  Autoregressive models are widely used for the analysis of time-series data,
but they remain underutilized when estimating effects of interventions. This is
in part due to endogeneity of the lagged outcome with any intervention of
interest, which creates difficulty interpreting model coefficients. These
problems are only exacerbated in nonlinear or nonadditive models that are
common when studying crime, mortality, or disease. In this paper, we explore
the use of negative binomial autoregressive models when estimating the effects
of interventions on count data. We derive a simple approximation that
facilitates direct interpretation of model parameters under any order
autoregressive model. We illustrate the approach using an empirical simulation
study using 36 years of state-level firearm mortality data from the United
States and use the approach to estimate the effect of child access prevention
laws on firearm mortality.
