Makita, K.

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Participatory risk assessment II - Risk modelling I -  ‘Learning Event’ on risk analysis and participatory methods CSRS, November 28, 2014 Kohei Makita Associate Professor of Veterinary Epidemiology at Rakuno Gakuen University (OIE Joint Collaborating Centre for Food Safety) Joint Appointment Veterinary Epidemiologist at International Livestock Research Institute (ILRI) Outline • Stochastic processes • Exposure assessment – Fault tree – Value chain – Mixture, separation, growth and inactivation • Hazard characterization – Dose-response 2 Bayesian inference 3 Prior belief Learning from  observations Current knowledge )( )|( Xl )|( Xf Prior distribution Likelihood function Posterior distribution Beta (23,59) Beta (2,29) Beta (25,88) Bayesian inference 4 )()|()()|()|(1jnjjiiiAPABPAPABPBAPBayes’ Theorem dXlXlXf)|()()|()()|(Bayes’ Theorem expressed in a different way The denominator normalizes the Posterior  distribution to have a total area equal to one. Bayesian inference 5 )()|()()|()|(1jnjjiiiAPABPAPABPBAPBayes’ Theorem dXlXlXf)|()()|()()|(Bayes’ Theorem expressed in a different way So, )|()()|(  XlXf Likelihood function Prior distribution Posterior distribution Stochastic processes • Systems of countable events • There are three fundamental stochastic processes – Binomial process – Poisson process – Hypergeometric process  6 Binomial ProcessPoisson Process Hypergeometric ProcessNumber oftrials n(NegBin)Number ofsuccesses s(Binomial)Probability ofsuccess p(Beta)Exposure 'time't (Gamma)Number ofobservations (Poisson)Mean numberof events perunit time (Gamma)Number oftrials n(InvHypergeo)Number ofsuccesses s(Hypergeo)Population M,Sub-population D(...)Binomial process • A random counting system where there are; –n independent identical trials  – each one of which has the same probability of success p – which produces s successes from n trials 7 Number oftrials n(NegBin)Number ofsuccesses s(Binomial)Probability ofsuccess p(Beta)Binomial process Distributions for the binomial process • s = Binomial(n,p) • n = s + Negbin(s,p) if we know trials stopped in the sth success • n = s + Negbin(s+1,p) if don’t know trials stopped in the sth success • p = Beta(s+1,n-s+1) for a Uniform(0,1) prior • p = Beta(s+a, n-s+b) for a Beta(a, b) prior  – and Negbin(1,p) = Geomet(p) – Binomial(1,p) = Bernoulli (p) Exercise for Binomial process Now start your @Risk 1. 3% of salad in a local restaurant in area A is known to be contaminated with Cryptosporidium parvum. When you sample 50 salads, how many of them are contaminated with C. parvum?  2. In the area B, a survey on prevalence of C. parvum in salad was conducted. Out of 156 samples, 5 were contaminated. What is the prevalence? 3. The probability of attending hospital if infected with C. parvum is 80%. We observed 53 patients who visited hospital and diagnosed with C. parvum infection in the outbreak last month. How many people were infected? 9 Poisson process Binomial ProcessPoisson Process Hypergeometric ProcessNumber oftrials n(NegBin)Number ofsuccesses s(Binomial)Probability ofsuccess p(Beta)Exposure 'time't (Gamma)Number ofobservations (Poisson)Mean numberof events perunit time (Gamma)Number oftrials n(InvHypergeo)Number ofsuccesses s(Hypergeo)Population M,Sub-population D(...)Back to the map… Poisson process • There is a continuous and constant opportunity for an event to occur- this is explained by; – the number of events that may occur in a period t – the amount of “time” one will have to wait to observe α events – the average number of events that could occur, λ  11 Exposure 'time't (Gamma)Number ofobservations (Poisson)Mean numberof events perunit time (Gamma)Poisson process Distributions for the Poisson process •  = Poisson(*t)   P(=0) = Exp(-t)   • t = Gamma(, b)   b = 1/(Average time between events) i.e. how much time until the next AI outbreak  •  = Gamma(, 1/t)   with a ()  1/ prior     and Gamma(1, b) = Expon(b)  Exercise • Food poisoning was reported in a village A for 40 times last 5 years. If food poisoning occurs regardless the season (a constant risk),  – how many outbreaks would be observed in the next three months? – how many months does it take to have the next outbreak since last one (suppose we had an outbreak yesterday)? • If a bulk of raw milk contains 4 cfu/l of E. coli O157:H7,  – how much milk can you drink before you ingest one E. coli? – what is the probability that you ingest at least one E. coli if you drink 300ml of the milk?  13 Hypergeometric process Binomial ProcessPoisson Process Hypergeometric ProcessNumber oftrials n(NegBin)Number ofsuccesses s(Binomial)Probability ofsuccess p(Beta)Exposure 'time't (Gamma)Number ofobservations (Poisson)Mean numberof events perunit time (Gamma)Number oftrials n(InvHypergeo)Number ofsuccesses s(Hypergeo)Population M,Sub-population D(...)Back to the map… 14 Hypergeometric process • When the population is not very large compared to the sample (population < 10 x sample size) • Out of a group of M individual items, D have a certain characteristic. Randomly picking n items from this group without replacement, where each of the M items has the same probability of being selected, is a hypergeometric process. 15 Number oftrials n(NegBin)Number ofsuccesses s(Binomial)Probability ofsuccess p(Beta)Number oftrials n(InvHypergeo)Number ofsuccesses s(Hypergeo)Population M,Sub-population D(...)Hypergeometric process The hypergeometric format  M (total population)D (infected)n (selected)s =number infected from selectionExamples: •Sampling sheep from an infected flock •Sampling food from a consignment •Defective items in a consignment •Capture-release-recapture surveys 16 Hypergeometric process Distributions for the hypergeometric process • s = Hypergeo(n, D, M)  • n = s + InvHypgeo(s, D, M)  • D, M have no standard distributions – Have to be worked out manually (see problems)  17 Exercise • In an informal market, Mrs A is selling 100 eggs of which 10 are contaminated with Salmonella. You purchased 5 eggs from Mrs A. How many contaminated eggs are included? 18 Outline • Stochastic processes • Exposure assessment – Fault tree – Value chain – Mixture, separation, growth and inactivation • Hazard characterization – Dose-response 19 Fault tree • Fault tree is a systematic method for acquiring information about a system 20 Source: NASA. 2002. Fault tree hand book  with aerospace applications.  Points of fault tree analysis in food safety • How the illness can occur 21 Onset of  illness Preceded by Infection Ingestion Purchase Production Preceded by Preceded by Or Direction of identification and diagraming 22 Illness due to Staphylococcal poisoning due to milk consumption A consumer is susceptible to SAET SA multiply to reach enough cfu producing ET Milk contains SA Milk contains SA at production Milk contaminated with SA By traders/handlers Milk shed by SA Mastitis cow Milk contaminated by a farmer Infected cow Human source Human source AND OR Initiating event Risk assessment for staphylococcal poisoning through consumption of informally-marketed milk in Debre Zeit, Ethiopia  Makita K, Dessisa F et al. (2011) International Journal of Food Microbiology Outline • Stochastic processes • Exposure assessment – Fault tree – Value chain – Mixture, separation, growth and inactivation • Hazard characterization – Dose-response 23 Value chain A producer A consumer 24 Value chain Producers Consumers Middle men 25 Designing a study based on fault tree • Design a study to collect information on the ‘Nodes’ identified in fault tree analysis • ‘Nodes’ are similar to Critical Control Points (CCPs) in HACCP • It usually include below segments   • In informal markets, marketing systems are sometimes not ‘linear’, which means unpredictable • So combination of below techniques are useful – Rapid rural appraisal – Probabilistic survey using questionnaires – Tracing back, tracing forward  26 Consumer Retail shop Middle men Producer Categorizing actors 27 • Retail shops or middle men can be categorized even further • In terms of risk modeling, it is important to have separate ‘branches’ to predict behavior more precisely • Examples are shown in the next slide Actors in informal milk sales in Kampala, Uganda • Plus milk retail shop without refrigerator and dairy farmers selling at farms Shop with a bulk cooler Shop with a small refrigerator Boiling centre Trader with cans on a bicycle Roadside vendor Roadside vendor 28 Probabilistic survey 29 • Random selection of either small administrative units or shops or farmers in a probabilistic manner • Collect quantitative information (e.g. number of shops, farmers, quantity of sales) • Divide the quantity with sampling fraction in order to estimate the total amounts of sales in the study area Probabilistic survey 30 Fig.1. Map of Kampala showing the locations of 48 urban LC1s studied.  Areas highlighted are peri-urban parishes. Source: Makita K. (2009). PhD Thesis.  The University of Edinburgh Field survey – Importance of diagnostic tests My bitter experience in Campylobacter risk assessment…  Nyama-choma in Tanzania <1st survey for prevalence> High prevalence using culture without rigorous identification <2nd survey for MPN> Low prevalence using PCR after culturing Tracing forward and/or backward 32 • Wholesale shops, abattoirs and markets identified in RRAs and interviews need to be trucked in order to complete the value chains • Interviews at such ‘hubs’ will give you the information on the chains after the ‘hubs’ • Tracking will fill the ‘gaps’ of quantitative information of sales Tracing forward and/or backward 33 Fig. 2. Spatial distributions of wholesale milk shop centres and milk boiling centres in Kampala  Source: Makita K. (2009). PhD Thesis.  The University of Edinburgh Tracing forward and/or backward 34 Fig. 3. Spatial distributions of milk shops with a bulk cooler.  Source: Makita K. (2009). PhD Thesis.  The University of Edinburgh Tracing forward and/or backward 35 Fig. 4. Spatial distributions of fresh milk shops with a small refrigerator Source: Makita K. (2009). PhD Thesis.  The University of Edinburgh 36 Quantitative dairy value chain in Kampala, Uganda Source: Makita K. et al. (2010). How human brucellosis incidence in urban Kampala can be reduced most efficiently? A stochastic risk assessment of informally-marketed milk. PLoS ONE 5 (12): e14188. 37 Dairy value chain- RRA and interviews Makita K, Dessisa F et al. (2011) International Journal of Food Microbiology Outline • Stochastic processes • Exposure assessment – Fault tree – Value chain – Mixture, separation, growth and inactivation • Hazard characterization – Dose-response 38 Modular Process Risk Model Microbial processes •Growth •Inactivation  Food handling processes •Mixing •Partitioning •Cutting •Cross-contamination 39 Separation • Separation in a value chain refers to sales to more than two customers 40 Bulk tank in a milk collection centre Traders with a bicycle Sales to customers Mixing • Mixing in a value chain refers to receiving from more than two sources 41 Bulk tank in a milk collection centre Urban smallholder dairy farmers Peri-urban commercial dairy farmers Inactivation • Inactivation in a value chain usually refers to heat treatment to kill pathogens (note: heat cannot inactivate heat-resistant toxins) 42 Milk sales to individual houses Raw milk from District A Raw milk from District B A boiling center in a town Wholesaler milk shops Milk sales to individual houses Bacterial growth 43 Mathematical modeling of growth • Several models exist – Logistic model – Michaelis-Menten model – Modified Gompertz model (Gibson et al., 1987) – Baranyi model (Baranyi and Roberts, 1994) – Modified logistic model (Fujikawa et al., 2003) • Several factors affect on bacteria growth- careful choice from literature is required – Temperature – pH – Water activity (aW) – Salinity 44 45 Contamination- a survey Isolation of  S aureus Boiling before sales Milk collection centre (n=25) 18 (70.4%) 0 Dairy farm (n=170) 74 (43.6%) 0 Example: Boil milk before consumption Percentage Dairy farming households (n=170) 116 68.2 Consumers (n=25) 16 64.0 Risk mitigation by consumers -participatory and interviews Example: 46 Cfu/ml Hour Stationary phase Exponential growth phase Lag phase Fujikawa and Morozumi (2006) modified logistic model Example Growth of Staphylococcus aureus in milk • Mathematical model of S. aureus growth in milk – Modified logistic model reported by Fujikawa and Morozumi (2006) – Experts say it also applies to meats 47 })min(1){max1( cNNNNrNdtdNWhere N is population of a microorganism at time t              r is rate constant or maximum specific rate of growth              Nmin is minimum cell concentration and set as slightly lower value than initial              concentration N0              Nmax is maximum concentration at stationary phase: 108.5 cfu/ml              c is an adjustment factor – variability of growth speed: 4.7±1.1              r0.5 = 0.0442T - 0.239              Where T is temperature in Celsius Modeling growth in @Risk 48 Time(h) Log N r dN/dt 0 0.35916 0.234521 2.684E-06 1 0.35916 0.234521 5.837E-06 2 0.359162 0.234521 1.269E-05 3 0.359164 0.234521 2.759E-05 4 0.359169 0.409327 0.000104 5 0.359189 0.409327 0.000319 6 0.35925 0.409327 0.000973 7 0.359434 0.409327 0.002964 8 0.359997 0.409327 0.009008 9 0.361701 0.409327 0.027184 10 0.366805 0.409327 0.080358 Time(h) Log N (D15) r (E15) dN/dt (F15) 0 =N0 =(0.0442*T-0.239)^2 =E16*10^(D16)*(1-10^(D16)/10^(Nmax))*(1-(Nmin/10^(D16))^c) 1 =LOG10(10^(D16)+F16) =(0.0442*T-0.239)^2 =E17*10^(D17)*(1-10^(D17)/10^(Nmax))*(1-(Nmin/10^(D17))^c) 2 =LOG10(10^(D17)+F17) =(0.0442*T-0.239)^2 =E18*10^(D18)*(1-10^(D18)/10^(Nmax))*(1-(Nmin/10^(D18))^c) 3 =LOG10(10^(D18)+F18) =(0.0442*T-0.239)^2 =E19*10^(D19)*(1-10^(D19)/10^(Nmax))*(1-(Nmin/10^(D19))^c) 49 Risk mitigation by traditional milk fermentation- Modeling using reported data (Gonfa et al., 1999) Bacteria growth stops at pH 4.9 1/pH=0.002 t (h)+1.187 (df=3, r2=0.90, p=0.009) Source: Makita et al., 2012  Int. J. Food Microbiol. 50 Stop of growth of S. aureus in milk by low pH (h) Stop of bacterial growth due to milk fermentation Outline • Stochastic processes • Exposure assessment – Fault tree – Value chain – Mixture, separation, growth and inactivation • Hazard characterization – Dose-response 51 Overview • Here we learn how to model the probability of infection/illness based on how much a person ingests pathogens • We learn different types of model • Later we work on an example of campylobacteriosis Ingestion of  pathogen/toxin Infection Illness Death Illness Death The four most common no-threshold DR models D-R model Dose measure P(effect) Exponential  Mean dose  )exp(1 p  Beta-Poisson Mean dose  b 11  Beta-binomial Actual dose D (  ( (  ( bbbbDD1  Weibull-gamma Actual dose D bbD11   53 Microbiology Dose-Response Data set for infection Black RE et al (1988), Experimental Campylobacter jejuni infections in humans. J infectious Diseases, 157(3), 472-479. Example Applications: C. jejuni Mean dose Tested Infected 8x102 10 5 8x103 10 6 9x104 13 11 8x105 11 8 1x106 19 15 1x108 5 5 0%10%20%30%40%50%60%70%80%90%100%1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08Mean doseObserved fraction infected54 Microbiology Dose-Response Beta-Poisson model. MLE fit has  = 0.145, b = 7.589  Example Applications: C. jejuni Mean dose Infected/Tested B-P MLE probability 8x102 5/10 49% 8x103 6/10 64% 9x104 11/13 74% 8x105 8/11 81% 1x106 15/19 82% 1x108 5/5 91% 0%10%20%30%40%50%60%70%80%90%100%1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08Mean doseObserved fraction infected55 Questions?  Thank you for your efforts to catch up… 

Participatory risk assessment: Risk modelling: I

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Participatory risk assessment: Risk modelling: I

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