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Best Practices for Kinetic Modeling in Environmental Assessments

Learn the recommended procedures for deriving endpoints of parent compounds for environmental exposure models in this informative workshop chapter. Understand the importance of fitting different kinetic models for trigger values and exposure models. Get insights into visual and statistical techniques for assessing model fits.

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Best Practices for Kinetic Modeling in Environmental Assessments

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  1. FOCUS Kinetics training workshop Chapter 7 Recommended Procedures to Derive Endpoints for Parent Compounds Ralph L. Warren, Ph.D.DuPont Crop ProtectionDelaware, USA Page 1 26-27 Jan 2005

  2. FOCUS Kinetics training workshop • Objectives of this part of the training: • Description of the procedures to follow for a parentcompound 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. Page 2 26-27 Jan 2005

  3. 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. Page 3 26-27 Jan 2005

  4. FOCUS Kinetics training workshop The same DT50 does not mean the same pattern of decline when calculated using different kinetic models Page 4 26-27 Jan 2005

  5. FOCUS Kinetics training workshop • Regulatory triggers – examplesAnnex 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 Page 5 26-27 Jan 2005

  6. FOCUS Kinetics training workshop So what’s involved in the fitting procedure? Check optimized parameter uncertainty! Page 6 26-27 Jan 2005

  7. FOCUS Kinetics training workshop Chi-square (2) test statistic whereC = calculated valueO = observed value = 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 wherem = 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! Page 7 26-27 Jan 2005

  8. 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. 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) Page 8 26-27 Jan 2005

  9. 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. Page 9 26-27 Jan 2005

  10. 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 Page 10 26-27 Jan 2005

  11. 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. 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. Page 11 26-27 Jan 2005

  12. FOCUS Kinetics training workshop Parent only flow chart for deriving trigger endpoints(zoom to view) Triggers flowchart Page 12 26-27 Jan 2005

  13. FOCUS Kinetics training workshop modelling flowchart Parent only flow chartfor deriving exposure modelling endpoints(zoom to view) Page 13 26-27 Jan 2005

  14. FOCUS Kinetics training workshop Let’s look at an example for the triggers flowchart… Laboratory degradation of a compound in aerobic soil Page 14 26-27 Jan 2005

  15. FOCUS Kinetics training workshop Page 15 26-27 Jan 2005

  16. FOCUS Kinetics training workshop Page 16 26-27 Jan 2005

  17. FOCUS Kinetics training workshop Parameter uncertainty Page 17 26-27 Jan 2005

  18. 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. Page 18 26-27 Jan 2005

  19. FOCUS Kinetics training workshop Continuing with the same data, now let’s look at it using the modelling flowchart… Page 19 26-27 Jan 2005

  20. FOCUS Kinetics training workshop Page 20 26-27 Jan 2005

  21. 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. Page 21 26-27 Jan 2005

  22. FOCUS Kinetics training workshop FOMC DT90/3.32 example (assume last point did reach 10%) SFO DT50 = 18.1 d DT90 = 60.2 dFOMC DT50 = 10.6 d DT90 = 160 dFOMC 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!) Page 22 26-27 Jan 2005

  23. FOCUS Kinetics training workshop Page 23 26-27 Jan 2005

  24. FOCUS Kinetics training workshop Parameter uncertainty Page 24 26-27 Jan 2005

  25. 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). Page 25 26-27 Jan 2005

  26. FOCUS Kinetics training workshop Questions? Page 26 26-27 Jan 2005

  27. FOCUS Kinetics training workshop Now it’s your turn to work through the flowcharts using the observed and fitted data from this morning… Page 27 26-27 Jan 2005

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