Pooled data fit of multiple data sets from different model parameters

Hello,

I have two sets of PK data from two versions of a molecule which is designed to bind to a target with a given Kd. Each data set represents the PK of the molecule which binds to the target at the corresponding Kd value. I'm looking to perform a pooled fit of both data sets to five parameters of a model which describes the kinetics of the molecule - it's a standard TMDD model -, kdeg, kint, R0, kon, koff. The objective of the fit is to obtain two parameter sets corresponding to the two data sets, where the value of kdeg, kint, and R0 are the same in each fit, and the value of kon and koff can vary per data set; but with the constraint that the Kd value is equal to the corresponding known experimentally measured value. How can I do this using the Model Analyzer GUI?

Answer 1

[Arthur Goldsipe]

If I understand correctly, you can do this in the Model Analyzer app. You just need to merge the two data sets into a single data set, and add a variable that identifies which version of the molecule the data is associated with. Then, you can configure whether each parameter you estimate is "pooled" or has a different estimate for each molecule version.

You can find a command-line example of this workflow here. I don't thin we have an example right now of how to do this in the app. But here’s how it works:

• Uncheck the box next to “Pooled fit”
• Configure the “Category Variable” column for each parameter you want to estimate, as follows:
• If you want one estimated parameter value to be used across all groups, set the value to <POOLED>
• If you want group-specific parameter estimates, set the value to empty or to the name of your grouping variable (e.g., “Group”).
• If you want to estimate subgroup-specific parameter values, set the value to a variable in your dataset that identifies membership in the groups. In your case, you should add a variable that identifies which molecule version is associated with that row of the data. Set the Category Variable to the name of this variable, and you’ll estimate one parameter value for each version of the molecule.

[mitpi_182]

Hello Arthur,

Thank you for your response. Where can I configure the "Category Variable" for each of the parameters I want to estimate? I don't see the option anywhere in the app. I'm using MATLAB 2020b.

Best,

Marco.

[Fulden Buyukozturk]

Hi Marco,

That option to define a Category Variable for an estimated parameter should be available in the app in R2020b on a Fit Program. Please see the screenshot below.

Regarding estimating kon and koff with the constraint of an experimentally known Kd: in your model you can define the releationship for example as koff = kon*Kd using a repeated assignment rule and in the Fit program estimate only kon (koff will be calculated based on kon and Kd). If the experimentally measured Kd is different per group/dataset, starting with R2021b you can apply group specific variants using the Variant and Dose Setup table of a Fit Program. For more information on this, please see the first bullet under R2021b release notes "Specify different parameter values for different groups during fitting".

Fulden

[mitpi_182]

Hello Fulden and Arthur,

The experimentally measured Kd is different in the two groups. In this sense, I would like to do a fit that estimates kon in such a way that koff = Kd*kon, where the value of Kd varies for each group. So all the other parameters would be pooled but the koff will vary per group. Can I do this using version 2020b? Specifically, regarding Arthur's proposed procedure to do this, I'm looking to know where in the process of configuring a Category Variable do I define the different initial assignment koff = Kd*kon for the two gorups. Should I add a variable with the Kd value for each data point?

[Fulden Buyukozturk]

Hello, if I understand correctly, you only want to estimate a single kon, and want to specify a different Kd value for each group.

If that's the case, you can use group-specific variants to specify different Kd values during fitting and you don't need to do a category-specific fit/define a Category Variable.

Ability to use group-specific variants are available in R2021b and later. Would you be able to upgrade? If so, below are the steps that you could follow in R2021b and later. If you're unable to upgrade, please let me know and I can share a hacky way to do this in R2020b.

• Add an initial assignment to your model: koff = kon*Kd
• Add two Variants to your model to store different Kd values of your molecules, let's say you name these variants as MoleculeV1 and MoleculeV2
• In the Fit Program, populate the Variant and Dose Setup table as follows so that MoleculeV1 variant is applied to Group 1 and MoleculeV2 is applied to Group 2 (note that you will see tha Variant and Dose Setup table only in R2021b and later)