@RISK'S ROLE IN
BIOSECURITY: REDUCING
DISEASE RISK WHEN DATA IS
LIMITED
C. I Walster BVMS MVPH MRCVS
Background
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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
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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
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Economics – it must be worth
something, input < outcome
Training – understand procedures
Education – understand disease
processes
Responsibility – greater the stake
increased compliance
Biosecurity Formulae
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P(D-)= 1-P(D+) = 1- p
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P(A|B) =
Basic Bayes Theorem
Multiple Suppliers and
Quarantine
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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)
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P(x≥ 1)= 1- Exp( )
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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:
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P(x≥ 1)= 1- Exp( ) = 0.22
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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
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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
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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:
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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
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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
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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