statisticasl sampling applyed to biological hazard
TRANSCRIPT
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Principles of microbiologicalPrinciples of m icrobiological
t est ing: Stat ist ical basis oft est ing: Stat ist ical basis ofsamplingsampling
Mart in Cole
Symposium on Relati ng Microbiologi calTesting and Microbiologi cal Crit eria t o Public
Health Goals
October 31- November 1, 2005
OverviewOverview
{{ Sampling plansSampling plans
{{ ICMSF CasesICMSF Cases
{{ Statistical basisStatistical basis
{{ Performance of sampling plansPerformance of sampling plans
{{ Summary and ConclusionsSummary and Conclusions
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Sampling PlansSampling Plans
{{ Define t he probabilit y ofDefine t he probability of
detecting a microorganisms ordetecting a microorganisms or
other hazards in a lotother hazards in a lot
{{ None can ensure the absence of aNone can ensure the absence of a
part icular hazardpart icular hazard
{{ Should be administ rat ively andShould be administ rat ively and
economically feasibleeconomically feasible
Types of MicrobiologicalTypes of Microb iological
Sampling PlansSampling Plans
Attributes plans:
Qualitative analytical results (presence/absence) orquantitative results that have been grouped(e.g. 100 cfu/g)
Variables plans:
Non-grouped quantitative analytical results
Require distributional assumptions be made
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Tw oTw o-- Class AttributesClass Attributes
Sampling PlansSampling Plans
Tw oTw o--class sampl ing plansclass sampl ing plans designed t o decidedesigned t o decideon acceptance or rej ection of a lot consist ofon acceptance or rej ect ion of a lot consist of
{{ nnnum ber of sample unit s t o be chosennumber of sample unit s to be chosenindependently and randomly fr om t he lotindependently and randomly fr om t he lot
{{ mm a microbiological l imit (i.e. in cfu/ g);a microbiological l imit (i.e. in cfu/ g);a sample is defined t o be posit ive, if it sa sample is defined to be posit ive, if it smicrobial content exceeds this l imitmicrobial content exceeds this l im it
{{ ccmaxim um allow able num ber of samplemaxim um allow able num ber of sampleunit s yielding a posit ive resultunit s yielding a posit ive result(presence/ absence testing) or exceeding t he(pr esence/ absence testing) or exceeding themicrobiological l imit m; for pat hogens c ismicrobiological l imit m; for pat hogens c isusually set t o 0usually set t o 0
Log cfu/g
ProbabilityDensity
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
0.5
0.6m
Proportion defective
Two-class sampling plan:
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OC Curve for Tw oOC Curve for Tw o-- ClassClass
PlansPlans
Operation characteristics (OC) or performance fortwo-class sampling plans:
Probability of lot acceptance calculated for possibleproportions defective in lot
Plot of OC curve to visualize
sampling plan performance
dependency on n and c
Proportion defective
Accepta
nce
probability
Proportion Defective
ProbabilityofAcceptance
0.0 0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
P(acceptance)
P(rejection)
Probability of Acceptance by Proportion Defective
n=5, c=0
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Proportion Defective
ProbabilityofAcceptance
0.0 0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
P(acceptance)
P(rejection)
Probability of Acceptance by Proportion Defective
n=5, c=0
Consumers riskProbabili t y of
acceptingA defect ive lot
Producers r iskProbability t hat anacceptable lot isrejected
ThreeThree-- Class At t r ibut esClass At t ribut es
Sampling PlansSampling PlansThreeThree--class sampling plansclass sampling plans consist ofconsist of
{{ nn number of sample unit s to be chosennum ber of sample unit s to be chosenindependently and randomly fr om t he lotindependent ly and randomly from t he lot
{{ mm a microbiological l imit that separatesa microbiological l imit that separatesgood quality fr om m arginally acceptablegood quality f rom m arginally acceptablequal i tyqual i ty
{{ MMa microbiological l imit above whicha microbiological l imit above whichsampl ing r esult s are unaccept able orsampling r esult s are unaccept able ordefectivedefective
{{ ccmaxim um allow able number of samplemaxim um allow able num ber of sampleuni tsuni tsyielding result s betw een m and Myielding result s betw een m and M(m arginally acceptable);(m arginally acceptable);the number of sample unit s allowed tot he number of sample unit s allowed toexceed M is usually set t o 0exceed M is usually set t o 0
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Log cfu/g
ProbabilityDensity
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
0.5
0.6m M
Proportion
defective
Proportion marginallyacceptable
Three-class sampling plan:
OC Funct ion for ThreeOC Funct ion for Three-- ClassClass
PlansPlansOperation characteristics (OC) or performance forthree-class plans:
Probability of lot acceptance depending on twoproportions
marginally acceptable: between m and M
defective: above M
OC function plotted as athree-dimensional graph Ac
ceptance
pro
bability
Proportiondefective
Prop.m
arginall
yaccep
table
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Operating Characteristic Curves, 3-Class Plans
P(acc)
I CMSF CasesI CMSF Cases
15 cases w hich reflect :15 cases w hich reflect :
zz Degree of riskDegree of r isk
zz Condi t ions of useCondi t ions of use
zz I nt ended Populat ionI nt ended Populat ion
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Risk categorization matrixRisk categorization matrix
Food handling conditionsFood handling conditions
a b ca b c
AA
HealthHealth
hazardhazard BB
CCincreased
risk
{{ A) ModerateA) Moderate::
{{ B) SeriousB) Serious::
{{ C) SevereC) Severe::
S. aureustoxinV. parahaemolyticusB. cereus
EPEC
Salmonella (non typhi)ShigellaListeria monocytogenes
EHEC (STEC, VTEC)V. choleraeO1EPEC for infants
Categories of hazardsCategories of hazards
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Plan Stri ngency (Case) i n Relation t o Degree ofPlan Stri ngency (Case) i n Relation t o Degree of
Health Concern and Condi t ions of Use.Health Concern and Condi t ions of Use.
Type of Hazard Reduce Degreeof Hazard Cause No Changein Hazard May IncreaseHazard
No direct healthhazard
Utility (generalcontamination)
Case 1 Case 2 Case 3
Health HazardLow, indirect(indicator)
Case 4 Case 5 Case 6
Moderate, direct,limited spread
Case 7 Case 8 Case 9
Moderate, direct,
potentiallyextensive spread
Case 10 Case 11 Case 12
Severe, direct Case 13 Case 14 Case 15
Tw oTw o--Class Plans (c= 0): Probabilit ies of AcceptanceClass Plans (c= 0) : Probabilit ies of Acceptance
Compositi on of Lot% Acceptable % Defective
Number of Sample Units Tested5 10 20 60 100
98
95
90
80
70
50
40
30
2
5
10
20
30
50
60
70
.90
.77
.59
.17
.03
.01