focus kinetics training workshop

26-27 Jan 2005

FOCUS Kinetics training workshop

Chapter 7

Recommended Procedures to Derive Endpoints for Parent Compounds

Ralph L. Warren, Ph.D.DuPont Crop Protection

Delaware, USA

Presentation

26-27 Jan 2005


Objectives of this part of the training:• Description of the procedures to follow for a parent compound to derive endpoints for use as

a) trigger values for additional work

b) inputs for environmental exposure models (e.g. PECgw)

• Assessment of kinetic model fits to the observed data using visual and statistical techniques.

• Selection of the appropriate kinetic model and endpoints for the case of triggers and exposure modelling.

Hands on exercise using Excel spreadsheet

26-27 Jan 2005


Why the distinction between fitting for trigger endpoints versus exposure modelling endpoints?

• Current regulatory environmental exposure models are based on SFO kinetics. Therefore, an endpoint (i.e. DT50) calculated using a non-SFO kinetic model will not appropriately represent the observed behavior when input into a SFO-based exposure model. A SFO endpoint, if appropriate, or a conservative estimate or a ‘work around’ must be used.

• Regulatory triggers are based on DT50 and DT90 values which are not constrained to any kinetic model form. The model that most appropriately describes the observed data should be used to generate the endpoint values.

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The same DT50 does not mean the same pattern of decline when calculated using different kinetic models

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SFOFOMCDFOSDFOP

M0 = 100% and DT50 = 5 days in each case

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Regulatory triggers – examples

Annex II to Directive 91/414/EEC

• 7.1.1.2.2. Field dissipation studies are required when DT50lab > 60 days at 20C or 90 days at 10 C

Annex III to Directive 91/414/EEC

• 10.7.1 Testing for effects on soil micro-organisms required when DT90field > 100 days

Draft Guidance Doc. Terrestrial Ecotoxicology (SANCO/10329/2002 rev. 2 final)

• Sub-lethal earthworm tests required depending on number of applications and DT90field

Guidance Doc. Aquatic Ecotoxicology (SANCO/3268/2001 rev. 4 final)

• Chronic study on daphnids required when DT50 in water > 2 days

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So what’s involved in the fitting procedure?

Triggers for additional work modelling endpoints• Run SFO and FOMC as a first step • Run SFO as a first step• Check visual fit and calculate error percentage at which 2 test passed• If FOMC better than SFO, test other bi-phasic models

• Check visual fit and calculate error percentage at which 2 test passed• If error % < 15% and visual fit acceptable, use SFO DT50

• If error % > 15% and visual fit not acceptable, run bi-phasic model

• Use best model fit • If 10% of initial reached in study period then calculate DT50 as FOMC DT90/3.32• If 10% of initial not reached in study period then use longer DT50 from slow phase of HS or DFOP

Check optimized parameter uncertainty!

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Chi-square (2) test statistic

2

22

100 Oerr

OC

where C = calculated value O = observed value = mean of observed (element of scale) err = measurement error (element of proportionality)O

If 2 > 2m, then the model is not appropriate at the chosen sig. level

where m = degrees of freedom (No. of obs. used in the fitting – No. of optimized model parameters)

= level of significance, typically 5%

Remember to use average values where there are replicates!

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Chi-square (2) test statistic• Since the measurement error is typically unknown (would require numerous replicate measurements) a common error model was proposed. The percent error value is scaled to the mean of the observed values. Therefore, the error term is constant through the measurement period.

• The relative error is lower for early time points and increases for later time points, which is consistent with the recommendation for unweighted fitting.

• The minimum error percentage at which the test is passed can be directly calculated.

where: C = calculated, O = observed, = mean of observed, and 2tabulated = lookup value of 2 at

the 0.05 significance level for the appropriate degrees of freedom (no. obs. values used in fitting – no. optimized parameters)

2

2

2

1100O

OCerrtabulated

2O

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Chi-square (2) test statistic

• Note that field data are inherently more variable than lab data. Therefore the error percentages at which 2 is passed will be larger.

• The model with the lower 2 error percentage is defined as more appropriate.

• Further note there is no inherent and definitive error value for any given test system. Choice of an acceptable value is pragmatic and should be considered in light of the visual assessment and parameter uncertainty.

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Visual Assessment• Subjective, yet powerful tool for assessing goodness of fit.

• Keeps common sense in the assessment process.

• Two recommended plots> Plot of fitted versus observed over time (typical plot)> Plot of residuals (Predicted – Observed) over time

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Parameter uncertainty• Confidence intervals or t-tests may be used.

• The t-test is shown below, which assumes normally distributed parameters.

i

iatˆ

iai

where = estimate of parameter i = standard error of parameter i

• The probability (p-value) for the calculated t-value can be read from statistical tables or calculated with Excel TDIST(tcaclulated,df,1)

• If p is < 0.05 then the parameter is considered significantly different than zero. If p is between 0.05 and 0.1 then weight of evidence should be considered.

• The t-test is most applicable to degradation rates (k), not necessarily other parameters such as or for FOMC.

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NO

YES see text

YES

RUN SFO, FOMC

Data entry M0 free, use all data, no weighting

SFO more appropriate than FOMC and gives

acceptable fit?

RUN DFOP (unmodified &

modified fitting routine)

Does the best-fit model give an acceptable description

of the data?

STEP 1: SFO appropriate?

STEP 2: Identify best model other than SFO

Deviation from SFO due to experimental

artifact/decline in microbial activity?

NO

Case-by-case decision (see text)

Determine which of the models (FOMC, DFOP)

is best

NO

YES STOP

STEP 3: Evaluate goodness of fit

NO

Modify fitting routine stepwise: 1. Exclude outliers 2. Constrain M0 3. Weighting

RUN modified fitting

SFO more appropriate than FOMC & fit acceptable?

(modified fitting)

YES STOP

STOP

Parent only flow chart for deriving trigger endpoints

(zoom to view)

Triggers flowchart

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NO YES

RUN SFO

Data entry M0 free, use all data, no weighting

SFO statistically and visually acceptable? Modify fitting routine for

SFO stepwise: 1. Exclude outliers 2. Constrain M0 3. Weighting until best SFO fit achieved

STEP 1: SFO appropriate?

RUN modified SFO

Use SFO DT50 for fate modelling

Aim: modelling fate of parent only?

YES

YES 10% initially measured concentration reached

within experimental period?

NO RUN FOMC

RUN HS or DFOP

Use DT50 from slow phase of HS of DFOP

model for fate modelling


NO

HS or DFOP statistically and

visually acceptable?

YES

FOMC statistically and visually acceptable?

YES

Back-calculate DT50 from DT90 for FOMC (DT50 = DT90 / 3.32)


NO

YES

Use SFO DT50 (modified fitting routines) for fate modelling

NO

Bi-phasic pattern? (assess experimental

artefacts!)

SFO statistically and visually acceptable?

YES


NO

STEP 2:Correction procedure

Aim: modelling metabolite fate linked to

parent?

see text

YES

YES

Parent only flow chartfor deriving exposure modelling endpoints

(zoom to view)

modelling flowchart

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Let’s look at an example for the triggers flowchart…

Time (days)

% of applied radioactivity

00337714143030454562629090

120120

93.199.772.983.860.360.341.737.423.326.020.917.118.818.817.918.516.715.9

Laboratory degradation of a compound in aerobic soil

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residual

2 e r r o r = 1 9 %

D T 5 0 = 1 8 . 1 d

D T 9 0 = 6 0 . 2 d

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F O M C

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2 e r r o r = 7 %

D T 5 0 = 1 0 . 6 d

D T 9 0 = 1 6 0 d

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2 e r r o r = 7 %

D T 5 0 = 1 0 . 6 d

D T 9 0 = 1 6 0 d

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D F O P

2 e r r o r = 1 %

D T 5 0 = 1 0 . 0 dD T 9 0 = 4 7 2 d

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Parameter uncertaintyModel Parameter Optimized

valueStandard

errorDifferent than

zero?(t-test)

SFO M0k

86.980.0382

5.3990.0061

--Yes

FOMC M0

98.200.70636.372

3.0320.10381.976

------

DFOP M0gk1

k2

96.790.7914

0.093050.00149

1.7680.03260.0085

0.00195

----

YesNo (P=0.229)

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• Use DFOP with associated endpoints > DT50 = 10.0 d, DT90 = 472 d > Relax t-test criteria for k2 based on visual fit and 2. > Check if other aerobic soil deg and fate studies support this DT90.

• Use DFOP. Fix k2 to a conservative value (e.g. 1000 d) > 2 and visual fits equivalent to above. > DT50 = 10.1 d, DT90 = 922 d > Check if other aerobic soil deg and fate studies support this DT90.

Possible conclusions for this data set for the trigger flowchart

• For comparison with regulatory DT50 triggers, the result is the same.

• For comparison with regulatory DT90 triggers, the result is the same.

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Continuing with the same data, now let’s look at it using the modelling flowchart…

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2 e r r o r = 1 9 %

D T 5 0 = 1 8 . 1 d

D T 9 0 = 6 0 . 2 d

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F O M C

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residual

2 e r r o r = 7 %

D T 5 0 = 1 0 . 6 d

D T 9 0 = 1 6 0 d

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• Assuming no artifacts, the data is clearly bi-phasic. FOMC fit to the data is superior based on visual assessments and 2 error.

• If aim of modelling is to link parent with metabolites, then the guidance in Chapter 8 should be followed (covered tomorrow).

• If the aim is to model parent fate only then check to see if 10% of the initially measured value was reached during the study period.

> If yes, then use FOMC DT90/3.32 to derive a conservative estimate of SFO DT50 for modelling (i.e. 160 d/3.32 = 48.2 d).

> If no, then use slower k from HS or slower k from DFOP to derive a conservative estimate of DT50 for modelling.

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SFO DT50 = 18.1 d DT90 = 60.2 d

FOMC DT50 = 10.6 dDT90 = 160 d

FOMC DT90/3.32 = 48.2 d (SFO)

FOMC DT90/3.32 is a conservative option where parent only exposure modelling is desired (can’t link to metabolites!)

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OSFOFOMCFOMC DT90/3.32

FOMC DT90/3.32 example (assume last point did reach 10%)

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2 e r r o r = 3 %

D T 5 0 f a s t p h a s e = 1 0 . 7 dD T 5 0 s l o w p h a s e = 1 7 5 d

H S

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2 e r r o r = 1 %

D T 5 0 f a s t p h a s e = 7 . 4 dD T 5 0 s l o w p h a s e = 4 6 6 d

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Parameter uncertainty

Model Parameter Optimized value

Standard error

Different than zero?(t-test)

HS M0tbk1

k2

95.8121.92

0.064480.00397

1.821.70

0.003750.00162

----

YesYes

DFOP M0gk1

k2

96.790.7914

0.093050.00149

1.7680.03260.0085

0.00195

----

YesNo (P=0.229)

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• Use longest phase of HS to derive conservative value of DT50

> 10% of initial not reached, so HS and DFOP were assessed. > Longest k from DFOP is not different than zero so it is unreliable.

Possible conclusions for this data set for the modelling flowchart

• Conduct higher-tier modelling using conservative value for DFOP slow phase DT50 (e.g. 1000 d).

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Questions?

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Now it’s your turn to work through the flowcharts using the observed and fitted data from this morning…

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