1 S. Hayes, B. Harvey, Syngenta Z. Gao, W. Schmitt, R.L. Jones, Bayer J.W. Green, K. Paul, N. Mackay, DuPont C. Beigel, B. Erzgraeber, BASF D. Yon, Dow 

## Estimating Confidence Intervals for Metabolite Degradation Rates2 

## Outline

Introduction
Approaches to Estimating Confidence Intervals

Examples

Conclusions3 

## Introduction
Kinetic analysis to determine degradation rates of parent compounds and metabolites for EU registration is performed according to the report of the FOCUS Work Group on Degradation Kinetics (2006).
The FOCUS recommendation is that degradation rates for metabolites should preferentially be derived with studies starting with parent. Advantage of deriving formation fraction in the same experiment4 

## Introduction

If the confidence interval of the metabolite degradation rate includes zero, then the FOCUS approach cannot determine whether degradation is occurring, even when the observed data exhibit a decline. In these cases, a conservative decline rate or default half

- life of 1000 days can be imposed.


### When degradation rates of metabolites in parent applied studies are not significantly different from zero, additional degradation studies starting with the metabolite are often performed. Preferable to derive parent and metabolite kinetics from the same study.5 

## Introduction
As noted in the FOCUS kinetics report, confidence intervals from ordinary least squares analysis can be too wide.
This work has focused on implementation of standard and well

- established statistical techniques to more accurately represent confidence intervals.6 

## Conventional Approach
The OLS (ordinary least squares) method makes the following assumptions for determining confidence intervals Error variance is the same for parent and metabolite. The errors are normally distributed around zero.


## OLS provides conservative estimates of metabolite confidence intervals when the error variance of parent is larger than for the metabolite. This could occur, for example, when metabolite levels are low.7 

## Alternative Approaches

Two standard approaches can provide more refined estimates of confidence intervals: MCMC (Markov Chain Monte Carlo) analysis IRLS (Iteratively Reweighted Least Squares) routines 

### These approaches do not require the assumption that error variance is the same for parent and metabolite. No additional information is required to apply these techniques to standard data sets. Focus of this work will be to determine the effect of using of these techniques on: Values of resulting kinetic parameters Confidence intervals8 

## Markov Chain Monte Carlo
MCMC is a stochastic method that explores a given distribution of model parameter values.
The Markov Chain is a chain of parameter sets in which each element is generated from the previous one by a jump function that contains a random component.
Generates actual distributions for both parent and metabolite parameters which can be used to determine the confidence intervals.9 

## Iteratively Reweighted Least Squares
Similar to OLS, except that the variance of the errors of parent and metabolite can be different.
The observations are weighted according to the error variance.
Then the regression process is repeated and the weights adjusted according to the new error variance, until convergence is achieved.10 

## Testing Experiences

A number of data sets have been tested with both the IRLS and MCMC methods. Generally give about the same solution and confidence intervals. Narrower metabolite confidence intervals than OLS when error variance for parent is greater than for the metabolite. In cases when degradation is not occurring, both methods generate confidence intervals that do contain zero.11 

## Example 112 

### Example 1

Parameter Algorithm Estimate Lower CI Upper CI



## k p OLS IRLS MCMC 0.0058 0.0058 0.0058 0.0047 0.0042 0.0043 0.0069 0.0074 0.0077


## k m OLS IRLS MCMC 0.0084 0.0084 0.0085 -0.0178 0.0053 0.0058 0.0346 0.0115 0.0124


## C OLS IRLS MCMC 0.221 0.219 0.223 -0.278 0.130 0.150 0.719 0.309 0.352


## M 0 OLS IRLS MCMC 194.6 194.8 194.3 179.9 174.0 172.7 209.4 215.6 216.213 

### Example 214 

### Example 2

Parameter Algorithm Estimate Lower CI Upper CI



## k p OLS IRLS MCMC 0.0056 0.0055 0.0055 0.0046 0.0042 0.0043 0.0069 0.0074 0.0077


## k m OLS IRLS MCMC 0.0025 0.0026 0.0026 -0.0172 0.0012 0.0013 0.0346 0.0115 0.0124


## C OLS IRLS MCMC 0.098 0.100 0.101 -0.167 0.068 0.074 0.719 0.309 0.352


## M 0 OLS IRLS MCMC 219.8 219.1 218.7 204.9 198.1 197.5 234.6 240.1 240.815 

### Example 316 

### Example 3

Parameter Algorithm Estimate Lower CI Upper CI



## k p OLS IRLS MCMC 0.0007 0.0007 0.0007 0.0005 0.0004 0.0003 0.0010 0.0011 0.0011


## k m OLS IRLS MCMC 0.0019 0.0019 0.0022 -0.0470

-0.0044

-0.0050 0.0507 0.0081 0.0113


## C OLS IRLS MCMC 0.4183 0.4185 0.4268 -0.5871 0.1698 0.2412 1.424 0.667 1.011


## M 0 OLS IRLS MCMC 92.97 92.96 92.96 204.9 198.1 197.5 94.14 94.63 94.68

## Conclusions
Confidence intervals estimated using the OLS approach can be overly wide when the error variance for parent is greater than for the metabolite. The IRLS and MCMC approaches provide more realistic estimates of confidence intervals when the error variance for parent is greater than for the metabolite

.

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