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Abstract
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Andreuccetti et al. have reported a reduction in traffic-related injuries and fatalities using a 10-year-span time–series public data set from São Paulo, Brazil. This case constitutes an interesting example of how the choice of the appropriate statistical technique, and its correct interpretation, is crucial to avoid misleading results.
The authors have included an autoregressive parameter in an autoregressive integrated moving average (ARIMA) model with no justification, as no autocorrelation of the errors could be found when re-analysing the data set. If there was no seasonal component, a moving average component or autocorrelation, there seemed to be no justification for choosing ARIMA over ordinary regression models, as both should produce similar results.
Also, the effect of the intervention was modelled with a before–after dummy variable, but no interaction term was included, so the significance of the intervention effects was still confounded with the declining fatalities that could be observed from the beginning of the time–series. In this case, what was actually tested was the difference between means before and after the implementation of the law (which was not related directly to the intervention, but resulting from a long-term decreasing trend), instead of testing a change in the slope or level.
To demonstrate this, we re-analysed the same public domain data set, using a different technique: linear segmented regression. This approach was used to compare the levels and the slopes of a before–after punctual intervention situation, considering that no seasonality has been evidenced. The model included three independent variables: one indicating the time count (months) before the intervention and zeros representing the months after the intervention; a dummy variable with zeros for each observation prior to the intervention and 1 for those after the intervention; and a third predictor variable with the month counts after the intervention, with zeros for all observations before it. By using this model, it is possible to detect any significant change in the initial level and/or the predicted slope if no intervention had occurred. Thus, an existing previous trend was taken into account before comparing pre- and post-intervention trends.
Our results diverge from those reported previously. No significant slope was detected before July 2008, when the new drinking–driving law was implemented (P = 0.940). In the subsequent 30 months, the starting level was not significantly different from the predicted (P = 0.580) if no intervention had occurred, and the slope was also not altered significantly (P = 0.265).
Contrary to what has been reported, we concluded that there was no modification in the rate of reduction of traffic-related fatalities in the city of São Paulo 2 years after the implementation of the new drinking–driving law. Similar analysis of more extended time-periods (1980–2012) shows that traffic-related mortality has been decreasing in São Paulo during the last three decades; again, with no significant effect of the new law. Many other factors may be more relevant than harshening the drinking–driving law with regard to lowering mortality rates, especially in the context of a developing country.
Language: en |