To our knowledge, this study is the first to apply the ARIMA intervention time series analysis to evaluate the impact of Ohio’s concussion law on rates of concussion-related medical encounters over time among Medicaid-insured children aged ≤18 years. The ARIMA intervention time series model has several advantages over traditional time series analyses, including power, flexibility, and increased accuracy of predictions [26,27,28,29]. The findings suggest that the application of the ARIMA intervention time series analysis may be appropriate for explaining the effect of Ohio’s concussion law on concussion-related medical encounters. Our results revealed an increase in the monthly rates of concussion-related medical encounters from pre- to post-law, with two of the three upward breaks in the monthly rate of concussion-related medical encounters observed during the pre-law period. These results suggest that there was a potential “spillover” effect of other states’ concussion laws on concussion-related medical encounters in Ohio. Our results also showed a seasonal trend in the rate of concussion-related medical encounters, with rates highest in September and October of each year. Such findings may provide more precise and detailed information on the impact and nature of effect of Ohio’s concussion law on concussion-related medical encounters over time.
Although the traditional Poisson regression analysis could quantify rates ratios, comparing pre-law monthly concussion-related medical encounter rates to post-law rates, and the polynomial curve could describe the trend of yearly rates, these two traditional methods are limited by their ability to describe patterns of rate changes or forecast future trends of interest. ARIMA time series intervention analysis, on the other hand, has emerged as a standard statistical method to assess the impact of an intervention (i.e., a planned policy change) over time or in time series forecasting [19, 30, 31]. ARIMA time series intervention analysis has several advantages over traditional statistical methods (i.e., Poisson regression, a polynomial curve). These include that it is based on its own historical data  and the previous error terms for forecasting ; it allows for the identification and describing of temporal trends during the study period [34, 35]; and it enables the monitoring and forecasting of future monthly or annual trends [24, 33, 36]. However, it is important to note that the ARIMA intervention model is just one alternative method available to researchers when evaluating the impact of a law or forecasting trends of an outcome(s) of interest. The decision to employ the ARIMA time series model or traditional statistical methods should be guided by both the research question and the data type and structure.
The ARIMA time series intervention analysis has been increasingly used in epidemiologic research in recent years to assess intervention or policy impact [33, 34, 36]. Prior research shows that this model can be successfully applied to examine temporal trends and predict the incidence of various infectious diseases and injuries. For example, Lin et al.  used the ARIMA model to forecast monthly injury mortality trends and found that this model could be successfully applied to predict injury mortality. Despite its strengths and successful application in other fields [17, 19, 28, 29, 32], this study is the first to use the ARIMA time series intervention analysis to assess the impact of concussion laws on rates of concussion-related medical encounters over time from pre-law to post-law. Our findings may not only further our understanding of the effect of concussion laws on concussion-related healthcare utilization but may have important implications for future public health law impact research.
Using ARIMA intervention time series analysis, we identified three upward breaks in the monthly rates of concussion-related medical encounters during the study period. Two of these breaks were observed before Ohio’s concussion law went into effect. Such findings have not been previously reported; thus, further research is needed to confirm these findings. Possibly, the first identified break (February 2010) may have been influenced by the enactment of Washington State’s concussion law (The Zackery Lystedt Law) in 2009. Since the enactment of the Zackery Lystedt Law, media attention on and public awareness of concussion and the potential short- and long-term health consequences of concussion has increased dramatically throughout the US, which may partially explain the first observed increase in concussion-related medical encounters in Ohio. The second increase in concussion-related medical encounters was observed in July 2011. By then, 34 states had signed a state concussion law, 25 of which had been enacted . These results may reflect a positive spillover effect of concussion laws; the law intervention in other states may have affected rates of concussion-related medical encounters in Ohio, perhaps highlighting the widespread effectiveness and benefits of the law intervention . Finally, while not significant, we observed another increase in rates of concussion-related medical encounters in July 2013, immediately following the enactment of Ohio’s concussion law. As noted above, these three breaks may be the result of local and national policy efforts that aim to mitigate the potential negative consequences of concussion.
Consistent with previous research [7, 20], our results suggest a distinct seasonal trend in the rate of concussion-related medical encounters, with rates highest in September and October of each year. This finding was unsurprising given that American football is played during these months and prior research shows that American football has a high incidence of concussion as compared to other youth sports . Although knowledge and awareness about concussion has increased in recent years in both athletes and non-athletes [11,12,13, 40], our findings, in line with others, suggest that additional preventive strategies (i.e., rule changes, reduction of player-to-player contact in practice sessions) aimed to mitigate the risk of concussion among youth athletes are needed [10, 11, 40]. These preventive strategies would be especially beneficial for youth athletes who play contact or collision sports such as American football, ice hockey, and soccer [11, 39,40,41]. Identification and testing of such preventive strategies may reduce the incidence of concussion.
This study has several limitations that warrant attention. First, similar to most studies that investigate the effects of policy changes on health outcomes, the present study is ecological in design. Because individual-level exposure data were not available, we were unable to attribute the increased rate of concussion-related medical visits solely to the concussion law. It is possible that the observed changes in rates of concussion-related medical encounter were due to unobserved economic or environmental confounding variables; thus, our results should be interpreted with caution. In addition, the observed upward breaks and seasonal trend in the monthly rates of concussion-related medical encounters were largely driven by our data and the selection of model(s) and need to be further validated. Finally, our results were based on medical encounters among Medicaid-insured children in Ohio; thus, our results may not be generalizable across states and/or to youth with other types of insurance.