On the use of empirical bayes for comparative interrupted time series with an application to mandatory helmet legislation

Road safety interventions directed at a population such as mandatory helmet legislation (MHL) and seat belt laws are often assessed by interrupted time series (ITS) methods. Such interventions are often controversial since the pre- and post-intervention periods are not randomised making causal inference difficult. It is possible for changes in the time series of interest to be due to unmeasured confounders and not the intervention. For example, it is often argued by those opposing MHL that the decline in bicycle related head injuries following this intervention could be due to declines in cycling ridership and not a safety benefit. The inclusion of a comparative series in ITS designs is a potential way to account for unmeasured confounding; however, statistically rigorous criteria for selecting a comparator are yet to be developed. To that end, this paper examines the use of empirical Bayes methods as a means for detecting unmeasured confounding and for choosing the best comparative time series. ITS using empirical Bayes consists of estimating a post-intervention trajectory, or counterfactual, using the pre-intervention data. The trajectory is then compared to the post-intervention data for deviations from the counterfactual. These methods will be applied to NSW hospitalisation data around the mandatory helmet law as a demonstration.