Statistical analysis of a dynamic model for dietary contaminant exposure

Patrice Bertail (1, 2) , Stéphan Clémençon (3) , Jessica Tressou (4, 5)

1 MODAL'X - Modélisation aléatoire de Paris X
2 CREST - Centre de Recherche en Économie et Statistique
3 LTCI - Laboratoire Traitement et Communication de l'Information
4 MET@RISK - Méthodologies d'Analyse de Risque Alimentaire
5 HKUST-ISMT - Hong Kong University of Science and Technology - Information Systems, Business Statistics & Operations Management

This paper is devoted to the statistical analysis of a stochastic model introduced in Bertail, Clémençon \& Tressou (2007) for describing the phenomenon of exposure to a certain food contaminant. In this modeling, the temporal evolution of the contamination exposure is entirely determined by the accumulation phenomenon due to successive dietary intakes and the pharmacokinetics governing the elimination process in between intakes, in such a way that the exposure dynamic through time is described as a \textit{piecewise deterministic Markov process}. Paths of the contamination exposure process are scarcely observable in practice, therefore intensive computer simulation methods are crucial for estimating the time-dependent or steady-state features of the process. Here we consider simulation estimators based on consumption and contamination data and investigate how to construct accurate bootstrap confidence intervals for certain quantities of considerable importance from the epidemiology viewpoint. Special attention is also paid to the problem of computing the probability of certain rare events related to the exposure process path arising in dietary risk analysis using multilevel splitting or importance sampling techniques. Applications of these statistical methods to a collection of datasets related to dietary methyl mercury (MeHg) contamination are discussed thoroughly.

Mots clés: Food safety risk analysis; dietary contamination; linear pharmacokinetics model; piecewise deterministic Markov process; long run behavior; Monte-Carlo techniques; simulation estimator; bootstrap; rare event analysis

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Patrice Bertail, Stéphan Clémençon, Jessica Tressou. Statistical analysis of a dynamic model for dietary contaminant exposure. Journal of Biological Dynamics, 2010, 4 (2), pp.212-234. ⟨10.1080/17513750903222960⟩. ⟨hal-00308881v2⟩