Household Firearm Ownership and Firearm Mortality

This cohort study evaluates the population-level temporal sequencing of firearm death rates and household firearm ownership rates among US adults from 1990 to 2018.

Let   ,   be the standardized firearm suicide rate per 100,000 and HFR, respectively, for stratum  in two-year period .The cross-lag model is defined by the following two equations: (  | −1 ,  −1 ) =   +  1  −1 +  2  −1 where   denotes the time fixed effect to capture national trends in firearm suicide rate,  1 denotes the auto-regressive term relating previous suicide rates to current suicide rates, and  2 denotes the relationship between previous HFR and current suicide rate; and (  | −1 ,  −1 ) =   +  1  −1 +  2  −1 where   denotes the time fixed effect to capture national trends in HFR,  1 denotes the autoregressive term relating previous HFR to current HFR, and  2 denotes the relationship between previous suicide rate and current HFR.Specification of models for other outcomes like firearm homicide rate take the same form.Weighted least squares was used to estimate coefficients from these models, where weights correspond to the population in stratum  in two-year period .Add new final sentence to this section.Homicide rate models were preregistered at: https://osf.io/ncwds

Extrapolating model predictions over time
In Figures 2 and 3 in the main text, we play out the implications of the model over five two-year periods.Taking Figure 2 Panel A as an example, we fixed the suicide rate in 2010/2011 at its median value (call it  0 ), and we computed the 10 th , 25 th , 50 th , 75 th , and 90 th quantiles of HFR in 2010/2011.For each of the HFR quantile values (call it  0 ), we predicted the 2012/2013 firearm suicide rate and HFR from the baseline values of suicide rate and HFR based on the model coefficients as These HFR is household firearm ownership rate.TFSR combines firearm and nonfirearm suicides.Coefficients for cross-lagged effects (HFR -> NFSR; NFSR -> HFR) describe the standardized expected differences in the outcome at time 2 for groups with identical outcomes at time 1 but which differ by one standard deviation on the predictor.Coefficients for the association of HFR with later HFR and NFSR with later NFSR are autocorrelations.Total firearm suicides was not discussed in the paper, but is included here for completeness.The covariance of residuals are the partial correlations between these standardized variables at time t conditioned on their t-1 values.Coefficients for cross-lagged effects (HFR -> FHR; FHR -> HFR) describe the standardized expected differences in the outcome at time 2 for groups with identical outcomes at time 1 but which differ by one standard deviation on the predictor.Coefficients for the association of HFR with later HFR and FHR with later FHR are autocorrelations.The covariance of residuals are the partial correlations between these standardized variables at time t conditioned on their t-1 values.Coefficients for cross-lagged effects (HFR -> NFHR; NFHR -> HFR) describe the expected differences in the standardized outcome at time 2 for groups which differ by one standard deviation on the predictor at time 1.Coefficients for the association of HFR with later HFR and NHR with later NHR are autoregressions.The covariance of residuals are the partial correlations between these standardized variables at time t conditioned on their t-1 values.

eTable 1. Standardized Coefficients for Firearm Suicide Models 95% confidence interval Analysis Variable Coefficient Lower Upper p
NOTE: FSR is firearm suicide rate; HFR is household firearm ownership rate.Coefficients for cross-lagged effects (HFR -> FSR; FSR -> HFR) describe the standardized expected differences in the outcome at time 2 for groups with identical outcomes at time 1 but which differ by one standard deviation on the predictor.Coefficients for the association of HFR with later HFR and FSR with later FSR are autocorrelations.The covariance of residuals are the partial correlations between these standardized variables at time t conditioned on their t-1 values.

eTable 4 .
Standardized Coefficients for Homicide Rate Models: Subgroup Analyses NOTE: FHR is firearm homicide rate; HFR is household firearm ownership rate.Coefficients for cross-lagged effects (HFR -> FHR; FHR -> HFR) describe the standardized expected differences in the outcome at time 2 for groups with identical outcomes at time 1 but which differ by one standard deviation on the predictor.Coefficients for the association of HFR with later HFR and FHR with later FHR are autocorrelations.The covariance of residuals are the partial correlations between these standardized variables at time t conditioned on their t-1 values.
eTable 5. Standardized Coefficients for Homicide Rate Models: Sensitivity Analyses © 2024 Morral AR et al.JAMA Network Open NOTE: NFHR is non-firearm homicide rate; HFR is household firearm ownership rate.