Statistical analysis of a dynamic model for dietary contaminant exposure

This paper is devoted to the statistical analysis of a stochastic model introduced in [P. Bertail, S. Clémençon, and J. Tressou, A storage model with random release rate for modelling exposure to food contaminants, Math. Biosci. Eng. 35 (1) (2008), pp. 35-60] for describing the phenomenon of exposure to a certain food contaminant. In this modelling, 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 inbetween intakes, in such a way that the exposure dynamic through time is described as a 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 (CI) 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 (IS) techniques. Applications of these statistical methods to a collection of data sets related to dietary methyl mercury contamination are discussed thoroughly.