FOCUS Kinetics training workshop
Chapter 7
Recommended Procedures to Derive
Endpoints for Parent Compounds
Ralph L. Warren, Ph.D.
DuPont Crop Protection
Delaware, USA
26-27 Jan 2005
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FOCUS Kinetics training workshop
Presentation
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.
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Hands on exercise using
Excel spreadsheet
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FOCUS Kinetics training workshop
Why the distinction between fitting for trigger endpoints
versus exposure modelling endpoints?
• 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.
• 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.
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FOCUS Kinetics training workshop
The same DT50 does not mean the same pattern of decline
when calculated using different kinetic models
100
90
SFO
FOMC
DFOS
DFOP
M0 = 100% and DT50 = 5 days in
each case
80
% remaining_
70
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
time (days)
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FOCUS Kinetics training workshop
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
20C 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Draft Guidance Doc.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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FOCUS Kinetics training workshop
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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FOCUS Kinetics training workshop
Chi-square (2) test statistic
2  
C  O 2
err 100  O 
2
where
C = calculated value
O = observed value
O = mean of observed (element of scale)
err = measurement error (element of proportionality)
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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FOCUS Kinetics training workshop
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.
err  100 
1

2
tabulated

C  O 2
O
2
2
where: C = calculated, O = observed, O = 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)
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FOCUS Kinetics training workshop
Chi-square (2) test statistic
• The model with the lower 2 error percentage is defined as more appropriate.
• Note that field data are inherently more variable than lab data.
Therefore the error percentages at which 2 is passed will be larger.
• 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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FOCUS Kinetics training workshop
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
100
90
80
15
70
10
5
50
residual
% AR
60
40
30
0
0
20
40
60
80
100
120
140
-5
20
-10
10
-15
-20
0
0
20
40
60
80
100
120
t (days)
t (days)
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FOCUS Kinetics training workshop
Parameter uncertainty
• Confidence intervals or t-tests may be used.
• The t-test is shown below, which assumes normally distributed parameters.
t
where
âi = estimate of parameter i
 i = standard error of parameter i
aˆi
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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FOCUS Kinetics training workshop
Parent only flow chart for
deriving trigger endpoints
Triggers flowchart
Data entry
M0 free, use all data, no weighting
STEP 1: SFO appropriate?
RUN
SFO, FOMC
(zoom to view)
NO
Modify fitting routine
stepwise:
1. Exclude outliers
2. Constrain M0
3. Weighting
SFO more appropriate
than FOMC and gives
acceptable fit?
YES
STOP
RUN
modified fitting
SFO more appropriate than
FOMC & fit acceptable?
(modified fitting)
YES
STOP
NO
Deviation from SFO due
to experimental
artifact/decline in
microbial activity?
YES
see text
NO
STEP 2:
Identify best model other than SFO
RUN
DFOP (unmodified &
modified fitting routine)
Determine which of the
models (FOMC, DFOP)
is best
STEP 3:
Evaluate goodness of fit
Case-by-case decision
(see text)
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NO
Does the best-fit model give
an acceptable description
of the data?
YES
STOP
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FOCUS Kinetics training workshop
modelling flowchart
Parent only flow chart
for deriving exposure
modelling endpoints
(zoom to view)
Data entry
M0 free, use all data, no weighting
STEP 1: SFO appropriate?
RUN
SFO
NO
Modify fitting routine for
SFO stepwise:
1. Exclude outliers
2. Constrain M0
3. Weighting
SFO statistically and
visually acceptable?
YES
Use SFO DT50 for fate
modelling
RUN
modified SFO
until best SFO fit achieved
SFO statistically and
visually acceptable?
YES
Use SFO DT50
(modified fitting routines)
for fate modelling
YES
Aim: modelling
metabolite fate linked to
parent?
NO
STEP 2:Correction procedure
NO
Case-by-case
decision (see text)
Bi-phasic pattern?
(assess experimental
artefacts!)
YES
YES
see text
Aim: modelling fate of
parent only?
YES
NO
RUN
HS or DFOP
HS or DFOP
statistically and
visually acceptable?
NO
Case-by-case
decision (see text)
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YES
Use DT50 from slow
phase of HS of DFOP
model for fate modelling
10% initially measured
concentration reached
within experimental
period?
YES
RUN
FOMC
FOMC statistically and
visually acceptable?
NO
Case-by-case
decision (see text)
YES
Back-calculate DT50
from DT90 for FOMC
(DT50 = DT90 / 3.32)
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FOCUS Kinetics training workshop
Let’s look at an example for the triggers flowchart…
% of applied
radioactivity
0
0
3
3
7
7
14
14
30
30
45
45
62
62
90
90
120
120
93.1
99.7
72.9
83.8
60.3
60.3
41.7
37.4
23.3
26.0
20.9
17.1
18.8
18.8
17.9
18.5
16.7
15.9
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100
90
Laboratory degradation of a
compound in aerobic soil
80
70
60
% AR
Time
(days)
50
40
30
20
10
0
0
20
40
60
80
100
120
t (days)
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FOCUS Kinetics training workshop
100
100
90
90
SFO
80
80
70
2
70
error = 19%
% AR
DT50 = 18.1 d
50
DT90 = 60.2 d
40
2 error = 7%
60
60
% AR
FOMC
50
DT50 = 10.6 d
40
DT90 = 160 d
30
30
20
20
10
10
0
0
0
20
40
60
80
100
0
120
20
40
60
10
10
5
5
0
20
40
60
80
100
120
140
residual
residual
15
0
0
20
40
60
80
100
120
140
-5
-10
-15
-15
-20
-20
t (days)
120
0
-10
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100
t (days)
t (days)
15
-5
80
t (days)
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FOCUS Kinetics training workshop
100
100
FOMC
90
80
80
2 error = 7%
70
2 error = 1%
70
60
60
DT50 = 10.6 d
50
% AR
% AR
DFOP
90
DT90 = 160 d
40
DT50 = 10.0 d
DT90 = 472 d
50
40
30
30
20
20
10
10
0
0
0
20
40
60
80
100
0
120
20
40
60
10
10
5
5
0
20
40
60
80
100
120
140
residual
residual
15
0
0
20
40
60
80
100
120
140
-5
-10
-15
-15
-20
-20
t (days)
120
0
-10
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100
t (days)
t (days)
15
-5
80
t (days)
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FOCUS Kinetics training workshop
Parameter uncertainty
Model
Parameter
Optimized
value
Standard
error
Different than
zero?
(t-test)
SFO
M0
k
86.98
0.0382
5.399
0.0061
-Yes
FOMC
M0


98.20
0.7063
6.372
3.032
0.1038
1.976
----
DFOP
M0
g
k1
k2
96.79
0.7914
0.09305
0.00149
1.768
0.0326
0.0085
0.00195
--Yes
No (P=0.229)
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FOCUS Kinetics training workshop
Possible conclusions for this data set for the trigger flowchart
• 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.
• 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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FOCUS Kinetics training workshop
Continuing with the same data, now let’s look
at it using the modelling flowchart…
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FOCUS Kinetics training workshop
100
100
90
SFO
90
80
80
70
70
2 error = 19%
60
2 error = 7%
60
DT50 = 18.1 d
50
% AR
% AR
FOMC
DT90 = 60.2 d
40
50
DT50 = 10.6 d
40
DT90 = 160 d
30
30
20
20
10
10
0
0
0
20
40
60
80
100
120
0
20
40
60
15
10
10
5
5
0
0
20
40
60
80
-5
100
120
140
0
20
40
60
80
100
120
140
-5
-10
-15
-15
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120
0
-10
-20
100
t (days)
15
residual
residual
t (days)
80
-20
t (days)
t (days)
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FOCUS Kinetics training workshop
• 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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FOCUS Kinetics training workshop
FOMC DT90/3.32 example (assume last point did reach 10%)
100
O
SFO
FOMC
FOMC DT90/3.32
90
80
% AR
70
60
SFO
DT50 = 18.1 d
DT90 = 60.2 d
FOMC
DT50 = 10.6 d
DT90 = 160 d
FOMC DT90/3.32 = 48.2 d (SFO)
50
40
30
20
10
0
0
20
40
60
80
100
120
t (days)
FOMC DT90/3.32 is a conservative option where parent only
exposure modelling is desired (can’t link to metabolites!)
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FOCUS Kinetics training workshop
100
100
HS
90
2 error = 3%
80
90
DFOP
80
2 error = 1%
70
70
DT50 fast phase = 10.7 d
DT50 slow phase = 175 d
50
60
% AR
% AR
60
50
40
40
30
30
20
20
10
10
0
0
0
20
40
60
80
100
120
0
20
40
60
t (days)
15
80
100
120
t (days)
15
10
10
5
5
0
0
20
40
60
80
-5
100
120
residual
residual
DT50 fast phase = 7.4 d
DT50 slow phase = 466 d
0
140
0
-10
-10
-15
-15
-20
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20
40
60
80
100
120
140
-5
-20
t (days)
t (days)
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FOCUS Kinetics training workshop
Parameter uncertainty
Model
Parameter
Optimized
value
Standard
error
Different than
zero?
(t-test)
HS
M0
tb
k1
k2
95.81
21.92
0.06448
0.00397
1.82
1.70
0.00375
0.00162
--Yes
Yes
DFOP
M0
g
k1
k2
96.79
0.7914
0.09305
0.00149
1.768
0.0326
0.0085
0.00195
--Yes
No (P=0.229)
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FOCUS Kinetics training workshop
Possible conclusions for this data set for the modelling flowchart
• 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.
• Conduct higher-tier modelling using conservative value for DFOP slow phase
DT50 (e.g. 1000 d).
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FOCUS Kinetics training workshop
Questions?
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FOCUS Kinetics training workshop
Now it’s your turn to work through the flowcharts using the
observed and fitted data from this morning…
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