Burden analysis in public health often involves the estimation of exposure-attributable fractions from observed time series. When the entire population is exposed, the association between the exposure and outcome must be carefully modelled before the attributable fractions can be estimated. This article derives asymptotic convergences for the estimation of attributable fractions for commonly used time series models (ARMAX, Poisson, negative binomial, and Serfling), using for the most part the delta method. For the Poisson regression, the estimation of the attributable fraction is achieved by a Monte Carlo algorithm, taking into account both an estimation and a prediction error. A simulation study compares these estimations in the case of an epidemic exposure and highlights the importance of thorough analysis of the data: When the outcome is generated under an additive model, the additive models are satisfactory, and the multiplicative models are poor, and vice versa. However, the Serfling model performs poorly in all cases. Of note, a misspecification in the form or delay of the association between the exposure and the outcome leads to mediocre estimation of the attributable fraction. An application to the fraction of French outpatient antibiotic use attributable to influenza between 2003 and 2010 illustrates the asymptotic convergences. This study suggests that the Serfling model should be avoided when estimating attributable fractions while the model of choice should be selected after careful investigation of the association between the exposure and outcome.
Keywords: Monte Carlo approximation; attributable fraction; simulation study; time series.
© 2018 John Wiley & Sons, Ltd.