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@RISK'S ROLE IN BIOSECURITY: REDUCING DISEASE RISK WHEN DATA IS LIMITED C. I Walster BVMS MVPH MRCVS Background Increasing human population Static capture fisheries FAO – Aquaculture can supply protein Disease losses in aquaculture • $3 billion in 1997 • 40% of insured losses due to disease 2010 IABC – International Aquaculture Biosecurity Consortium WAVMA – World Aquatic Veterinary Medical Association Definitions Biosecurity Prevention, control and possible eradication of infectious diseases Disease Prevalence (p) The number of cases in a known population at an instance in time Test Sensitivity (Se) Test positive and truly disease positive Test Specificity (Sp) Test negative and truly disease negative Biosecurity Compliance Economics – it must be worth something, input < outcome Training – understand procedures Education – understand disease processes Responsibility – greater the stake increased compliance Biosecurity Formulae P(D-)= 1-P(D+) = 1- p P(A|B) = Basic Bayes Theorem Multiple Suppliers and Quarantine The probability that a supplier at level n in the supply chain will be free of infection is given by the formula: Pn = (Pn-1 + X(1 – Pn-1 ))S Pn = (0.95 + 0.5(1 – 0.95 ))4 = 0.9 with no control 0.81 Where Pn-1 is the probability that a supplier in the level below will be free of infection. X is the effectiveness of screening (e.g. testing or quarantine) S is the number of suppliers in the layer below. Pr of at least one (disease) event in an interval (of time) P(x≥ 1)= 1- Exp( ) No. of events that will occur in an interval t is Exp(-t)/β) . Pr. of at least one disease outbreak during the next 6 months given that the mean interval between disease outbreaks β is 24 months: P(x≥ 1)= 1- Exp( ) = 0.22 But Using @Risk x = the number of events that occur in interval (t) of space or time λ = average number of events per unit interval (t) β = the mean interval between events Figures in brackets were used to model the graphs Excel Function (@Risk) Function Value ≈ the mean Poisson Distribution Estimates No outbreaks per unit time or N o bacteria/cysts per unit volume X (number of events in time t) Mean (= t/β = 6/24 = 0.25) where t=6 months and β = 24 months Cumulative Note: This models the probability of the number of expected events (x) during time t where the mean interval between events is β 2 0.25 1 0 True =1 = cumulative probability (P of any events occurring between values 0 and x) TRUE 0.997838503 False = 0 = probability mass function (N o events occurring = x) FALSE 0.024337524 =POISSON.DIST(B10,B11,B12) =POISSON.DIST(B10,B11,C12) =RiskPoisson(B11,RiskName("Simulation Poisson(0.25){t/B}")) 0.00 Run Simulation Modeling Incubation Periods Inputs Minimum (a) Most Likely (b) Maximum (c) Calculated Values Mean (μ) Alpha 1 (α 1) 1 21 49 21.2649 12.75 Alpha 2 (α 2) Constrained Cell (Cell to Change) (ϒ = weight) Objective (Target) Cell (area under the curve) Equation for Pert mean = 17.45 28.2 0.900145 Solution Mean 21.2649 Alpha 1 12.75 Mean (μ) (@Risk Function) 22.33333 Pert (a, b, c) Alpha 2 Gamma Area 0.422185 Beta (α 1, α 2) 17.45 28.2 0.9 21.2649 Pert (a, b, c) using ϒ weight (28.2) or Mean (B6) ($B$2+$B$9*$B$3+$B$4)/($B$9+2) Formula for Alpha 1 (B7) (($B$6-$B$2)*(2*$B$3-$B$2-$B$4))/(($B$3-$B$6)*($B$4-$B$2)) Formula for Alpha 2 (B8) ($B$7*($B$4-$B$6))/($B$6-$B$2) B9 Value Either use Solver function in Excel or by trial and error Formula for B10 Risk Output () + BETA.DIST(28,$B$7,$B$8,1,$B$2,$B$4)-BETA.DIST(14,$B$7,$B$8,1,$B$2,$B$4)* Formula for I6 Risk Pert(B2,B3,B4) Formula for I8 Risk Beta(B7, B8) *Further enquiries refined this to "most chickens become infected between 14 and 28 days of age". This was interpreted as 90% of chickens being likely to become infected during this period. Solver Basic Sampling for Presence or Absence of Disease Review literature to obtain likely prevalence Considering initial prevalence at 50% maximises sample size/greatest confidence in any results regardless of actual/true prevalence. Decide confidence required (95%) Select testing regime. (www.oie.int). Use test Se & Sp if known. When multiple tests are used it is often safe to assume Sp is 100%. Sample size. Is dependent on prevalence, confidence level, test Se & Sp and population Use Freecalc (www.ausvet.co.au) Basic Sampling for Presence or Absence of Disease Decide on laboratory to use (in-house etc) www.aquavetmed.info. Collection of samples. Use OIE recommendations if available or record method used and ensure sample reflects the proportions of the whole population of interest (i.e. ALO or EU) and is random. Ensure sample is preserved correctly during transportation to the laboratory. Record all methodology and results (for future comparisons, transparency etc.). Risk based sampling for presence or absence of disease Assumes three things: There is no clustering (i.e. sampling at herd level) The Sp of the surveillance system is effectively one That the relative risk (RR) of the risk population is greater than 1. The advantage is it requires a smaller sample size so reducing cost. See Epitools Risk Based Surveillance for calculating sample size. Probability of Purchasing at Least One Infected Animal P(≥1 infected) = 1-(1-p)n P(≥1 infected) =1 – (1 – 0.02)100 = 0.87 or 87% Pr. all purchased animals are infected = pn = 0.02100 = very small! Pr. none of the purchased animals are infected = (1-p)n = (1-0.02)100 = 0.13 or 13% Using Freecalc Sample Size Freecalc Analysis The Information Curve A spreadsheet for a Bayesian inference simulation A spreadsheet for a Bayesian inference simulation Requires @Risk or equivelent software to run Number of iterations = 10,000 To run the simulation click on the output cells and start simulation in @Risk Uninformed p1 Prior for Pi Prevalence of infected fish p in the group M Likelihood a) Number of infected fish in the group selected n of infected fish that test positive b) Number c) Number of uninfected fish in the group selected d) Number of uninfected fish that test positive e)Number of test positives Posterior for Pi Input Variables M = Herd size n = Sample size Se = test sensitivity Sp = test specificity Informed p2 Formulae Uninformed p1 =IntUniform(0, M)/M 0.5 0.051666667 15 2 IF( pi = 0, 0, Binomial(n,pi)) 12 2 IF(B8 = 0, 0, Binomial(B8, Se)) 15 28 n-B8 0 1 IF(B10 = 0, 0, Binomial(B10, 1-Sp)) 12 3 B9+B11 #N/A #N/A Informed p2 =Pert(0.01, 0.05, 0.1) RiskOutput+IF(B12= 0, pi, NA()) Graph Parameters 1000 1000 30 30 80% 80% 98% 98% Graphs Produced Uninformed Prior Informed Prior Conclusions Analyse complex problems with minimal input Minimize costs of sampling and ongoing surveillance Improved accuracy in determining risk probabilities Simplify client understanding through use of visuals Therefor achieving greater compliance