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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