Analysis
We calculated the ratio of 15–29-year-olds presenting with alcohol-related harms to numbers in both the control groups. As presentations for alcohol-related harms, among others, may be subject to seasonal fluctuations, time series analyses were employed to test for any significant change in the ratio of presentations among 15–29-year-olds for alcohol-related harms before and after the ‘alcopops’ tax increase to those of the other two control groups. We used the X11 procedure to identify and adjust the series for trend, seasonality and autocorrelated data errors.25 This technique identifies seasonal factors and decomposes the original series into seasonal, irregular and trend components. Examination of the underlying trend can provide a more useful indication of the overall direction of a time series with significant seasonality.
Autoregressive integrated moving average (ARIMA) modelling was then used to test for any significant interruption to the time series following the tax increase.26 ,27 This is a regression analysis to test for a break at the time of the tax increase, taking into account any seasonal autocorrelations. Based on evidence of an increasing trend in most of the series prior to the ‘alcopops’ tax increase, we applied one order of differencing to create stationary series for modelling. Differencing takes into account long-term increases in alcohol-related presentations that could mask the effect of the increased tax. We found the ARIMA (1,1,0)(1,0,0)12 model to be the best fit, testing for white noise with the Ljung-Box statistic. We also included standard and seasonal autoregressive components to model the time series structure. We visually inspected residuals and used Q-tests to ensure there were no unexplained patterns over time.
We undertook several sensitivity analyses. First, we applied AAFs for all injuries without taking into account external cause of injury codes. As we could not find Australian AAFs for S and T codes, we used Swiss data.28 We then did a sensitivity analysis of including S codes for superficial injury. We also stratified the analyses by gender in case the proportion of males to females varied between the cases and any of the controls. Similarly, we assessed if there was any difference between younger and older age groups within the 15–29-year-old sample by looking at 15–19-year-olds only. Next, we investigated if there was any difference when we restricted alcohol-related presentations to the narrow definition. In addition, we only considered presentations between 22:00 and 06:00, or on weekends when alcohol would be most likely to be a factor. Finally, to test whether the introduction of the tax was associated with a change in the seasonal pattern of alcohol presentations or affected the underlying rate of growth in presentations for alcohol-related harms we fitted alternative forms of the overall models (males, females, persons, 15–29 years, broad definition) with dummy terms for each month and also with a deterministic trend without differencing.