A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Epidemiological, social, diagnostic and economic evaluation of population screening for genital chlamydial infection

OBJECTIVES: To investigate epidemiological, social, diagnostic and economic aspects of chlamydia screening in non-genitourinary medicine settings. METHODS: Linked studies around a cross-sectional population-based survey of adult men and women invited to collect urine and (for women) vulvovaginal swab specimens at home and mail these to a laboratory for testing for Chlamydia trachomatis. Specimens were used in laboratory evaluations of an amplified enzyme immunoassay (PCE EIA) and two nucleic acid amplification tests [Cobas polymerase chain reaction (PCR), Becton Dickinson strand displacement amplification (SDA)]. Chlamydia-positive cases and two negative controls completed a risk factor questionnaire. Chlamydia-positive cases were invited into a randomised controlled trial of partner notification strategies. Samples of individuals testing negative completed psychological questionnaires before and after screening. In-depth interviews were conducted at all stages of screening. Chlamydia transmission and cost-effectiveness of screening were investigated in a transmission dynamic model. SETTING AND PARTICIPANTS: General population in the Bristol and Birmingham areas of England. In total, 19,773 women and men aged 16-39 years were randomly selected from 27 general practice lists. RESULTS: Screening invitations reached 73% (14,382/19,773). Uptake (4731 participants), weighted for sampling, was 39.5% (95% CI 37.7, 40.8%) in women and 29.5% (95% CI 28.0, 31.0%) in men aged 16-39 years. Chlamydia prevalence (219 positive results) in 16-24 year olds was 6.2% (95% CI 4.9, 7.8%) in women and 5.3% (95% CI 4.4, 6.3%) in men. The case-control study did not identify any additional factors that would help target screening. Screening did not adversely affect anxiety, depression or self-esteem. Participants welcomed the convenience and privacy of home-sampling. The relative sensitivity of PCR on male urine specimens was 100% (95% CI 89.1, 100%). The combined relative sensitivities of PCR and SDA using female urine and vulvovaginal swabs were 91.8% (86.1, 95.7, 134/146) and 97.3% (93.1, 99.2%, 142/146). A total of 140 people (74% of eligible) participated in the randomised trial. Compared with referral to a genitourinary medicine clinic, partner notification by practice nurses resulted in 12.4% (95% CI -3.7, 28.6%) more patients with at least one partner treated and 22.0% (95% CI 6.1, 37.8%) more patients with all partners treated. The health service and patients costs (2005 prices) of home-based postal chlamydia screening were 21.47 pounds (95% CI 19.91 pounds, 25.99) per screening invitation and 28.56 pounds (95% CI 22.10 pounds, 30.43) per accepted offer. Preliminary modelling found an incremental cost-effectiveness ratio (2003 prices) comparing screening men and women annually to no screening in the base case of 27,000 pounds/major outcome averted at 8 years. If estimated screening uptake and pelvic inflammatory disease incidence were increased, the cost-effectiveness ratio fell to 3700 pounds/major outcome averted. CONCLUSIONS: Proactive screening for chlamydia in women and men using home-collected specimens was feasible and acceptable. Chlamydia prevalence rates in men and women in the general population are similar. Nucleic acid amplification tests can be used on first-catch urine specimens and vulvovaginal swabs. The administrative costs of proactive screening were similar to those for opportunistic screening. Using empirical estimates of screening uptake and incidence of complications, screening was not cost-effective.

The potential effect of population development, smoking and antioxidant supplementation on the future epidemiology of age-related macular degeneration in Switzerland

BACKGROUND: Due to the predicted age shift of the population an increase in the number of patients with late AMD is expected. At present smoking represents the only modifiable risk factor. Supplementation of antioxidants in patients at risk is the sole effective pharmacological prevention. The aim of this study is to estimate the future epidemiological development of late AMD in Switzerland and to quantify the potential effects of smoking and antioxidants supplementation. METHODS: The modelling of the future development of late AMD cases in Switzerland was based on a meta-analysis of the published data on AMD-prevalence and on published Swiss population development scenarios until 2050. Three different scenarios were compared: low, mean and high. The late AMD cases caused by smoking were calculated using the "population attributable fraction" formula and data on the current smoking habits of the Swiss population. The number of potentially preventable cases was estimated using the data of the Age-Related Eye Disease Study (AREDS). RESULTS: According to the mean population development scenario, late AMD cases in Switzerland will rise from 37 200 cases in 2005 to 52 500 cases in 2020 and to 93 200 cases in 2050. Using the "low" and the "high" scenarios the late AMD cases may range from 49 500 to 56 000 in 2020 and from 73 700 to 118 400 in 2050, respectively. Smoking is responsible for approximately 7 % of all late AMD cases, i. e., 2600 cases in 2005, 3800 cases in 2020, 6600 cases in 2050 ("mean scenario"). With future antioxidant supplementation to all patients at risk another 3100 cases would be preventable until 2020 and possibly 23 500 cases until 2050. CONCLUSION: Due to age shift in the population a 2.5-fold increase in late AMD cases until 2050 is expected, representing a socioeconomic challenge. Cessation of smoking and supplementation of antioxidants to all patients at risk has the potential to reduce this number. Unfortunately, public awareness is low. These data may support health-care providers and public opinion leaders when developing public education and prevention strategies.

Multivariate modelling of responses to conditional items: New possibilities for latent class analysis

Questionnaire data may contain missing values because certain questions do not apply to all respondents. For instance, questions addressing particular attributes of a symptom, such as frequency, triggers or seasonality, are only applicable to those who have experienced the symptom, while for those who have not, responses to these items will be missing. This missing information does not fall into the category 'missing by design', rather the features of interest do not exist and cannot be measured regardless of survey design. Analysis of responses to such conditional items is therefore typically restricted to the subpopulation in which they apply. This article is concerned with joint multivariate modelling of responses to both unconditional and conditional items without restricting the analysis to this subpopulation. Such an approach is of interest when the distributions of both types of responses are thought to be determined by common parameters affecting the whole population. By integrating the conditional item structure into the model, inference can be based both on unconditional data from the entire population and on conditional data from subjects for whom they exist. This approach opens new possibilities for multivariate analysis of such data. We apply this approach to latent class modelling and provide an example using data on respiratory symptoms (wheeze and cough) in children. Conditional data structures such as that considered here are common in medical research settings and, although our focus is on latent class models, the approach can be applied to other multivariate models.

Effectiveness and cost-effectiveness of traditional and new partner notification technologies for curable sexually transmitted infections: observational study, systematic reviews and mathematical modelling

BACKGROUND Partner notification is essential to the comprehensive case management of sexually transmitted infections. Systematic reviews and mathematical modelling can be used to synthesise information about the effects of new interventions to enhance the outcomes of partner notification. OBJECTIVE To study the effectiveness and cost-effectiveness of traditional and new partner notification technologies for curable sexually transmitted infections (STIs). DESIGN Secondary data analysis of clinical audit data; systematic reviews of randomised controlled trials (MEDLINE, EMBASE and Cochrane Central Register of Controlled Trials) published from 1 January 1966 to 31 August 2012 and of studies of health-related quality of life (HRQL) [MEDLINE, EMBASE, ISI Web of Knowledge, NHS Economic Evaluation Database (NHS EED), Database of Abstracts of Reviews of Effects (DARE) and Health Technology Assessment (HTA)] published from 1 January 1980 to 31 December 2011; static models of clinical effectiveness and cost-effectiveness; and dynamic modelling studies to improve parameter estimation and examine effectiveness. SETTING General population and genitourinary medicine clinic attenders. PARTICIPANTS Heterosexual women and men. INTERVENTIONS Traditional partner notification by patient or provider referral, and new partner notification by expedited partner therapy (EPT) or its UK equivalent, accelerated partner therapy (APT). MAIN OUTCOME MEASURES Population prevalence; index case reinfection; and partners treated per index case. RESULTS Enhanced partner therapy reduced reinfection in index cases with curable STIs more than simple patient referral [risk ratio (RR) 0.71; 95% confidence interval (CI) 0.56 to 0.89]. There are no randomised trials of APT. The median number of partners treated for chlamydia per index case in UK clinics was 0.60. The number of partners needed to treat to interrupt transmission of chlamydia was lower for casual than for regular partners. In dynamic model simulations, > 10% of partners are chlamydia positive with look-back periods of up to 18 months. In the presence of a chlamydia screening programme that reduces population prevalence, treatment of current partners achieves most of the additional reduction in prevalence attributable to partner notification. Dynamic model simulations show that cotesting and treatment for chlamydia and gonorrhoea reduce the prevalence of both STIs. APT has a limited additional effect on prevalence but reduces the rate of index case reinfection. Published quality-adjusted life-year (QALY) weights were of insufficient quality to be used in a cost-effectiveness study of partner notification in this project. Using an intermediate outcome of cost per infection diagnosed, doubling the efficacy of partner notification from 0.4 to 0.8 partners treated per index case was more cost-effective than increasing chlamydia screening coverage. CONCLUSIONS There is evidence to support the improved clinical effectiveness of EPT in reducing index case reinfection. In a general heterosexual population, partner notification identifies new infected cases but the impact on chlamydia prevalence is limited. Partner notification to notify casual partners might have a greater impact than for regular partners in genitourinary clinic populations. Recommendations for future research are (1) to conduct randomised controlled trials using biological outcomes of the effectiveness of APT and of methods to increase testing for human immunodeficiency virus (HIV) and STIs after APT; (2) collection of HRQL data should be a priority to determine QALYs associated with the sequelae of curable STIs; and (3) standardised parameter sets for curable STIs should be developed for mathematical models of STI transmission that are used for policy-making. FUNDING The National Institute for Health Research Health Technology Assessment programme.

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Application of a computational model for complex fluvial ecosystems: The population dynamics of zebra mussel Dreissena polymorpha as a case study

The potential and adaptive flexibility of population dynamic P-systems (PDP) to study population dynamics suggests that they may be suitable for modelling complex fluvial ecosystems, characterized by a composition of dynamic habitats with many variables that interact simultaneously. Using as a model a reservoir occupied by the zebra mussel Dreissena polymorpha, we designed a computational model based on P systems to study the population dynamics of larvae, in order to evaluate management actions to control or eradicate this invasive species. The population dynamics of this species was simulated under different scenarios ranging from the absence of water flow change to a weekly variation with different flow rates, to the actual hydrodynamic situation of an intermediate flow rate. Our results show that PDP models can be very useful tools to model complex, partially desynchronized, processes that work in parallel. This allows the study of complex hydroecological processes such as the one presented, where reproductive cycles, temperature and water dynamics are involved in the desynchronization of the population dynamics both, within areas and among them. The results obtained may be useful in the management of other reservoirs with similar hydrodynamic situations in which the presence of this invasive species has been documented.

Evaluating the surveillance for swine dysentery and progressive atrophic Rhinitis in closed multiplier herds using Scenario tree modelling

Background: The Swiss pig population enjoys a favourable health situation. To further promote this, the Pig Health Service (PHS) conducts a surveillance program in affiliated herds: closed multiplier herds with the highest PHS-health and hygiene status have to be free from swine dysentery and progressive atrophic rhinitis and are clinically examined four times a year, including laboratory testing. Besides, four batches of pigs per year are fattened together with pigs from other herds and checked for typical symptoms (monitored fattening groups (MF)). While costly and laborious, little was known about the effectiveness of the surveillance to detect an infection in a herd. Therefore, the sensitivity of the surveillance for progressive atrophic rhinitis and swine dysentery at herd level was assessed using scenario tree modelling, a method well established at national level. Furthermore, its costs and the time until an infection would be detected were estimated, with the final aim of yielding suggestions how to optimize surveillance. Results: For swine dysentery, the median annual surveillance sensitivity was 96.7 %, mean time to detection 4.4 months, and total annual costs 1022.20 Euro/herd. The median component sensitivity of active sampling was between 62.5 and 77.0 %, that of a MF between 7.2 and 12.7 %. For progressive atrophic rhinitis, the median surveillance sensitivity was 99.4 %, mean time to detection 3.1 months and total annual costs 842.20 Euro. The median component sensitivity of active sampling was 81.7 %, that of a MF between 19.4 and 38.6 %. Conclusions: Results indicate that total sensitivity for both diseases is high, while time to detection could be a risk in herds with frequent pig trade. From all components, active sampling had the highest contribution to the surveillance sensitivity, whereas that of MF was very low. To increase efficiency, active sampling should be intensified (more animals sampled) and MF abandoned. This would significantly improve sensitivity and time to detection at comparable or lower costs. The method of scenario tree modelling proved useful to assess the efficiency of surveillance at herd level. Its versatility allows adjustment to all kinds of surveillance scenarios to optimize sensitivity, time to detection and/or costs.

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Bayesian models for the analysis of genetic structure when populations are correlated

Motivation: Population allele frequencies are correlated when populations have a shared history or when they exchange genes. Unfortunately, most models for allele frequency and inference about population structure ignore this correlation. Recent analytical results show that among populations, correlations can be very high, which could affect estimates of population genetic structure. In this study, we propose a mixture beta model to characterize the allele frequency distribution among populations. This formulation incorporates the correlation among populations as well as extending the model to data with different clusters of populations. Results: Using simulated data, we show that in general, the mixture model provides a good approximation of the among-population allele frequency distribution and a good estimate of correlation among populations. Results from fitting the mixture model to a dataset of genotypes at 377 autosomal microsatellite loci from human populations indicate high correlation among populations, which may not be appropriate to neglect. Traditional measures of population structure tend to over-estimate the amount of genetic differentiation when correlation is neglected. Inference is performed in a Bayesian framework.

A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

Territorial Intelligence of Vulnerability Systems 2- Sustainable Modelling of Globalization Challenge

Globalization as progress of economic development has increased population socioeconomical vulnerability when unequal wealth distribution within economic development process constitutes the main rule, with widening the gap between rich and poors by environmental pricing. Econological vulnerability is therefore increasing too, as dangerous substance and techniques should produce polluted effluents and industrial or climatic risk increasing (Woloszyn, Quenault, Faburel, 2012). To illustrate and model this process, we propose to introduce an analogical induction-model to describe both vulnerability situations and associated resilience procedures. At this aim, we first develop a well-known late 80?s model of socio-economic crack-up, known as 'Silent Weapons for Quiet Wars', which presents economics as a social extension of natural energy systems. This last, also named 'E-model', is constituted by three passive components, potential energy, kinetic energy, and energy dissipation, thus allowing economical data to be treated as a thermodynamical system. To extend this model to social and ecological sustainability pillars, we propose to built an extended E(Economic)-S(Social)-O(Organic) model, based on the three previous components, as an open model considering feedbacks as evolution sources. An applicative illustration of this model will then be described, through this summer's american severe drought event analysis

Territorial Intelligence of Vulnerability Systems 2- Sustainable Modelling of Globalization Challenge

Globalization as progress of economic development has increased population socioeconomical vulnerability when unequal wealth distribution within economic development process constitutes the main rule, with widening the gap between rich and poors by environmental pricing. Econological vulnerability is therefore increasing too, as dangerous substance and techniques should produce polluted effluents and industrial or climatic risk increasing (Woloszyn, Quenault, Faburel, 2012). To illustrate and model this process, we propose to introduce an analogical induction-model to describe both vulnerability situations and associated resilience procedures. At this aim, we first develop a well-known late 80?s model of socio-economic crack-up, known as 'Silent Weapons for Quiet Wars', which presents economics as a social extension of natural energy systems. This last, also named 'E-model', is constituted by three passive components, potential energy, kinetic energy, and energy dissipation, thus allowing economical data to be treated as a thermodynamical system. To extend this model to social and ecological sustainability pillars, we propose to built an extended E(Economic)-S(Social)-O(Organic) model, based on the three previous components, as an open model considering feedbacks as evolution sources. An applicative illustration of this model will then be described, through this summer's american severe drought event analysis

Territorial Intelligence of Vulnerability Systems 2- Sustainable Modelling of Globalization Challenge

Globalization as progress of economic development has increased population socioeconomical vulnerability when unequal wealth distribution within economic development process constitutes the main rule, with widening the gap between rich and poors by environmental pricing. Econological vulnerability is therefore increasing too, as dangerous substance and techniques should produce polluted effluents and industrial or climatic risk increasing (Woloszyn, Quenault, Faburel, 2012). To illustrate and model this process, we propose to introduce an analogical induction-model to describe both vulnerability situations and associated resilience procedures. At this aim, we first develop a well-known late 80?s model of socio-economic crack-up, known as 'Silent Weapons for Quiet Wars', which presents economics as a social extension of natural energy systems. This last, also named 'E-model', is constituted by three passive components, potential energy, kinetic energy, and energy dissipation, thus allowing economical data to be treated as a thermodynamical system. To extend this model to social and ecological sustainability pillars, we propose to built an extended E(Economic)-S(Social)-O(Organic) model, based on the three previous components, as an open model considering feedbacks as evolution sources. An applicative illustration of this model will then be described, through this summer's american severe drought event analysis