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Letter to the Editor R E T H I N K I N G T H E DE B A T E O N D R I NK I N G A N D DR I V I N G L A W S IN SÃO PAULO: R ESPONSE T O T H E LE TT E R B Y V O L P E & FA N T ON I We thank Volpe & Fantoni [1] for their comments on our article about the effects of reducing the blood alcohol concentration (BAC) limit in São Paulo, Brazil. We hoped that our paper would generate exactly this kind of discussion among Brazilian traffic researchers and stakeholders, as policy decisions in this area have been dominated by non-epidemiological analysis. However, we do not believe the arguments they provide are enough to contradict our previous findings. They fitted a model, Y = β0 + β1 × t0 + β2 × t1 + β3 × intervention, where t0 and t1 were continuous time indicators for before and after intervention. The intervention effect was estimated by comparing the intercepts derived from two fitted deterministic trends. One key difference between this model and the autoregressive integrated moving average (ARIMA) model we used concerned the issue of how to adjust for secular trend. We followed a standard approach in the ARIMA model: first, testing whether the series was stationary, and if not, taking the first-order difference, then re-testing it to make sure the differenced data were stationary. As shown in Table 1 of our paper [2], the two traffic injury series (top of Table 1) were obtained by first-order differencing of original data in order to make them stationary, while the two traffic fatality series (bottom of Table 1) were stationary without the need of differencing. Volpe & Fantoni used time ‘t’ in their regression to model the time trend explicitly, which might explain why their results are different from ours. Instead, time trend is not modelled explicitly in our approach. The two approaches used to modelling time–series data are based on different assumptions and estimated differently, thus the results may not be directly comparable without knowing the underlying data-generating process. Also, because of the different methods used, some of their critiques are not relevant to our analysis. For example, they state that in our model: ‘the effect of the intervention was modelled with a before–after dummy variable, but no interaction term was included’. However, by fitting an ARIMA model, we assume an underlying stochastic trend, rather than a deterministic trend as presented by their model. Therefore, there is no time effect in our model, and an interaction term between time and intervention is not needed. The two different approaches (modelling the time trend and using a differencing process) have been commonly used to de-trend time-series data. While we are © 2014 Society for the Study of Addiction

not arguing for one approach over another, the literature seems to suggest that using the differencing process is recommended [3]. In the alcohol field, the ARIMA model using differencing processes are used more commonly [4–11]. In addition, the proposed model suggested by Volpe & Fantoni did not adjust for seasonality, when traffic accidents in general are clearly seasonal, nor did it take into account other factors that might have affected data collection during the study period (e.g. we have included a dummy variable for the police strike period in the intervention analysis), which we believe might be extremely important in affecting the interpretation of the results. Besides the discussion of which statistical technique is more appropriate and the relevance of the results derived from each option, which we believe is a valid and important discussion, there is a crucial limitation in the comparison between our work and the newly suggested model that seems to have been overlooked by Volpe & Fantoni. They selected a national health data set [12] to extract information from traffic-related fatalities for the region studied, while we used a regional criminal database provided by the State of São Paulo. Although both data sets have merit, they may not be comparable; it has been found that the number of traffic fatalities can vary considerably depending on the data source [13]. For example, the data used by Volpe & Fantoni seemed to be derived from the total number of fatally injured victims in the city of São Paulo, whereas we used the number of fatal traffic accident events per 100 000 inhabitants for the same period and locality. Regarding their conclusion that many other factors might have been more relevant in reducing traffic accidents in São Paulo than reducing the BAC limit, we believe that this kind of argument is not based on evidence provided by their current analysis. The inclusion of other factors that could have influenced the mortality due to traffic accidents in São Paulo is certainly desirable, but it was not possible in our study due to the lack of such data, especially in the form of time–series. This should be acknowledged as a study limitation, as we did in our paper. In conclusion, we believe that our findings should not be considered misleading, and we hope that this kind of debate will help to strengthen discussion on the effectiveness of drinking and driving laws for developing countries such as Brazil, bringing a more in-depth epidemiological approach to a serious public health issue. Declaration of interests G.A. collaborated more than 4 years ago as a research consultant with a Social Aspect Organization (SAO) funded by Addiction

Letter to the Editor

the alcohol industry in Brazil. He is no longer affiliated with any of these organizations and none of his research has ever been funded by the alcohol industry. He is currently supported by a grant provided by São Paulo Research Foundation (FAPESP) and CAPES Foundation from Brazil (#2014/01054-0). All other authors have no conflicts of interest to declare. All the opinions, conclusions and recommendations expressed in this material are the responsibility of the authors and do not necessarily reflect the point of view from FAPESP and CAPES. Keywords Alcohol, ARIMA, BAC limit, Brazil, Drinking and driving, Injury, Law, Time-series, Traffic accident. 1

GABRIEL ANDREUCCETTI , HERACLITO BARBOSA DE 1

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CARVALHO , CHERYL J. CHERPITEL , YU YE & VILMA LEYTON

Department of Preventive Medicine, University of São Paulo Medical School, Av. Dr Arnaldo, 455–2° Andar, CEP 01246-903, São Paulo SP, Brazil1, Alcohol Research Group, Emeryville, CA, USA2, and Department of Legal Medicine,University of São Paulo Medical School, São Paulo, Brazil3. E-mail:[email protected]

References 1. Volpe F. M., Fantoni R. Reanalyzing traffic-related mortality in São Paulo. Addiction 2014. 2. Andreuccetti G., Carvalho H. B., Cherpitel C. J., Ye Y., Ponce J. C., Kahn T. et al. Reducing the legal blood alcohol concentration limit for driving in developing countries: a time for change? Results and implications derived from a time– series analysis (2001–10) conducted in Brazil. Addiction 2011; 106: 2124–31.

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3. Raffalovich L. E. Detrending time series: a cautionary note. Sociol Methods Res 1994; 22: 492–519. 4. Chandran A., Pérez-Núñez R., Bachani A. M., Híjar M., Salinas-Rodríguez A., Hyder A. A. Early impact of a national multi-faceted road safety intervention program in Mexico: results of a time-series analysis. PLOS ONE 2014; 9: e87482. 5. Cunningham J. K., Bojorquez I., Campollo O., Liu L.-M., Maxwell J. C. Mexico’s methamphetamine precursor chemical interventions: impacts on drug treatment admissions. Addiction 2010; 105: 1973–83. 6. Herttua K., Mäkelä P., Martikainen P. An evaluation of the impact of a large reduction in alcohol prices on alcohol-related and all-cause mortality: time series analysis of a populationbased natural experiment. Int J Epidemiol 2011; 40: 441–54. 7. Norström T., Stickley A., Shibuya K. The importance of alcoholic beverage type for suicide in Japan: a time-series analysis, 1963–2007. Drug Alcohol Rev 2012; 31: 251–6. 8. Ramstedt M. Alcohol and fatal accidents in the United States —a time series analysis for 1950–2002. Accid Anal Prev 2008; 40: 1273–81. 9. Stickley A., Razvodovsky Y. The effects of beverage type on homicide rates in Russia, 1970–2005. Drug Alcohol Rev 2012; 31: 257–62. 10. Gómez-García L., Pérez-Núñez R., Hidalgo-Solórzano E. Short-term impact of changes in drinking-and-driving legislation in Guadalajara and Zapopan, Jalisco, Mexico. Cad Saude Publica 2014; 30: 1281–92. 11. Brubacher J. R., Chan H., Brasher P., Erdelyi S., Desapriya E., Asbridge M. et al. Reduction in fatalities, ambulance calls, and hospital admissions for road trauma after implementation of new traffic laws. Am J Public Health 2014; 104: e89–97. 12. Departamento de Informática do Sistema Único de Saúde (DATASUS). Informações de saúde (TABNET): epidemiológicas e morbidade [Department of Informatics (DATASUS). Health information (TABNET): epidemiologic and morbidity]. Available at: http://www2.datasus.gov.br/DATASUS/index.php? area=0203 (accessed 10 October 2014). 13. Pechansky F., Chandran A. Why don’t northern American solutions to drinking and driving work in southern America? Addiction 2012; 107: 1201–6.

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Rethinking the debate on drinking and driving laws in São Paulo: response to the letter by Volpe & Fantoni.

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