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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 Rates
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Outline

Introduction

Approaches to Estimating Confidence Intervals

Examples

Conclusions
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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 

experiment
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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.
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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.
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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.
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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 intervals
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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.
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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.
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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.
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Example 1
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Example 1

Parameter Algorithm Estimate Lower CI Upper CI

kp

OLS

IRLS

MCMC

0.0058

0.0058

0.0058

0.0047

0.0042

0.0043

0.0069

0.0074

0.0077

km

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

M0

OLS

IRLS

MCMC

194.6

194.8

194.3

179.9

174.0

172.7

209.4

215.6

216.2
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Example 2
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Example 2

Parameter Algorithm Estimate Lower CI Upper CI

kp

OLS

IRLS

MCMC

0.0056

0.0055

0.0055

0.0046

0.0042

0.0043

0.0069

0.0074

0.0077

km

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

M0

OLS

IRLS

MCMC

219.8

219.1

218.7

204.9

198.1

197.5

234.6

240.1

240.8
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Example 3
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Example 3

Parameter Algorithm Estimate Lower CI Upper CI

kp

OLS

IRLS

MCMC

0.0007

0.0007

0.0007

0.0005

0.0004

0.0003

0.0010

0.0011

0.0011

km

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

M0

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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