Probabilistic Inversion in Priority Setting of Food Borne Pathogens. Ángela Patricia Vargas Galindo. Supervisor: Prof. Roger Cooke - PDF

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Probabilistic Inversion in Priority Setting of Food Borne Pathogens Ángela Patricia Vargas Galindo Supervisor: Prof. Roger Cooke Delft University of Technology Department of Applied Mathematics and Risk

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Probabilistic Inversion in Priority Setting of Food Borne Pathogens Ángela Patricia Vargas Galindo Supervisor: Prof. Roger Cooke Delft University of Technology Department of Applied Mathematics and Risk Analysis Table of Contents CHAPTER 1: INTRODUCTION... 1 CHAPTER 2: PROBLEM DESCRIPTION AND STATE OF THE ART... 3 CHAPTER 3: EXPERT JUDGEMENT... 8 Calibration... 8 Information CHAPTER 4: PROBABILISTIC INVERSION PROBABILISTIC INVERSION Iterative Proportional Fitting IPF CHAPTER 5: MODELS The Experts The Elicitation Methodology Sample Distributions CHAPTER 6: RESULTS CHAPTER 7: PAIRED COMPARISONS CHAPTER 8: EXPERIMENT WITH PAIRED COMPARISONS CHAPTER 9: CONCLUSIONS AND RECOMMENDATIONS APPENDIX A: RESULTS PATHWAYS FOOD CATEGORIES APPENDIX B APPENDIX C BIBLIOGRAPHY i Tables Table Table Table Table 4. Minimum and maximum values of Ui using the uniform distribution for 5 variables Table 5. Minimum and maximum values variables Ui using the uniform distribution for 11 variables Table 6. Values for the parameter of the gamma distribution Table Table 8. Comparison of the quantiles for the Decision Maker distribution Table Table Table 11 Bradley and Terry results for pathways Table 12 Bradley and Terry results for food categories Table 13 Bradley and Terry results for pathways filtering Table 14. s for the trial exercise - Pathways Table 15. s for the trial exercise Food Categories ii Figures Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 10: Cobweb plot of 200 samples using uniform distribution for 11 variables. 24 Figure 11: Cobweb plot of 200 samples using uniform distribution for 11 variables 24 Figure Figure Figure iii Acknowledgment This document reflects not only the work of the author but also the effort of many people related to this project. I am very thankful to Dr. Arie Havelaar for the trust and time he dedicated to this project. I want to thank my supervisor Prof. Roger Cooke for all his contributions, suggestions and support throughout the project. My thanks are also to Rabin Neslo for the design and construction of the website for the data recollection and for Patrycja Jesionek s help in the first stages of the project. Finally I would like to express my gratitude to all the who participated in this exercise. During the past two years I have learned a lot; about mathematics, life and myself. I want to thank all the people who helped in this learning process. I will always be thankful to Dr. Roger Cooke and Dr. Dorota Kurowicka for always being open to hear my problems and worries, to Sandra and Oswaldo for being a great support and offering their friendship and finally to all my classmates: I couldnot ask for better group, thanks for you help and patience, especially to Wiktoria Ławniczak, Marcin Glegola and Carlos Gonzalez. My special thanks to David García, who was my everyday encouragement and companion in small and big crisis. Finally, to my parents who supported me all the way through. iv CHAPTER 1: INTRODUCTION Food safety is a growing concern in world s health. All population is at risk of getting a food borne illness. Both developed and developing countries have multiple cases of deaths due to food poisoning. According to the World Health Organization during year 2000, 2.1 million people died from diarrhea diseases from which a large proportion can be related with contamination of food borne illnesses As an example of developed countries, each year in the United States there are approximately 76 million cases of food borne illnesses, from which 325,000 are hospitalized and 5,000 die. In developing countries there is a bigger diversity of food borne diseases and the cases are often not reported. Additionally to single cases there are food borne diseases outbreaks, which often create huge health crisis. In September 2006 one deceased and 113 ill Americans were the victims of an outbreak of E. coli affecting 21 states; apparently the source of the bacteria was fresh spinach from infected by manure from a California cattle ranch near spinach fields. In the Netherlands, there are between 300,000 and 700,000 cases of gastroenteritis and between 20 and 200 deaths caused by food borne infections, each year. (Knaap, et al. 2006) Infections diseases may be far from being number one cause of death, but for the elderly, infant population, pregnant women and the HIV/AIDS persons, this type of disease is one of the most dangerous, since their immune system is especially vulnerable. For instance, malnutrition affects 100 million young children and pregnant women, which weakens their immune system making more vulnerable to pathogens and infections. The transmission of infections diseases is related to various pathogens, agents which cause a disease or illness. Pathogens can be bacteria, viruses or parasites among other. However pathogens like Salmonella and E. coli are not exclusively transmitted by food. Transmission can also be possible by animal contact, having contact with an ill person or even by air. The National Institute for Public Health and the Environment (RIVM) is an organization dedicated to do research and modeling in health, nutrition and environmental protection. In the Netherlands, RIVM, is responsible for studying food safety issues. According to RIVM, it is important to focus on the most relevant pathogens in order to control, prevent and monitor the behavior of these illnesses effectively. In a previous study, RIVM calculated the disease burden and costs for a set of pathogens. However it is needed to have a more detailed study in order to 1 develop preventive measures and policies meaning that, it is very valuable to have desegregated data regarding the origin of the pathogen and how transmission takes place. The aim of this project is to determine the fraction of transmission route for each pathogen included in the study and the fraction transmission due to specific food groups, within the cases caused by food ingestion. The objective is to find a fast, not resource intensive and accurate method of estimation for these fractions. The present document is organized as follows: Chapter two includes a brief explanation of the content of previous RIVM documents and state of the art. Chapter three and four include an explanation of the mathematical tools used in this study. Chapter five describes the methodology used to apply Probabilistic Inversion as well as an explanation the data, the and the models used. Conclusions and recommendations are contained in chapter six. Finally, a detailed description of the results is included in the appendix. 2 CHAPTER 2: 2 : PROBLEM DESCRIPTION AND STATE OF THE ART The criteria often used to determine the relative importance of food borne illnesses include: disease burden, social cost, trends, response, perception, exposure, infectivity, incidence, severity, preventability potential, potential hazard, potential exposure, number of hospitalizations, number of deaths, response, and infectivity. (Kemmeren, et al. 2006) In 2006, RIVM published the document Priority Setting of Foodborne Pathogens. This document is intended to be a tool for decision makers to establish priorities over the main pathogens that affect public health in the Netherlands in order to be able to control, prevent and supervise the situation. Scientists involved in the development of this document believe that in order to have effective policies, is essential to determine which are the pathogens that create more damage to society. The prior study included the following seven pathogens: Thermophilic Campylobacter spp. Shinga-toxin producing Escherichia coli O157, Salmonella spp. Norovirus, Listeria Monocytogenes and Toxoplasma Gondii. The pathogens are compared using the following criteria: - Disease Burden - Cost of illness - Food attributable fraction - Trends - Involved food products - Perception The Disease Burden is an index calculated to measure the impact of an illness in the patients life and it is calculated using a population of patients. It is measured using the Disability Adjusted Life Year (DALY) and it depends on Years of Life Lost due to mortality (YLL) and the number of Years Lived with a Disability (YLD), which includes a weight that depends on the severity of the disability. The Cost of Illness is calculated based on the Direct Health care Costs (DHC ) and the Direct Non-health care Costs (DNHC) and the Indirect Non-health Costs (INHC). The Cost of illness includes evaluation of doctors, hospitalization, medication, rehabilitation, travel costs, diapers as well as the value of production lost to society due to the illness due to temporary, long term or permanent absence of work. Notice that the discussion and conclusions of the previous study do not give information about the routes of infection; in fact the cases related with food ingestion can not be compared to the cases of illnesses transmitted abroad or by animal 3 contact. Being able to identify the possible contamination routes allow the decision maker to go deeper and construct better and more accurate policies providing more effort and recourses in specific areas. The aim of this project is to determine the fraction of the total health burden and cost that can be attributable to each of the possible contamination pathways, and within the food ingestion cases, the fraction for each food category. Notice that this fraction can be understood as the probability of transmission of certain disease by a specific route or ingestion of a particular food type. Both, the pathways and the food categories are collectively exhaustive and mutually exclusive. In the case of the pathways, contamination does not take place through a different route than the ones defined in Table 1. Additionally, contamination occurs through one of the pathways but not through more than one pathway simultaneously. Similarly, cases due to food ingestion are originated by one and only one of the food categories described in Table 2. In general, pathogens may be transmitted by contaminated food, water, soil, air, contact with a sick person, and contact with a contaminated animal. The exposure pathways are defined in five groups as follows; the name and explanation can be found in Table 1. The last pathway is defined because of the nature of the study. In fact the causes of transmission abroad are the same that inside The Netherlands, but for policy-making it is important to know what proportion of the illnesses are effect of other countries sanitary problems. Pathways Food borne Environmental Human-human Direct animal Traveling Figure 1 4 Transmission through food that is contaminated when it enters the Food borne kitchen or during preparation (e.g. by food handlers). Transmission through contaminated water (drinking water, Environmental recreational water), soil, air or other environmental media (fomites*). Human-human Transmission from person to person by the fecal-oral route. Transmission by direct contact with live animals including pets, Direct animal farm animals, petting zoos etc. Cases when exposure takes place by any of the above pathways Abroad during foreign travel. * Inanimate objects or substances capable of absorbing, retaining, and transporting contagious or infectious organisms Table 1 Additionally, it is possible to make a finer estimate of the fraction of the pathogens due to specific food products. Having these fractions allows the decision makers to pay special attention to the more dangerous food industries when fighting against and controlling outbreaks of a certain pathogen. For this purpose, the food categories in Table 2 were defined. Other foods incl. composite foods Food Handlers Bread, grains, pastas and bakery products Beef and lamb Beverages Food Categories Pork Fruit and vegetables Chicken and other poultry Fish and shellfish Dairy products Figure 2 Eggs 5 Beef and lamb Pork Chicken and other poultry Eggs Dairy products Fish and shellfish ruit and vegetables Beverages Bread, grains, pastas and bakery products Other foods incl. composite foods Beef, veal, lamb and mutton. Includes processed and non-processed beef products (sausages, filet américain, hamburgers etc.). Includes processed and non-processed pork products (susages, luncheon meats etc.). Includes duck, goose, ostrich and turkey. Includes processed and non-processed poultry products (chicken wings, marinated chicken, confits etc.) Including egg products Milk, cheese, butter, cream etc. Includes all finfish, shellfish (mussels, oysters, etc.) and crustaceans (lobster, shrimps etc.). Includes (mixtures of) vegetables that are consumed raw or cooked. Includes all non-alcoholic and alcoholic beverages, except milk. Includes pastries Includes all categories not listed above (e.g. nuts, oils, confectionery, spices) and all foods that are sold to the consumer as a composite of two or more of the above categories (e.g. pizzas, lasagna, nasi-goreng, sandwiches). Infected humans or animals Includes food handlers, vermin, pets etc. * Contamination is assigned to the food category (or other vehicle) as it enters the kitchen. Defined by Arie Havelaar et al Table 2 It is expected that by the end of this project, it would be possible to have a fraction of the cases due to the different pathways and the food categories for a given pathogen. The pathogens included are listed in Table 3. The sum of the fractions of the five pathways as well as the sum of the eleven food categories will be equal to one because of the assumptions that these are the only possible pathways and food categories respectively. 6 Campylobacter spp. STEC O157 Non-O157 STEC Listeria monocytogenes Mycobacterium avium Salmonella spp. Bacillus cereus toxin Clostridium perfringens toxin Staphylococcus aureus toxin Enterovirus Hepatitis A virus Hepatitis E virus Norovirus Rotavirus Cryptosporidium parvum Giardia lamblia Toxoplasma gondii Table 3 7 CHAPTER 3: 3 EXPERT JUDGEMENT In general, statistical data is an important base to build forecast, calculate estimates or support decisions. Unfortunately it is common to find real life examples where data is not always available and complete. One possible solution to this situation is Expert Judgment. Expert Judgment is a methodology to obtain information from people who know about a certain subject, instead of drawing conclusions from data. The idea of behind this tool is to rely on knowledge and understanding of a particular subject to substitute the missing information. One of the final objectives of Expert Judgment is to reach rational consensus among a group of. (Cooke, 1991). The Classical Method for Expert Judgment is a methodology to process data given by in order to reach a rational conclusion. Experts are supposed to provide their assessments through an elicitation giving quantiles from the unknown distribution of variables under study; are usually asked to give the 5%, 50% and 95%. The data collected is used to build a probability distribution that represents the uncertainty and the knowledge that the group of collectively has. This distribution is called the Decision Maker () distribution. In order to understand how the Decision Maker distribution is constructed is important to make a distinction among the elicitated variables. Along with the variables for which there is not data, there are a set of variables for which the true value is available for the analyst. Knowing the value of these variables enables to score the assessments with respect to calibration and information. (Cooke and Bedford, 2001). Actually, the classical model is a weighted average model, where the weights are calculated based on the calibration and information scores. Basically, the weights are used to combine expert distributions according to their performance. Intuitively, the that made better assessments regarding the seed variables will have more influence in the Decision Maker distribution. Calibration Calibration is a measure for statistical likelihood. An expert will have a good calibration score if he or she gives quantiles such that 5% of the realizations are less than the 5% quantile, 45% of the realizations are between the 5% and 50% quantiles, and so on. The idea is to measure how similar the empirical distribution and the uncertainty distribution are. See (Cooke, 1991). 8 The calibration score is a numerical value calculated for each of the participating. Assuming the usual scenario, where give 5%, 50% and 95% quantiles, there are going to be 4 inter quantile intervals. Vector p is defined such that p i denotes the probability that a realization of the variable falls in the corresponding inter quantile interval. According to the assumption, vector p would be equal to p = ( ). In general, if an expert is asked to give n quantiles, then p will have the corresponding probabilities of n + 1 inter quantile intevals. s = ( s s s s ) be the empirical probability vector which contains the relative Let frequencies that fall in the corresponding inter quantile inrevals. For example s 1 is equal to the number of realizations that are less than or equal to the 5% quantile, s 2 is equal to the number of realizations that are less than or equal to the 50% quantile and greater that the 5% quantiles divided by the total number of realizations. s 3 and s 4 are defined similarly. A well calibrated expert should give intervals for which vector s would be similar to vector p. The Relative Information I ( s; p ) is used to measure how similar or how close the two vectors are. 4 si I ( s; p) = si ln( ) p 1 The relative information is equal to 0 if and only if vector s is identical to vector p. This is of course the ideal scenario. A well calibrated expert will have a relative information score close to 0. Assume that there are N seed variable. For large numbers of N, then the distribution of the product of 2N and the relative information 2 N I ( s; p ), can be approximated by the Chi-square distribution with n degrees of freedom (3 for this case). (Bedford and Cooke, 2001). Usually, one realization is available for the seed variables. This value can be understood as an independent sample from the distribution with quantiles equal to the ones given by the expert. Finally, the calibration score is defined as follows ( N I ( s p) ) C =. 2 1 χn 2 ; i 9 2 Where χ n is the cumulative distribution of the Chi-square with n degrees of freedom. Then considering N seed variables, the calibration score is an approximation of the probability of a having a Relative Information less than or equal to I ( s; p ). A poor calibrated expert will have a calibration score close to 0. On the other hand, a perfectly calibrated expert will have a relative information to 0 which would lead to a calibration score of 1. Doing a comparison with hypothesis testing, it is possible to define the hypothesis that expert s assessments are accurate. Then the calibration score can interpreted as the p-value at which this hypothesis would be rejected. Information Intuitively, an expert that gives quantiles with a very broad inter quantile interval is less informative than one that is given narrow intervals. This idea is formalized using the information score which can be interpreted as a measure of the degree to which the distribution is concentrated (Cooke and Goossens, 2000). Information is measured with respect to a background measure; the uniform and log-uniform distributions are commonly used. The background measure is the either the uniform of log-uniform distribution over an intrinsic range for each variable which is defined as smallest interval that contains all quantiles given by plus a k% overshoot. Even though the value of k is chosen by the analyst, the default value is 10. Note that the relative information with respect to a background measure is measured for both, the variables of interest and the seed variables; the information score does not depend on the value of the true realizations of the seed
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