Strong mixing condition for Hawkes processes and application to Whittle estimation from count data

This paper focuses on the time series generated by the event counts of stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, existing methods of estimation are not applicable. We first establish a strong mixing condition with polynomial decay rate for Hawkes processes, from their Poisson cluster structure. This allows us to propose a spectral approach to the estimation of Hawkes processes, based on Whittle's method, which provides consistent and asymptotically normal estimates under common regularity conditions on their reproduction kernels. Simulated datasets and a case-study illustrate the performances of the estimation, notably of the Hawkes reproduction mean and kernel when time intervals are relatively large.Comment: 29 pages, 10 figure

Mixing properties for multivariate Hawkes processes

Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the proof to the multivariate case. We illustrate these properties by establishing a functional central limit theorem for multivariate Hawkes processes

Infectious Diseases and Aggregate Data : Estimating Attributable Fractions and Controlling for Bias

La surveillance épidémiologique repose le plus souvent sur l'analyse d'indicateurs de santé agrégés. Nous étudions les problèmes méthodologiques rencontrés lorsque l'on travaille sur ce type de données dans un contexte de santé publique. Dans un premier temps, nous nous intéressons au calcul de la fraction attribuable lorsque l'exposition est épidémique et le nombre d'événements de santé saisonnier. Pour les modèles statistiques de séries temporelles les plus souvent utilisés, nous présentons une méthode d'estimation de cette fraction et de ses intervalles de confiance. Ce travail nous a permis de montrer que la campagne de sensibilisation "Les antibiotiques, c'est pas automatique !" avait conduit à une diminution de plus de moitié des prescriptions antibiotiques associées aux épidémies de syndromes grippaux dès 2005. Par ailleurs, récemment 17% des prescriptions seraient attribuables aux infections virales des voies respiratoires basses pendant la période hivernale, et près de 38% chez les enfants, dont la moitié attribuables aux bronchiolites. Dans un second temps, nous proposons les processus de Hawkes comme modèles pour les maladies contagieuses et étudions l'impact de l'agrégation des données sur leur estimation. Dans ce contexte, nous développons une méthode d'estimation des paramètres du processus et prouvons que les estimateurs ont de bonnes propriétés asymptotiques. Ces travaux fournissent des outils statistiques pour éviter certains biais dus à l'agrégation de données individuelles pour l'étude de fractions attribuables et de maladies contagieuses.Epidemiological surveillance is most often based on the analysis of aggregate health indicators. We study the methodological problems encountered when working with this type of data in a public health context. First, we focus on calculating the attributable fraction when the exposure is epidemic and the number of health events exhibits a seasonality. For the most frequently used time series models, we present a method for estimating this fraction and its confidence intervals. This work enabled us to show that the awareness campaign "Antibiotics are not automatic!" led to a reduction of more than half of the antibiotic prescriptions associated with influenza epidemics as early as 2005. Moreover, recently 17% of prescriptions are thought to be attributable to viral infections of the lower respiratory tract during the cold period, and nearly 38% in children, half of which attributable to bronchiolitis. In a second step, we propose Hawkes processes as models for contagious diseases and study the impact of data aggregation on their estimation. In this context, we develop a method for estimating the process parameters and prove that the estimators have good asymptotic properties. This work provides statistical tools to avoid some biases due to the use of aggregate data for the study of attributable fractions and contagious diseases

Maladies infectieuses et données agrégées : estimation de la fraction attribuable et prise en compte de biais

Epidemiological surveillance is most often based on the analysis of aggregate health indicators. We study the methodological problems encountered when working with this type of data in a public health context. First, we focus on calculating the attributable fraction when the exposure is epidemic and the number of health events exhibits a seasonality. For the most frequently used time series models, we present a method for estimating this fraction and its confidence intervals. This work enabled us to show that the awareness campaign "Antibiotics are not automatic!" led to a reduction of more than half of the antibiotic prescriptions associated with influenza epidemics as early as 2005. Moreover, recently 17% of prescriptions are thought to be attributable to viral infections of the lower respiratory tract during the cold period, and nearly 38% in children, half of which attributable to bronchiolitis. In a second step, we propose Hawkes processes as models for contagious diseases and study the impact of data aggregation on their estimation. In this context, we develop a method for estimating the process parameters and prove that the estimators have good asymptotic properties. This work provides statistical tools to avoid some biases due to the use of aggregate data for the study of attributable fractions and contagious diseases.La surveillance épidémiologique repose le plus souvent sur l'analyse d'indicateurs de santé agrégés. Nous étudions les problèmes méthodologiques rencontrés lorsque l'on travaille sur ce type de données dans un contexte de santé publique. Dans un premier temps, nous nous intéressons au calcul de la fraction attribuable lorsque l'exposition est épidémique et le nombre d'événements de santé saisonnier. Pour les modèles statistiques de séries temporelles les plus souvent utilisés, nous présentons une méthode d'estimation de cette fraction et de ses intervalles de confiance. Ce travail nous a permis de montrer que la campagne de sensibilisation "Les antibiotiques, c'est pas automatique !" avait conduit à une diminution de plus de moitié des prescriptions antibiotiques associées aux épidémies de syndromes grippaux dès 2005. Par ailleurs, récemment 17% des prescriptions seraient attribuables aux infections virales des voies respiratoires basses pendant la période hivernale, et près de 38% chez les enfants, dont la moitié attribuables aux bronchiolites. Dans un second temps, nous proposons les processus de Hawkes comme modèles pour les maladies contagieuses et étudions l'impact de l'agrégation des données sur leur estimation. Dans ce contexte, nous développons une méthode d'estimation des paramètres du processus et prouvons que les estimateurs ont de bonnes propriétés asymptotiques. Ces travaux fournissent des outils statistiques pour éviter certains biais dus à l'agrégation de données individuelles pour l'étude de fractions attribuables et de maladies contagieuses

Strong-mixing rates for Hawkes processes and application to Whittle estimation from count data

29 pages, 10 figuresIn this paper, we study the time series generated by the event counts of the stationary Hawkes process. Using the cluster properties of the stationary Hawkes process, we prove an upper bound for its strong-mixing coefficient, and for its count series', provided that the reproduction kernel has a finite (1 + β)-th order moment (for a β > 0). When the exact locations of points are not observed, but only counts over fixed time intervals, we propose a spectral approach to the estimation of Hawkes processes, based on Whittle's likelihood. This approach provides consistent and asymptotically normal estimates provided common regularity conditions on the reproduction kernel. Simulated datasets illustrate the performances of the estimation, notably, of the Hawkes reproduction mean and kernel, even with relatively large time intervals

Spectral estimation of Hawkes processes from count data

International audienceThis paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle's method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated data sets and a case-study illustrate the performances of the estimation, notably of the reproduction function even when time intervals are relatively large

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

International audienceBurden 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

Association of Pneumococcal Conjugate Vaccine Coverage With Pneumococcal Meningitis: An Analysis of French Administrative Areas, 2001–2016

International audienceGeographic variations of invasive pneumococcal disease incidence and serotype distributions were observed after pneumococcal conjugate vaccine introduction at regional levels and among French administrative areas. The variations could be related to regional vaccine coverage (VC) variations that might have direct consequences for vaccination-policy impact on invasive pneumococcal disease, particularly pneumococcal meningitis (PM) incidence. We assessed vaccine impact from 2001 to 2016 in France by estimating the contribution of regional VC differences to variations of annual local PM incidence. Using a mixed-effect Poisson model, we showed that, despite some variations of VC among administrative areas, vaccine impact on vaccine-serotype PM was homogeneously confirmed among administrative areas. Compared with the prevaccine era, the cumulative VC impact on vaccine serotypes led, in 2016, to PM reductions ranging among regions from 87% (25th percentile) to 91% (75th percentile) for 7-valent pneumococcal conjugate vaccine serotypes and from 58% to 63% for the 6 additional 13-valent pneumococcal conjugate vaccine serotypes. Nonvaccine-serotype PM increases from the prevaccine era ranged among areas from 98% to 127%. By taking into account the cumulative impact of growing VC and VC differences, our analyses confirmed high vaccine impact on vaccine-serotype PM case rates and suggest that VC variations cannot explain PM administrative area differences

Outpatient antibiotic use attributable to viral acute lower respiratory tract infections during the cold season in France, 2010-2017

International audienceAntibiotic stewardship requires clear insight into antibiotic overuse and the syndromes that lead to prescription. The aim of this study was to estimate the proportion of antibiotic prescriptions attributable to acute lower respiratory tract infections (LRTIs) during the cold season. Using individual data from the French National Health Insurance (NHI) database, weekly time series were constructed of outpatient antibiotic (beta-lactams and macrolides) prescriptions between January 2010 and December 2017. Time series were also constructed of tenth edition of the International Classification of Diseases (ICD-10) discharge diagnoses from a national network of emergency departments (EDs), stratified by specific syndromes (pneumonia, bronchitis, bronchiolitis and influenza-like illness). The number of outpatient antibiotic prescriptions attributable to these syndromes during the cold season in France was modeled and estimated for the entire population, young children (≤5 years) and the elderly (≥75 years). LRTIs accounted for 40% (95% confidence interval [95% CI]: 29, 52) of outpatient antibiotic use during the cold season for the entire population, including 23% (95% CI: 13, 33) and 17% (95% CI: 13, 22) for bacterial and viral infections, respectively. In children and the elderly, viral LRTIs were the reason for 38% (95% CI: 31, 46) and 20% (95% CI: 16, 25) of outpatient antibiotic use, respectively (with bronchiolitis accountable for half of use in young children). In the entire population and in children, respectively, outpatient antibiotic overuse attributable to viral LRTIs was estimated to be 289 (95% CI: 221, 374) and 1588 (95% CI: 1295, 1922) prescriptions per 100 000 inhabitants per week. These results highlight the major role of viral infections in driving antibiotic prescriptions, particularly in young children

Dynamic spatiotemporal coordination of neural stem cell fate decisions through local feedback in the adult vertebrate brain

Posté le 16 juillet 2020 sur BiorXiv : https://www.biorxiv.org/content/10.1101/2020.07.15.205021v1Neural stem cell (NSC) populations persist in the adult vertebrate brain over a life time, and their homeostasis is controlled at the population level. The nature and properties of these coordination mechanisms remain unknown. Here we combine dynamic imaging of entire NSC populations in their in vivo niche over weeks, pharmacological manipulations, mathematical modeling and spatial statistics, and demonstrate that NSCs use spatiotemporally resolved local feedbacks to coordinate their decision to divide. These involve a Notch-mediated inhibition from transient neural progenitors, and a dispersion effect from dividing NSCs themselves, exerted with a delay of 9-12 days. Simulations from a stochastic NSC lattice model capturing these interactions demonstrate that they are linked by lineage progression and control the spatiotemporal distribution of output neurons. These results highlight how local and temporally delayed interactions occurring between brain germinal cells generate self-propagating dynamics that maintain NSC population homeostasis with specific spatiotemporal correlations