy alcohol use may aid in efforts to reduce the suicide mortality rate, particularly suicides involving a firearm.

Such an intervention may be successful if the probability of a suicide with a firearm increases with alcohol consumption, at least over a relevant range, i.e., that the P(suicide and firearm)=f(alcohol) and, at least over some relevant range, f(alcohol) is an increasing function. Call this kind of statement S2.

S2 is not implied by S1.

For example, suppose that increasing alcohol consumption is associated with fewer suicides, but that those that do occur are more likely to involve firearms with more alcohol consumption. Then decreasing alcohol consumption will increase suicides and the percentage of suicides that involve firearms.

Abstract

Importance Firearms are the method of suicide used most often in the US. Acute alcohol use is associated with an increased risk of suicide by firearm. However, the dose-response association between acute alcohol use and the probability of using a firearm as the method of suicide is unknown.

The study does not appear to address whether acute alcohol use is associated with an increased frequency of suicide or an increased frequency of suicide by firearm.

Objective To evaluate the association between the amount of alcohol consumed and the probability of using a firearm as the method of suicide.

This is S2, not S1. But the paper addresses S1, not S2.

Design, Setting, and Participants This cross-sectional study used mortality data from the US National Violent Death Reporting System on suicide decedents aged 18 years or older with a positive blood alcohol concentration (BAC; ie, ≥0.01 g/dL). Statistical analysis was performed from January 2003 to December 2020.

Exposure Acute alcohol use, ascertained via postmortem toxicologic examination.

Main Outcomes and Measures Probability of using a firearm as the method of suicide compared with all other methods of suicide.

This is S1.

Results The study included 45 959 male suicide decedents (mean [SD] age, 42.6 [14.8] years) and 12 136 female suicide decedents (mean [SD] age, 44.2 [13.8] years) with a positive BAC; of those, 24 720 male decedents (53.8%) and 3599 female decedents (29.7%) used a firearm as the method of suicide. The probability of using a firearm as the method of suicide when alcohol is consumed was higher for male decedents, with the probability starting at just below 0.50 and increasing to approximately 0.75. In contrast, for female decedents, the probability began at just above 0.30 and increased to approximately 0.55. For both male and female decedents, the dose-response curves were an inverted U shape; as BAC increased, the probability of firearm-involved suicide initially increased and then decreased at very high BACs (approximately 0.40 g/dL for male decedents and approximately 0.30 g/dL for female decedents; these BACs were present among only a small percentage of alcohol-involved suicides: male decedents, 589 [1.3%]; female decedents, 754 [6.2%]).

Conclusions and Relevance This cross-sectional study of suicide decedents who had consumed alcohol prior to their death suggests that, as alcohol consumption increased, the probability of a firearm-involved suicide increased until a certain BAC, at which point the probability started to decrease.

This is S2, not S1.

It appears that the authors misinterpret their probability statements so that while their statistics suggest S1, their conclusion is S2. If so, the paper is fatally flawed.