Modeling Dose-Response-Time data

Dose-Response-Time data

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#1 Mercuri

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Posted 09 January 2023 - 04:32 PM

Hello and Happy New Year!

I am trying to write a model for describing Dose-Response-Time data of oligonucleotides using PML. I am using the data from Tsimikas et al. 2015 Lancet 386, 1472-1483 and the model described in Jansson-Lofmark and Gennemark 2018 Nucleic Acid Therapeutics 28 (6), 319-325

Because I am learning how to use PML using the PML school videos (thank you so much for them!), I would like to make sure that I am doing the right thing. Hence, I have attached the raw data and the model code.

It would be great to know if everything is correct and if I am on the right path.

Many thanks

Annalisa

#2 bwendt@certara.com

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Posted 09 January 2023 - 05:10 PM

Hi Annalisa,

I cannot check the original reference but there are a few flaws in the PML code, e.g.

you should not use the exponential function in the deriv statement, rather use it as follows:

deriv(D = Aa * Ka - Ke * D)

The amount of drug in the absorption compartment is typically decreasing:

deriv(Aa = -Aa * Ka)

The effect statement should read like this:

deriv(E = Kin * (1 - Emax * D ^ gam / (D ^ gam + IC50 ^ gam)) - Kout * E)

I can't easily fit the PK/indirect model to the raw data because it would need some concentrations to get estimates for Ka and Ke.

Bernd

Edited by bwendt@certara.com, 09 January 2023 - 05:19 PM.

#3 Mercuri

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Posted 10 January 2023 - 07:46 AM

Dear Bernd,

thanks for your reply! The equations reported in the publication are as follow:

D'(t) = A * ka * exp(-ka*t) - ke * D(t)

where D is the drug biophase

The response is

R'(t) = kin * (1-I(D)) - kout * R(t)

and I(D) = Imax*(D^n/(ED50^n+D^n)

in the model they assume:

ka = 10 days-1

apparent PK with linear uptake and linear elimination from the drug biophase

I hope it helps. many thanks!

Annalisa

#4 bwendt@certara.com

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Posted 10 January 2023 - 07:56 AM

Dear Annalisa,

thanks, this is very helpful. What is the estimated KE - first order elimination rate from drug biophase?

Bernd

#5 Mercuri

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Posted 10 January 2023 - 08:14 AM

Dear Bernd,

In the paper it is not reported ke as set parameter, so I guess they have fitted it to the data. The value of ke reported from their population model (they are fitting more than one dose at the same time), is 0.0193 day-1.

I get 0.0277287 as ke after fitting, using the following values to initialise the model:

tvKe 0.019
tvKa 0.26
tvEmax 1
tvED50 150
tvKin 0.108
tvKout 0.108
tvGam 1

#6 bwendt@certara.com

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Posted 10 January 2023 - 09:14 AM

Perfect! With those initial estimates I was able to fit the model to the data:

Please also see the Phoenix project file attached.

Bernd

#7 Mercuri

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Posted 10 January 2023 - 09:49 AM

Dear Bernd,

thank you so much! So basically I should not have added the exponential function in the deriv statement and use the negative sign in the amount estimation.

Thanks so much for your help!

Annalisa

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