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Background: Numerous studies have investigated the impact of smoke-free laws on health outcomes. Large differences in estimates are in part attributable to how the long-term trend is modelled. However, the choice of appropriate trend is not always straightforward. We explore these complexities in an analysis of myocardial infarction (MI) mortality in England before and after the introduction of smoke-free legislation in July 2007. Methods: Weekly rates of MI mortality among men aged 40+ between July 2002 and December 2010 were analysed using quasi-Poisson generalised additive models. We explore two ways of modelling the long-term trend: (1) a parametric approach, where we fix the shape of the trend, and (2) a penalised spline approach, in which we allow the model to decide on the shape of the trend. Results: While both models have similar measures of fit and near identical fitted values, they have different interpretations of the legislation effect. The parametric approach estimates a significant immediate reduction in mortality rate of 13.7% (95% CI: 7.5, 19.5), whereas the penalised spline approach estimates a non-significant reduction of 2% (95% CI:-0.9, 4.8). After considering the implications of the models, evidence from sensitivity analyses and other studies, we conclude that the second model is to be preferred. Conclusions: When there is a strong long-term trend and the intervention of interest also varies over time, it is difficult for models to separate out the two components. Our recommendations will help further studies determine the best way of modelling their data

Interpreting Long-Term Trends in Time Series Intervention Studies of Smoke-Free Legislation and Health