Analysis of “Stand Your Ground” Self-defense Laws and Statewide Rates of Homicides and Firearm Homicides

Key Points Question Are “stand your ground” (SYG) laws associated with increases in violent deaths, and does this vary by US state? Findings In this cohort study assessing 41 US states, SYG laws were associated with an 8% to 11% national increase in monthly rates of homicide and firearm homicide. State-level increases in homicide and firearm homicide rates reached 10% or higher for many Southern states, including Alabama, Florida, Georgia, and Louisiana. Meaning These findings suggest that SYG laws were associated with increased homicides each year and that the laws should be reconsidered to prevent unnecessary violent deaths.

Data checks also identified a potential error with the coding of homicide and firearm homicide by race in Texas from Sept 2007 to Feb 2009. Data checks included thorough data visualisations, as well as comparisons across data sources (e.g., the FBI's Supplementary Homicide Reports, see eFigure 2). We escalated this query to Texa's DSHS Center for Health Statistics, Vital Events Data Management team but, due to the COVID-19 pandemic, they did not have the capacity to investigate the issue (response received: 22/01/2021). We therefore replaced these data points by random sample imputation with bounded lower and upper values using imputeTS, see eFigure 3. 17 We present the imputed results in the main paper and the results using the original data with the suspected data error in eTables 6 & 7. Note, there were no identified errors in the overall counts of homicide and firearm homicide.

Model Equation
The underlying model for our main analyses can be represented by the following simplified equation: where t is the sequence of times of observations, m the variable indicating the month (1 as January, 2 as February, and so on until 12 as December), and s is state. represents monthly counts (ie the outcome following a quasi-Poisson distribution) and log ( ) represents the offset of the logarithm of the population from which the events originated; results are thus interpreted as monthly rates. The term is a state-specific intercept and is a smooth function describing state-specific long-term trends, while ℎ models seasonality using harmonic terms -Fourier series of pairs of sine and cosine terms with coefficients , which we consistently modelled as 3 and 12, respectively. 18 The variable x is a dummy variable indicating the presence of the law; taking the value of 1 in the presence of SYG law (in the post-law period in SYG states) and 0 in the absence of SYG law (non-SYG states and the pre-SYG law period in SYG states). The parameter can be interpreted as the log-relative risk of the outcomehomicide or firearm homicidein the presence vs. absence of the SYG law.

Evidence of Non-Linear Trends
In addition to data visualizations of long-trend trends at the state and national level, we evaluated assumptions of linearity by comparing different model specifications. We fitted a series of generalized linear mixed models (GLMMs) and evaluated their model fit with respect to likelihood ratio (LR) tests and Akaike information criterion (AIC) to determine whether state-specific and national long-term trends were most parsimoniously described by linear or non-linear trends. We found that model fit improved when modelling long-term trends with higher polynomials for both statespecific and national trendsas lower AIC values represent more parsimonious models (see eTable 5). LR tests were also used to directly compare whether model fit significantly improved (p<0.01) when using higher polynomials to describe trends. These findings indicate that both state-specific and national long-trend trends for homicide and firearm homicide violate assumptions of linearity. Evidence for non-linearity of trends was further supported through model diagnostics by inspecting the distributions of autocorrelation for linear (e.g., GLMMs with linear trends) versus non-linear (e.g., GAMs) models (eFigure 4).

Non-Penalized Approach
Our main analyses use a GAM framework to estimate the impacts of SYG laws. However, due to the penalisation approach, there may be concerns relating to overfitting and a reduced confidence in the pvalues 19 . To check the robustness of our penalized approach, we conducted complementary analyses using a non-penalized approach: generalized linear mixed models (GLMMs). We fitted a series of GLMMs specifying a cubic term for national and state-specific time trends (i.e., fixed and random effects, respectively) as higher order polynomial terms resulted in superior model fit (eTable 5). Due to convergence problems for some of the stratified models, cubic terms for state-specific trends could not always be fitted. In these incidences, state-specific trends were fitted using the next highest order polynomial, quadratic. This nonpenalized approach replicated our main GAM models, providing even higher estimates of the impacts of SYG laws (see eTable 8). This provides evidence to support confidence in our estimated effects and corresponding p values, indicating that our penalization approach provides more conservative estimates than a non-penalized approach.

Restricted Linear Analyses
Another potential drawback of using models with non-linear trends is a loss of certainty when forecasting the estimated counterfactualwhat would have happened in the absence of the intervention. This is due to the increased flexibility, thus variability, when using polynomials and/or splines to fit underlying trends and forecast predicted trends. We therefore conducted a supplementary analysis of SYG states; restricting the study period from 36 months (3 years) before and 36 months (3 years) SYG laws were enacted. We modelled simple ITS quasi-Poisson regression analyses with linear trends and pooled the effect estimates for each SYG state using fixed effects meta-analysis. These restricted analyses replicated our main results, finding an average 9% increase in homicide rates (IRR=1.09; 95%CI: 1.05-1.13; p<0.0001) and firearm homicide rates (IRR=1.09; 95%CI: 1.04-1.14; p<0.0001) following the enactment of SYG laws (eFigures 8 & 9). We also continued to find no impact of SYG laws on monthly rates of suicide (IRR=0.99; 95%CI: 0.97-1.02; p=0.4643) and firearm suicide (IRR=0.99; 95%CI: 0.96-1.02; p=0.4681).   White homicide counts        Incidence rate ratios by sociodemographic group are estimated by the stratified models while p values are based on Wald tests comparing stratified models within each sociodemographic group. The results broken down by race are based on the original data, which has suspected errors in its coding of race for Texas from Sept 2007 to Feb 2009 (inclusive), for the imputed results see Table 1 in the manuscript. Other races includes all races other than White or Black under the main categories of American Indian, Asian, and Pacific Islander. CI=confidence intervals; IRR= incidence rate ratios; SD=standard deviation.