On computer-intensive simulation and estimation methods for rare-event analysis in epidemic models.

This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of public health. In general, no close analytic form for their occurrence probabilities is available, and crude Monte Carlo procedures fail. We show how recent intensive computer simulation techniques, such as interacting branching particle methods, can be used for estimation purposes, as well as for generating model paths that correspond to realizations of such events. Applications of these simulation-based methods to several epidemic models fitted from real datasets are also considered and discussed thoroughly.

PBPK and population modelling to interpret urine cadmium concentrations of the French population.

As cadmium accumulates mainly in kidney, urinary concentrations are considered as relevant data to assess the risk related to cadmium. The French Nutrition and Health Survey (ENNS) recorded the concentration of cadmium in the urine of the French population. However, as with all biomonitoring data, it needs to be linked to external exposure for it to be interpreted in term of sources of exposure and for risk management purposes. The objective of this work is thus to interpret the cadmium biomonitoring data of the French population in terms of dietary and cigarette smoke exposures. Dietary and smoking habits recorded in the ENNS study were combined with contamination levels in food and cigarettes to assess individual exposures. A PBPK model was used in a Bayesian population model to link this external exposure with the measured urinary concentrations. In this model, the level of the past exposure was corrected thanks to a scaling function which account for a trend in the French dietary exposure. It resulted in a modelling which was able to explain the current urinary concentrations measured in the French population through current and past exposure levels. Risk related to cadmium exposure in the general French population was then assessed from external and internal critical values corresponding to kidney effects. The model was also applied to predict the possible urinary concentrations of the French population in 2030 assuming there will be no more changes in the exposures levels. This scenario leads to significantly lower concentrations and consequently lower related risk.

Improving dietary exposure models by imputing biomonitoring data through ABC methods.

New data are available in the field of risk assessment: the biomonitoring data which is measurement of the chemical dose in a human tissue (e.g. blood or urine). These data are original because they represent direct measurements of the dose of chemical substances really taken up from the environment, whereas exposure is usually assessed from contamination levels of the different exposure media (e.g. food, air, water, etc.) and statistical models. However, considered alone, these data provide little help from the perspective of Public Health guidance. The objective of this paper is to propose a method to exploit the information provided by human biomonitoring in order to improve the modeling of exposure. This method is based on the Kinetic Dietary Exposure Model which takes into account the pharmacokinetic elimination and the accumulation phenomenon inside the human body. This model is corrected to account for any possible temporal evolution in exposure by adding a scaling function which describes this evolution. Approximate Bayesian Computation is used to fit this exposure model from the biomonitoring data available. Specific summary statistics and appropriate distances between simulated and observed statistical distributions are proposed and discussed in the light of risk assessment. The promoted method is then applied to measurements of blood concentration of dioxins in a group of French fishermen families. The outputs of the model are an estimation of the body burden distribution from observed dietary intakes and the evolution of dietary exposure to dioxins in France between 1930 and today. This model successfully fit to dioxins data can also be used with other biomonitoring data to improve the risk assessment to many other contaminants.

Deterministic modelling for transmission of Human Papillomavirus 6/11: impact of vaccination.

This paper is devoted to assess the impact of quadrivalent human papillomavirus (HPV) vaccine on the prevalence of non-oncogenic HPV 6/11 types in French males and females. For this purpose, a non-linear dynamic model of heterosexual transmission for HPV 6/11 types infection is developed, which accounts for immunity due to vaccination, in particular. The vaccinated reproduction number Rv is derived using the approach described by Diekmann et al. (2010) called the next generation operator approach. The model proposed is analysed, with regard to existence and uniqueness of the solution, steady-state stability. Precisely, the stability of the model is investigated depending on the sign of Rv-1. Prevalence data are used to fit a numerical HPV model, so as to assess infection rates. Our approach suggests that 10 years after introducing vaccination, the prevalence of HPV 6/11 types in females will be halved and that in males will be reduced by one-quarter, assuming a sustained vaccine coverage of 30% among females. Using the formula, we derived for the vaccinated reproduction number, we show that the non-oncogenic HPV 6/11 types would be eradicated if vaccine coverage in females is kept above 12%.

New approach for the assessment of cluster diets.

Dietary risk assessment is a major public health concern, positioned in the context of establishing overall food safety policy. It requires some understanding of population food choices although geographical location and social-cultural environment are variable. Several years ago, a cluster analysis based on FAO consumption data, ranging from 1990 to 1994, was at the origin of the 13, so called, GEMS/Food cluster diets. This analysis required the initial identification of 19 food markers based on geographical and cultural differences. This paper proposes a new modelling of FAO food consumption database in order to define new cluster diets based on updated consumption data from 2002 to 2007 and better adapted statistical methods. Two statistical methods were combined to extract, consumption systems that generate a substructure from the initial food consumption database and then by deriving a clustering of countries according to their consumption system profiles. The clustering resulted in 17 cluster diets composed of 2 up to 30 countries. The few discrepancies between these new clusters and former ones may be due to more recent data, and to the fact that the new approach is based on another mathematical modelling which does not require any initial identification of food markers.

Efficacy of vaccination against HPV infections to prevent cervical cancer in France: present assessment and pathways to improve vaccination policies.

BACKGROUND: Seventy percent of sexually active individuals will be infected with Human Papillomavirus (HPV) during their lifetime. These infections are incriminated for almost all cervical cancers. In France, 3,068 new cases of cervical cancer and 1,067 deaths from cervical cancer occurred in 2005. Two vaccines against HPV infections are currently available and vaccination policies aim to decrease the incidence of HPV infections and of cervical cancers. In France, vaccine coverage has been reported to be low. METHODS: We developed a dynamic model for the heterosexual transmission of Human Papillomavirus types 16 and 18, which are covered by available vaccines. A deterministic model was used with stratification on gender, age and sexual behavior. Immunity obtained from vaccination was taken into account. The model was calibrated using French data of cervical cancer incidence. RESULTS: In view of current vaccine coverage and screening, we expected a 32% and 83% reduction in the incidence of cervical cancers due to HPV 16/18, after 20 years and 50 years of vaccine introduction respectively. Vaccine coverage and screening rates were assumed to be constant. However, increasing vaccine coverage in women or vaccinating girls before 14 showed a better impact on cervical cancer incidence. On the other hand, performing vaccination in men improves the effect on cervical cancer incidence only moderately, compared to strategies in females only. CONCLUSION: While current vaccination policies may significantly decrease cervical cancer incidence, other supplementary strategies in females could be considered in order to improve vaccination efficacy.

Extraction of food consumption systems by nonnegative matrix factorization (NMF) for the assessment of food choices.

In Western countries where food supply is satisfactory, consumers organize their diets around a large combination of foods. It is the purpose of this article to examine how recent nonnegative matrix factorization (NMF) techniques can be applied to food consumption data to understand these combinations. Such data are nonnegative by nature and of high dimension. The NMF model provides a representation of consumption data through latent vectors with nonnegative coefficients, that we call consumption systems (CS), in a small number. As the NMF approach may encourage sparsity of the data representation produced, the resulting CS are easily interpretable. Beyond the illustration of its properties we provide through a simple simulation result, the NMF method is applied to data issued from a French consumption survey. The numerical results thus obtained are displayed and thoroughly discussed. A clustering based on the k-means method is also achieved in the resulting latent consumption space, to recover food consumption patterns easily usable for nutritionists.

A storage model with random release rate for modeling exposure to food contaminants.

This paper presents the study of a continuous-time piecewise-deterministic Markov process for describing the temporal evolution of exposure to a given food contaminant. The quantity X of food contaminant present in the body evolves through its accumulation after repeated dietary intakes on the one hand, and the pharmacokinetics behavior of the chemical on the other hand. In the dynamic modeling considered here, the accumulation phenomenon is modeled by a simple marked point process with positive i.i.d. marks, and elimination in between intakes occurs at a random linear rate theta X, randomness of the coefficient theta accounting for the variability of the elimination process due to metabolic factors. Via embedded chain analysis, ergodic properties of this extension of the standard compound Poisson dam with (deterministic) linear release rate are investigated, the latter being of crucial importance in describing the long-term behavior of the exposure process (X(t))t> or =0 and assessing values such as the proportion of time the contaminant body burden is over a certain threshold. We also highlight the fact that the exposure process is generally not directly observable in practice and establish a validity framework for simulation-based statistical methods by coupling analysis. Eventually, applications to methyl mercury contamination data are considered.

A stochastic SIR model with contact-tracing: large population limits and statistical inference.

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.

The HIV/AIDS epidemic in Cuba: description and tentative explanation of its low HIV prevalence.

BACKGROUND: The Cuban HIV/AIDS epidemic has the lowest prevalence rate of the Caribbean region. The objective of this paper is to give an overview of the HIV/AIDS epidemic in Cuba and to explore the reasons for this low prevalence. METHODS: Data were obtained from the Cuban HIV/AIDS programme established in 1983. This programme has an extensive adult HIV testing policy, including testing of all pregnant women. HIV and AIDS cases have been recorded since 1986. Persons found to be HIV-positive are interviewed on their sexual behaviour and partners. Tracing and voluntary testing of these partners are organised. Epidemiological description of this epidemic was obtained from analysis of this data set. Using elementary mathematical analyses, we estimated the coverage of the detection system (percentage of HIV-positive adults detected) and the average period between HIV infection and detection. Estimated HIV prevalence rates were corrected to account for the coverage. RESULTS: HIV prevalence has increased since 1996. In 2005, the prevalence among pregnant women was 1.2 per 10,000 (16/137000). Estimated HIV prevalence among 15- to 49-year-olds was 8.1 per 10,000 (4913/6065000; 95%CI: 7.9 per 10,000 - 8.3 per 10,000). Most (77%) of the HIV-positive adults were men, most (85.1%) of the detected HIV-positive men were reported as having sex with men (MSM), and most of the HIV-positive women reported having had sex with MSM. The average period between HIV infection and detection was estimated to be 2.1 years (IQR = 1.7 - 2.2 years). We estimated that, for the year 2005, 79.6% (IQR: 77.3 - 81.4%) of the HIV-positive persons were detected. CONCLUSION: MSM drive the HIV epidemic in Cuba. The extensive HIV testing policy may be an important factor in explaining the low HIV prevalence. To reduce the HIV epidemic in Cuba, the epidemic among MSM should be addressed. To understand this epidemic further, data on sexual behaviour should be collected. Now that antiretroviral therapy is more widely available, the Cuban policy, based on intensive HIV testing and tracing of partners, may be considered as a possible policy to control HIV/AIDS epidemics in other countries.

The HIV/AIDS epidemic in Cuba: description and tentative explanation of its low HIV prevalence

Background: The Cuban HIV/AIDS epidemic has the lowest prevalence rate of the Caribbean region. The objective of this paper is to give an overview of the HIV/AIDS epidemic in Cuba and to explore the reasons for this low prevalence. Methods: Data were obtained from the Cuban HIV/AIDS programme established in 1983. This programme has an extensive adult HIV testing policy, including testing of all pregnant women. HIV and AIDS cases have been recorded since 1986. Persons found to be HIV-positive are interviewed on their sexual behaviour and partners. Tracing and voluntary testing of these partners are organised. Epidemiological description of this epidemic was obtained from analysis of this data set. Using elementary mathematical analyses, we estimated the coverage of the detection system (percentage of HIV-positive adults detected) and the average period between HIV infection and detection. Estimated HIV prevalence rates were corrected to account for the coverage.Results: HIV prevalence has increased since 1996. In 2005, the prevalence among pregnant women was 1.2 per 10,000 (16/137000). Estimated HIV prevalence among 15- to 49-year-olds was 8.1 per 10,000 (4913/6065000; 95percentCI: 7.9 per 10,000 8.3 per 10,000). Most (77percent) of the HIV-positive adults were men, most (85.1percent) of the detected HIV-positive men were reported as having sex with men (MSM), and most of the HIV-positive women reported having had sex with MSM. The average period between HIV infection and detection was estimated to be 2.1 years (IQR = 1.7 2.2 years). We estimated that, for the year 2005, 79.6percent (IQR: 77.3 81.4percent) of the HIV-positive persons were detected. Conclusion:MSM drive the HIV epidemic in Cuba. The extensive HIV testing policy may be an important factor in explaining the low HIV prevalence. To reduce the HIV epidemic in Cuba, the epidemic among MSM should be addressed......(AU)