quantitative testing plans may 8-10, 2006 iowa state university, ames – usa jean-louis laffont...

Quantitative Testing Plans

May 8-10, 2006

Iowa State University, Ames – USAJean-Louis Laffont

Kirk Remund

ISTA Statistics Committee 2

Overview

• Statistical framework

• Implementation in Seedcalc


Testing plan design: statistical framework for quantitative methods

Seed lot:

true AP% = p

• Suppose n pools of m seeds were taken from the lot and that J flour sub-samples from each pool were measured K times.

n pools of m seeds … …

Grinding seeds into flour

… …

J flour sub-samples per pool

Measurement

K measures per floursub-sample

Measure 1 Measure 2 … Measure K

Flour sub-sample 1

Flour sub-sample 2

…Flour sub-sample J

Pool iyijk



• Model:

ijk)i(jiijk ebapy Measurement k made on flour sub-sample j from pool i

True AP%= + + +

Random effect of pool i

2sampling,0N

Random effect of flour sub-sample j from pool i

2flour,0N

Random effect of measurmnt k for flour sub-sample j from pool i

2tmeasuremen,0N

The parameter p is estimated by the sample mean:

2p̂

k,j,iijk p,N~y

nJK

1p̂

nJKnJntmeasuremen

2flour

2sampling

22p̂


0.0 0.5 1.0 1.5 2.0

AP%


Overall distribution of )N(p,~y y2yijk

nJKnJntmeasuremen

2flour

2sampling

22p̂

-1.0 -0.5 0.0 0.5 1.0

AP%

p +

Flour sub-sampling

Measurement

Sampling n pools of m seeds : derived from the variance of

2sampling

2 ker nel ker nelsampling

p (1 p )

m

2flour

2tmeasuremen

ker nelB(m,p )

and are obtained from historical experiments

flour2 tmeasuremen

2


• Homozygous reference material and hemizygous test lots


• Remember that the true AP% p in the lot is expressed in %DNA when using quantitative methods

and that is expressed on a kernel basis.

2 ker nel ker nelsampling

p (1 p )

m

Introduction of the b-Factor (biological factor) to convert from %DNA to %Seed units: %Seed = b-Factor x %DNA or

ker nelp b p • Examples:

• Reference material and test lots have the same zygosity/ploidy/copy number b-Factor= 1

b-Factor= 2



• Re-expression of in %DNA units:

2sampling

p(1 bp)

bm

2sampling

nJKnJntmeasuremen

2flour

2sampling

2

p̂2

2 22 flour measurement

p̂

(pCV )p(1 bp)

bnm nJ nJK

• Re-expression of :

Having observed in some experiments that ²measurement

seems to depend on p, the true AP probability, whileCVmeasurement is fairly constant, we can rewrite as: p̂

2



• This formula serves as a basis for elaborating an OC curve that can be used to investigate properties of a testing plan

• We can then calculate the probability to “accept” the lot, given a true unknown AP% p:

where is the cumulative distributionfunction for the standard normal distribution

p̂p̂p̂

pALp|

pALpp̂Pr)p|ALp̂Pr(

• Lets now define an Acceptance Limit (AL) such that:

• if AL, “accept” the lot

• if > AL, “reject” the lot

p̂p̂



• Example: testing plan components: 2 pools of 3000 seeds, 1 flour sub-sample/pool, 3 measurements/flour sub-sample, Std-Dev of flour sub-sampling error = 0.011%, measurement CV = 15%, Acceptance Limit (AL) = 0.1% (lot « accepted » if average of the 2 x 1 x 3 readings is AL)

True AP% in lot

Pro

ba

bili

ty o

f a

cce

pta

nce

(%

)

0.0 0.1 0.2 0.3 0.4 0.5

02

04

06

08

01

00

95%

5%



• Consumer risk and producer risk are given respectively by:

where is the cumulative distributionfunction for the standard normal distribution

p̂

LQLAL)LQL|ALp̂Pr(riskConsumer

p̂

AQLAL1)QLA|ALp̂Pr(riskoducerPr


Testing plan design: implementation for quantitative methods

• All of the methods discussed have been implemented in the newest version of the Microsoft Excel® spreadsheet Seedcalc

Estimating AP%

Designingtesting plans

Comparingtesting plans



Testing plan design

Enter n, m, J, K and …

historical assay variation and…

LQL, AQL and AL

and get consumerand producer risks and OC curve

b-Factor and …



The « Find Plan » tool can help the user to find testing plans satisfying certain conditions given some parameters



Parameters for the search algorithms



Find the highest AL that meets target consumer

risk for the LQL. No consideration of the

producer risk target.n, m, J and K are held

fixed



Consumer and producerrisk targets satisfied

by changing AL, n, I and J




by changing AL, m, I and J




by changing AL, n, m, I and J



Compare plans

Visual comparison of OC curves along with testing plan parameters


Historical data gave 0.15% for the estimate of the flour standard-deviation. We expect that the measurement CV range is from 10% to 30% and weconsider the following testing plan: . LQL = 0.7% for a consumer confidence = 95%. AQL = 0.15% for a producer confidence = 95%. 1 pool of 3000 seeds, 2 flour sub-samples, 3 measurements. AL = 0.39% 1. Does this plan meet consumer and producer requirements when the measurement CV = 10%? 2. Compare the outcomes of this testing plan when the CV is varying from 10% to 30%.

Example


Example

1. Does this plan meet consumer and producer requirements when the measurement CV = 10%?

YES


Example2. Compare the outcomes of this testing plan when the CV is varying from 10% to 30%.

quantitative testing plans may 8-10, 2006 iowa state university, ames – usa jean-louis laffont...

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flour subsamplepool

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