FOCUS Kinetics training workshop
Chapter 7
Recommended Procedures to Derive
Endpoints for Parent Compounds
Ralph L. Warren, Ph.D.
DuPont Crop Protection
Delaware, USA
30 Jan 2006
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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 kinetic fitting endpoints
a) “best fit” values (compared to triggers for additional work in EU)
b) inputs for environmental exposure models
• 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 modeling in the EU.
Hands-on exercise
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Why the distinction between fitting for trigger endpoints
versus exposure modeling endpoints?
• EU 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 EU 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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EU regulatory trigger 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Draft Guidance Doc.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
Modeling endpoints
• Run SFO and FOMC as a first step
• Run SFO as a first step
• Check visual fit and calculate error
• Check visual fit and calculate error
percentage at which 2 test passed
• Check parameter uncertainty
• Check parameter uncertainty
• If FOMC better than SFO, test other
bi-phasic models
• If error % < 15% and visual fit
acceptable, use SFO DT50
percentage at which 2 test passed
• Use best fit model
• If error % > 15% and visual fit not
acceptable, run bi-phasic model
• 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
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FOCUS Kinetics training workshop
Chi-square (2) test statistic – test of association
( C  O )2
 
(err / 100 x O )2
2
err  100 
1
χ 2tabulated

C  O 2
O2
where
C = calculated value
O = observed value
O = mean of observed (element of scale)
err = measurement error (element of proportionality)
If calculated 2 > tabulated 2 then the model is not
appropriate at the chosen level of significance (5%)
Error percentage unknown
 Calculate error level at which 2 test is passed
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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
100
Observed and predicted
through time
90
Residuals
(predicted - observed)
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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Parameter uncertainty
• Confidence intervals or t-tests may be used.
• The t-test is shown below, which assumes normally distributed parameters.
t
aˆi
i
where
âi = estimate of parameter i
 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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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
Modeling flowchart
Parent only flow chart
for deriving exposure
modeling 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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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
Percent of applied radioactivity (% AR)
Time
(days)
Laboratory degradation of a
compound in aerobic soil
80
60
40
20
0
0
20
40
60
80
100
120
Time (days)
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FOCUS Kinetics training workshop
SFO
FOMC
Measured & Predicted vs. Time
Measured & Predicted vs. Time
100
100
Parent
Concentration
Concentration
Parent
50
0
0
20
40
60
Time
Residual Plot
80
100
50
0
120
20
0
20
40
60
Time
Residual Plot
80
100
10
Parent
10
Residuals
Residuals
Parent
0
-10
-20
120
5
0
-5
0
20
40
60
Time
80
100
2 error (%) = 19.0
DT50 (d) = 18.1
DT90 (d) = 60.1
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120
-10
0
20
40
60
Time
80
100
120
2 error (%) = 6.69
DT50(d) = 10.6
DT90 (d) = 158
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FOCUS Kinetics training workshop
FOMC
DFOP
Measured & Predicted vs. Time
Measured & Predicted vs. Time
100
100
Parent
Concentration
Concentration
Parent
50
0
0
20
40
60
Time
Residual Plot
80
100
50
0
120
0
20
40
60
Time
Residual Plot
80
100
10
10
Parent
Parent
5
Residuals
Residuals
120
0
5
0
-5
-10
0
20
40
60
Time
80
100
2 error (%) = 6.69
DT50(d) = 10.6
DT90 (d) = 158
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120
-5
0
20
40
60
Time
80
100
120
2 error (%) = 1.36
DT50(d) = 10.6 d
DT90 (d) = 481 d
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FOCUS Kinetics training workshop
Parameter uncertainty
Model
Parameter
Optimized
value
Standard
error
Different than
zero?
(P<0.05)
SFO
M0 (%)
k (d-1)
87.0163
0.0383
5.3928
0.0060
-Yes
FOMC
M0 (%)


98.1769
0.7100
6.4023
3.0289
0.0971
1.8756
----
DFOP
M0 (%)
g
k1 (d-1)
k2 (d-1)
96.7497
0.7924
0.0931
0.0015
1.7689
0.0327
0.0085
0.0020
--Yes
No (P=0.225)
-- = not applicable
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FOCUS Kinetics training workshop
Possible conclusions for this data set for the triggers flowchart
• Use DFOP with associated endpoints
> DT50 = 10.6 d, DT90 = 481 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 = 10.7 d, DT90 = 962 d
> Check if other aerobic soil deg and fate studies support this DT90.
• For comparison with EU regulatory DT50 triggers, the result is the same.
• For comparison with EU 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 modeling flowchart…
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FOCUS Kinetics training workshop
SFO
FOMC
Measured & Predicted vs. Time
Measured & Predicted vs. Time
100
100
Parent
Concentration
Concentration
Parent
50
0
0
20
40
60
Time
Residual Plot
80
100
50
0
120
20
0
20
40
60
Time
Residual Plot
80
100
10
Parent
10
Residuals
Residuals
Parent
0
-10
-20
120
5
0
-5
0
20
40
60
Time
80
100
2 error (%) = 19.0
DT50 (d) = 18.1
DT90 (d) = 60.1
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120
-10
0
20
40
60
Time
80
100
120
2 error (%) = 6.69
DT50(d) = 10.6
DT90 (d) = 158
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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 modeling is to link parent with metabolites, then the guidance in
Chapter 8 should be followed (covered later).
• 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 modeling (i.e. 158 d/3.32 = 47.6 d).
> If no, then use slower k from DFOS (HS) or slower k from DFOP to derive a
conservative estimate of DT50 for modeling.
We did not reach 10% of initial in this example so further analysis is required.
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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 = 60.1 d
FOMC
DT50 = 10.6 d
DT90 = 158 d
FOMC DT90/3.32 = 47.6 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 modeling is desired (can’t link to metabolites!)
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FOCUS Kinetics training workshop
DFOP
DFOS (HS)
Measured & Predicted vs. Time
Measured & Predicted vs. Time
100
100
Parent
Concentration
Concentration
Parent
50
0
0
20
40
60
Time
Residual Plot
80
100
50
0
120
10
0
20
40
60
Time
Residual Plot
80
100
5
Parent
5
Residuals
Residuals
Parent
0
-5
120
0
20
40
60
Time
80
100
2 error (%) = 1.36
DT50(d) = 10.6 d
DT90 (d) = 481 d
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120
0
-5
-10
0
20
40
60
Time
80
100
120
2 error (%) = 2.59
DT50(d) = 10.7
DT90 (d) = 244
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FOCUS Kinetics training workshop
Parameter uncertainty
Model
Parameter
Optimized
value
Standard
error
Different than
zero?
(t-test)
DFOP
M0 (%)
g
k1 (d-1)
k2 (d-1)
96.7497
0.7924
0.0931
0.0015
1.7689
0.0327
0.0085
0.0020
--Yes
No (P=0.225)
DFOS (HS)
M0 (%)
tb (d)
k1 (d-1)
k2 (d-1)
95.8119
21.9150
0.0646
0.0040
1.8259
1.6365
0.0038
0.0016
--Yes
Yes
-- = not applicable
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FOCUS Kinetics training workshop
DFOP
fast phase, k1, DT50 = ln(2)/0.0931 = 7.45 d
slow phase, k2, DT50 = ln(2)/0.0015 = 462 d
DFOS (HS)
fast phase, k1, DT50 = ln(2)/0.0646 = 10.7 d
slow phase, k2, DT50 = ln(2)/0.0040 = 173 d
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FOCUS Kinetics training workshop
Possible conclusions for this data set for the modeling flowchart
• Use longest phase of DFOS (HS) to derive conservative value of DT50
> 10% of initial not reached, so DFOS (HS) and DFOP were assessed.
> Longest k from DFOP is not different than zero so it is unreliable.
• Conduct higher-tier modeling using conservative value for DFOP slow phase
DT50 (e.g. 1000 d).
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FOCUS Kinetics training workshop
Summary
• Standardized procedures (flow charts) can be readily
followed for deriving parent only endpoints
• Two flow charts are provided, one for determination of
“best fit” kinetic parameters, the other for deriving
inputs for use with SFO environmental exposure
models
• Statistical and visual methods described provide a
consistent way to assess kinetic model fits
• There is still room for judgment and discussion in the
fitting and endpoint selection process, but the
procedures described here should lead to greater
consistency and transparency
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Questions?
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FOCUS Kinetics training workshop
Now it’s your turn to work through the flowcharts using
some other real data sets…
If you finish the exercise and have additional time, you
might try duplicating the fitting (SFO, FOMC, DFOS,
DFOP) of the example data given in this presentation.
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