- On 20 Feb 2013 at 03:52:28, wangjian (wj801126.-at-.hotmail.com) sent the message

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Hi, All:

Rate constant (k) is often used in the in vitro studies as a initial parameter

to further calculate other important parameters such as intrinsic clearance

(CLint) in metabolic stability study and inactive parameters in the inhibition

studies (KI and kinact in time-dependent inhibition study, where kobs is

used to

describe rate constant), which is calculated from the slope of the initial

linear phase of the plots. For example: In the metabolic stability study, k is

determined with a linear regression analysis of the logarithm of remaining

percent (C%) of parent drug against incubation-time. While in the

time-dependent inhibition study, the logarithm of the enzymatic activity

is

firstly plotted against the pre-incubation time, then the apparent inactivation

rate constant (kobs) can be calculated from the slope of the initial linear

phase. My question is when we plot these lines to obtain slope values,

is it

necessary to set the intercept to a constant value such as 0 since when

t=0, the

initial value of y should also be 0 based on the equation of y=ln(C0)-kt? We

all know that the data quality can influence the intercept values, if we

don't

set the intercept values when doing linear regression, the intercept will be

changed a lot with different data set especially when Microsoft excel was used

as the tool, which obviously conflicts with the equation and at the same

time,

the R2 is still possibly good enough (>0.9). I have reviewed a lot of paper and

surprisingly noticed that no one set the intercept to a constant value when

calculating k so I guess that if the intercept was not constrained, a criterion

is necessary to judge if the regression is acceptable as well as the calculated

slope is correct. I will be appreciated that if anyone can share your

experiences on this kind of data processing.

Many thanks!

Regards,

Jian Wang - On 20 Feb 2013 at 18:29:28, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message

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Hi,

My advice is to use what you already know to be true without doubt. The

intercept must be zero so fix it to zero when doing the regression.

If you find that the intercept is importantly different from zero then

you need to think very carefully about the methodology you are using and

find the problem.

R^2 is a waste of time. It is not a reliable measure of goodness of

fit.

Nick - On 20 Feb 2013 at 09:46:40, "Jones, Michael - Pharmacy" (Michael.Jones.aaa.uch.edu) sent the message

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The following message was posted to: PharmPK

Hi Nick,

Which statistical method provides the best measure of goodness of fit

for clinical PK data?

Thanks,

Mike

Michael A. Jones, Pharm.D.

Informatics Pharmacist - Clinical Decision Support

University of Colorado Hospital - On 21 Feb 2013 at 07:57:13, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message

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Mike,

Visual predictive check is my gold standard for showing the model fits the data.

Nick - On 20 Feb 2013 at 13:21:59, "Jones, Michael - Pharmacy" (Michael.Jones.aaa.uch.edu) sent the message

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The following message was posted to: PharmPK

Thanks Nick,

Are there any statistical methods that can be automated that would be as

good as visual inspection of the curve and data?

Thanks,

Mike

Michael A. Jones, Pharm.D.

Informatics Pharmacist - Clinical Decision Support

University of Colorado Hospital

[I once had a statistics professor 'offer' to leave the dissertation

committee of one of my graduate students (a week before the defense)

unless we removed R^2 from standard curve plots ;-) A visual check of

the data and best-fit line is always an important part of the process

but as far as automating the fit the use of a number of statistics could

be useful including R^2 in a controlled fashion. I've recently seen it

used to automatic the process of selecting the number of points to use

in the determination of the terminal half-life or rate constant.

However, it didn't work very well and I feel that I did a (much) better

job looking at each plot individually. This can especially important

with sparse data sets. - db] - On 21 Feb 2013 at 10:23:46, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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Mike,

Anybody with common sense will always look at the data and the fit. Statistics have a limited role. They can be helpful in guiding the search for an appropriate model eg. I use the extended least squares log-likelihood. The final decision rests with the human brain via the eyes.

Nick - On 20 Feb 2013 at 14:29:42, "Jones, Michael - Pharmacy" (Michael.Jones.-at-.uch.edu) sent the message

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The following message was posted to: PharmPK

That makes sense. So my takeaway from this is; even with automated

methods we still must provide a sufficiently granular plot for the

end-user to inspect.

Thanks again Nick,

Mike

Michael A. Jones, Pharm.D.

Informatics Pharmacist - Clinical Decision Support

University of Colorado Hospital - On 21 Feb 2013 at 02:48:29, P C (parnalic.-at-.hotmail.com) sent the message

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My question is when we plot these lines to obtain slope values is it

necessary to set the intercept to a constant value such as 0 since when

t=0

the initial value of y should also be 0 based on the equation of y=ln(C0)-kt?

-In any kinetic exp it is often difficult to get concn data for t=0 unless you

have a cell-free incubation. Hence=2C one uses t= 2 or 3 min to obtain 1st

concn value which is close to initial conc. The y-axis is usually Ln (Concn).

Parnali Chatterjee - On 21 Feb 2013 at 10:01:28, Nathan Teuscher (nathan.aaa.learnpkpd.com) sent the message

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Parnali,

Calculation of the terminal rate constant by linear regression involves

estimating both the slope and intercept. The slope value will be

negative because the concentrations are declining as time increases.

Thus the slope value is equal to -1 * terminal rate constant. The

intercept is not fixed to zero, and the intercept value may be useful

depending on the pharmacokinetic profile. If you have a IV bolus dose,

and the drug exhibits 1-compartment kinetics, then the intercept value

corresponds to C(0), or the "concentration at time=0". More

appropriately the intercept value can be used to calculate the volume

of distribution using the following equation: V = Dose/C(0).

Good luck in your analysis.

Nathan S. Teuscher, PhD

Founder, PK/PD Associates

www.learnpkpd.com

nathan.-at-.learnpkpd.com

Twitter: www.twitter.com/learnpkpd

Facebook: www.facebook.com/LearnPKPD

YouTube Channel: www.youtube.com/learnpkpd

[I think Nathan means, semi-log linear regression, that is linear regression of the log/ln of Cp versus time.

For example http://www.boomer.org/c/php/pk0202a.php

and http://www.boomer.org/c/php/pk0504a.php

- db] - On 1 Mar 2013 at 18:38:17, Yi Gu (gooey1981.-a-.yahoo.com.cn) sent the message

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Hi all,

It seems the discussion is biased from what it was originally asked. I think

Jian is talking about the in vitro metabolism assay, so theratically at

time zero, the drug should be of no loss and the remaining should be 100%. From this

point, I agree with Nick to set the intercept.

However, actaully calculating k is a process of linear model fitting. in terms

of linear model fitting, manully setting the intercept should be better avoided,

because it will change the model variance. That's why it is generally not fixing

the intercept.

However, regarding to this question itself, if the method is robust and the

result is reliable, there may be an intercept but it will be not statistically

significantly different from the ideal (theratical) value (for example, 0 or

100, depended on what kind of model equation). Assuming the theratical value is

100, always the modeling intercept result will range around 100. But the

significane (p value) of the linear model parameters is more meaningful, for

this intercept it is better to be not significant. However, if the modeling

intercept is significantly different from the ideal (theratical) value, such as

p<0.05, it implicates the data has some problems. You need to refine the

experiment. But for early projects or screening purpose, I think manually fixing

the intercept of this kind of questionable data to generate a k is reasonable.

Thanks

Yi

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