Firearm Purchase Behavior and Subsequent Adverse Events, United States, 1985-2018 (ICPSR 39169)

A. Case-control analysis: Researchers conducted a case-control analysis with a study population of a total of 22 individuals from California who perpetrated an attack between 1996 and 2018 and had a record of transaction in the state's DOJ Dealer Record of Sale database. Researchers used risk-set sampling to select controls (individuals with purchasing records in DROS who did not perpetrate a mass shooting) at a ratio of 1:15, and matched cases and controls based on gender and age, and compared purchasing behaviors and other relevant risk factors using conditional logistic regression.

B. Mixed Model examining legal and illegal transactions: In the second analysis of mass shooters, the sample comprised all identified California mass and active shooters between 1985 and 2018 (n = 55), irrespective of whether they had a record of transaction in California's Dealer Record of Sale (DROS) database. Researchers implemented a mixed model to evaluate factors associated with firearms acquired in close temporal proximity to the attack, including firearms acquired through unauthorized means. Unauthorized acquisitions included theft, acquisition through an unlicensed dealer, home manufacture, and straw purchasing.

A. Machine Learning Analysis: Criminal history information, legal handgun purchasing trends, and purchaser demographics were used as input features to predict time to arrest. Features in the model were included as one of four types: constant, the time since an event, characteristics of the most recent purchase or arrest, and lifetime purchase and arrest characteristics. Criminal history features included the cumulative number of times a purchaser had been arrested at a given date for felonies and for misdemeanors, the years since the purchaser was last arrested; using 58 categories of crime defined by the California department of justice, which category of crime did the most recent arrest corresponds to; and indicators denoting if a purchaser has ever been arrested for each of the 58 crime categories. All criminal history features were time dependent. Handgun purchasing trends were captured with features including the total number of handguns purchased at a given date, years since last legal handgun purchase, and characteristics of the last legal handgun purchase such as the type of handgun (single shot, semi-automatic, revolver, derringer or other); caliber, categorized into small, medium, and large; median cost of a handgun from a manufacturer, categorized into two groups; the type of retailer (licensed dealer, private party, pawn shop, or other; and if the handgun was purchased at a gun show. Finally, demographic features included the purchasers age, race, and gender. Researchers used a gradient boosting machine (GBM) with a Cox proportional hazards loss function to predict risk of arrest for violent crime.

B. Case-control Analysis: For the case-control analyses, individuals entered the cohort at the time of their first purchase and are considered at risk until December 31, 2021, their death from any cause, or if they could no longer be identified as a resident of California. To ensure that researchers had complete legal handgun purchasing records for individuals from the age at which they were legally eligible to purchase (age 21), individuals were enrolled based on age, over a twenty-four-year period (1996-2020): those with a record of purchase who were age 21 in 1996, individuals aged 21-22 in 1997, individuals aged 21-23 in 1997, and so on, up to individuals aged 21-45 in 2020. Though this approach sacrifices the study of older purchasers, given our study focus on interpersonal violence and the well-established finding that criminal risk peaks in the early to mid-twenties and declines significantly with age, are primary interest was in younger individuals. Importantly, they did not enroll or match on age at time of entry into the study population. That is, an individual who was 21 in 1996 could have, for example, purchased their first handgun in 2010 and entered the cohort at age 35. Researchers used incidence density sampling to select 10 controls from DROS who were still at-risk at the time of the case's arrest. Under this sampling approach, controls may be randomly selected as controls more than once, and a person selected as control may later become a case the odds ratio provides an estimate of the rate ratio for the full cohort. Cases and controls were matched on gender for statistical efficiency. Also, the criminal history arrest data was included. These variables included arrests for a violent crime involving a firearm (pre-purchase), violent crime not involving a firearm, non-violent misuse of a firearm, property crime, drug or alcohol related crime, and other crime.