Estimation of exposure‐attributable fractions from time series: A simulation study

Abstract

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.

Common Seasonal Pathogens and Epidemiology of Henoch-Schönlein Purpura Among Children

“…The estimated percentage of HSP incidence associated with each pathogen was calculated as the relative change in the incidence of HSP that would occur over the whole study period if the exposure to each pathogen was removed (eMethods in Supplement 1 ). 11 , 18 …”

“…Seasonal Pathogens and Epidemiology of Henoch-Schönlein Purpura Among Children the relative change in the incidence of HSP that would occur over the whole study period if the exposure to each pathogen was removed (eMethods in Supplement 1). 11,18 We performed 4 sensitivity analyses to assess the robustness of the study findings: (1) a quasi-Poisson model with 6-and 12-month period seasonality; (2) a trigonometric quasi-Poisson regression with the monthly counts of the outcomes of interest instead of incidences; (3) a quasi-Poisson model excluding highly correlated covariates that could affect the multiple regression model; and (4) a model calculating the percentage of HSP cases associated with SARS-CoV-2. This multicollinearity was assessed using the generalized variance inflation factor.…”