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IVPO_NonLinear Data

Nonlinear VMax Km

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#1 raghava choudary

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Posted 13 September 2016 - 05:51 AM

Dear All,

 

I have rat data from both iv and po at different doses. The dose normalized AUC indicate nonlinear increase AUC. I am trying to fit the data using IVPO model ( graphical model, saturable clearance) but with no success.

 

Best Regards,

 

Ragha

 

 

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#2 serge guzy

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Posted 13 September 2016 - 09:02 AM

Dear Raghava

Your data set and the model had issues that are not easy to handle.

I will try to explain  all what I did.

1: You had many "0" observations. I deleted those. It is never  agood idea to keep "0" observed values

2: If you look at your Oral data, you will see many animals exhibit double absorption. Without taking that into account, there iwll be a serious misfit

3: We have oral and IV data but putting the same animal with both IV and Oral as a cross over design created problems as same animal data could not explained with the model under corss over. I put different ID for IV and Oral animals

4: i added non linear kinetics

5: The model is quite complex but the fit is relatively good.

Look at the lst model I made and the plot just above the last model that show you  the obs vs IPRED. The CWRES are not too bad.

This is the best I can do with your data.

Hope it helps.

Best Regards

Serge

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#3 raghava choudary

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Posted 13 September 2016 - 09:24 AM

Dear Serge,

 

Thank you for the reply,

 

I will go through the project and get back to you if i have any queries or doubts.

 

Meanwhile, we have generated the Vmax and Km for the compound in rat liver microsomes / hepatocytes and would like to use those values for simulating rat PK profile. Will this work with this compound. Any thoughts?

 

Regards,

 

Raghav,



#4 raghava choudary

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Posted 13 September 2016 - 11:19 AM

Dear Raghava

Your data set and the model had issues that are not easy to handle.

I will try to explain  all what I did.

1: You had many "0" observations. I deleted those. It is never  agood idea to keep "0" observed values

2: If you look at your Oral data, you will see many animals exhibit double absorption. Without taking that into account, there iwll be a serious misfit

3: We have oral and IV data but putting the same animal with both IV and Oral as a cross over design created problems as same animal data could not explained with the model under corss over. I put different ID for IV and Oral animals

4: i added non linear kinetics

5: The model is quite complex but the fit is relatively good.

Look at the lst model I made and the plot just above the last model that show you  the obs vs IPRED. The CWRES are not too bad.

This is the best I can do with your data.

Hope it helps.

Best Regards

Serge

Dear Serge,

 

I didn't understand the ilogit and logitfraction terms for bioavailability and also the reset function you used for the analysis.

Can you help me in detail.

 

Thanks 



#5 serge guzy

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Posted 13 September 2016 - 12:32 PM

Dear Raghava

Your oral data show 2 peaks. I therefore add one extravascular compartment and assumed a fraction of the drug goes via first absorption site and the remaining through the second one. A fraction must be between 0 and 1 and we have the inverse logit function that does that. ilogit(x)=exp(x)/(1+exp(x))  ; x between -infinity and plus infinity will give ilogit(x) between 0 and 1. That is why x must be normally distributed an not log normally distributed (see structural parameters).

 

Now when you have both oral and IV, we can estimate the bioavailability which is the fraction of the drug that goes systemic. This fraction is called ilogit(flogit) where flogit is normally distributed.

ilogit(flogit) is the fraction of the drug that goes systemic(between 0 and 1).

 

Now the real fraction that goes from the first absorption site is equal to the product of the fraction bioavailable multiplied by the fraction from the first site. The real fraction that goes from the second absorption site to Plasma is the bioavailability x by the fraction that goes to Plasma through the second site.

 

Now if you really have cross over and the time was reset to 0 as in your data set. It assumes that the IV and oral dose were given at different occasions and that there was a full washout between the two occasions.

If you reset the time to 0, you need to tell hat to the program and also washout need to be told to the program.

 

The fact that the time is reset to 0 can be handled by first putting the data by ID and then occasion and then time and when you have the second occasion tell the program to washout all the compartments.

This is done by first uncheck the sort input option (in run options) and then in input options select reset option.

I put 4 to 4 because I defined a column called reset and put 4 when I want the reset.

 

Let me ,know if you need further clarificaitons.

 

No reset if you consider different ID'S for IV and oral.

Best

Serge



#6 LLLi

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Posted 13 September 2016 - 09:06 PM

Dear Serge,

 

I am not sure if it is OK to post my question here. The reason why I did so is that both Ragha and I are dealing with the nonlinear kinetics. 

 

I am trying to use NLME to analyze plasma concentration-time data following two consecutive intravenous infusion, using both first-order and Michaelis-Menten elimination (this is the PK17 application in Dr. Dan Weiner's textbook).

 

The results of linear model are almost the same as those from the book but the parameter estimates of nonlinear kinetic model is different from those in the book and the CV% is very huge (the two ASCII are models used in the book). I tried the same initial estimates, lower bounds and upper bounds as the book did but still got the different results. Would you please take a look at my project? 

 

Thank you!

 

LLLi

 

 

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#7 raghava choudary

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Posted 14 September 2016 - 07:45 AM

Dear Raghava

Your oral data show 2 peaks. I therefore add one extravascular compartment and assumed a fraction of the drug goes via first absorption site and the remaining through the second one. A fraction must be between 0 and 1 and we have the inverse logit function that does that. ilogit(x)=exp(x)/(1+exp(x))  ; x between -infinity and plus infinity will give ilogit(x) between 0 and 1. That is why x must be normally distributed an not log normally distributed (see structural parameters).

 

Now when you have both oral and IV, we can estimate the bioavailability which is the fraction of the drug that goes systemic. This fraction is called ilogit(flogit) where flogit is normally distributed.

ilogit(flogit) is the fraction of the drug that goes systemic(between 0 and 1).

 

Now the real fraction that goes from the first absorption site is equal to the product of the fraction bioavailable multiplied by the fraction from the first site. The real fraction that goes from the second absorption site to Plasma is the bioavailability x by the fraction that goes to Plasma through the second site.

 

Now if you really have cross over and the time was reset to 0 as in your data set. It assumes that the IV and oral dose were given at different occasions and that there was a full washout between the two occasions.

If you reset the time to 0, you need to tell hat to the program and also washout need to be told to the program.

 

The fact that the time is reset to 0 can be handled by first putting the data by ID and then occasion and then time and when you have the second occasion tell the program to washout all the compartments.

This is done by first uncheck the sort input option (in run options) and then in input options select reset option.

I put 4 to 4 because I defined a column called reset and put 4 when I want the reset.

 

Let me ,know if you need further clarificaitons.

 

No reset if you consider different ID'S for IV and oral.

Best

Serge

Dear Serge,

 

Thank you for the detailed explanation !

 

Do we have to use the ilogit function for simple IVPO graphic model with only single site absorption ? to keep the fraction between 0 and 1 ?

 

Best regards,

 

Raghav



#8 serge guzy

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Posted 14 September 2016 - 09:35 AM

If the assumption is that the IV has bioavailability of 1 and that PO must be <1 (which is almost if not always the case), then yes, the ilogit function will make sure you stay between 0 and 1. Now, if you have random effects, you must define the logit of the bioavailability being normally distributed, not lognormally distributed as y=ilogit(x) is between 0 and 1 only if x between -infinity and plus infinity. If x is positive like lognormal defines it, then ilogit(x) will be between 0.5 and 1.

 

y=ilogit(x), therefore logit(y)=logit(ilogit(x))=x. ilogit is your bioavailability F, therefore logit(F)=x and x must be normally distributed



#9 serge guzy

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Posted 14 September 2016 - 10:24 AM

Dear Serge,

 

I am not sure if it is OK to post my question here. The reason why I did so is that both Ragha and I are dealing with the nonlinear kinetics. 

 

I am trying to use NLME to analyze plasma concentration-time data following two consecutive intravenous infusion, using both first-order and Michaelis-Menten elimination (this is the PK17 application in Dr. Dan Weiner's textbook).

 

The results of linear model are almost the same as those from the book but the parameter estimates of nonlinear kinetic model is different from those in the book and the CV% is very huge (the two ASCII are models used in the book). I tried the same initial estimates, lower bounds and upper bounds as the book did but still got the different results. Would you please take a look at my project? 

 

Thank you!

 

LLLi

 

Dear LLLi

I looked at your model and it took me sometime to understand that you had an initial condition for Z1 and that Z1 is concentration while A1 is amount.

In the non linear model you defined in Phoenix, you did not put the initial condition that requires the use of the textual mode.

 

now C=A1/V and you had C=0.105 as initial condition.

Since the differential equation is in amount in Phoenix, you must put the initial condition in amount and not in concentration.

 

Therefore C=A1/V=0.105 and A1=0.105*V is the initial conditions oyu must put in the code

 

It is written as

 

sequence{A1=0.105*V}

 

I got now estimates similar to old winnonlion.

now the optimization algorithm uses weighted least square in Winnonlin and not maimum likelihood which could explain the small difference. I am not surprised that Phoenix gives relatively alrge se for Vmax and/or Km.

I hope it helps.

 

Look at the last model in the attached projectAttached File  PK17 Nonlinear Kinetics_capacity I.phxproj   1.37MB   225 downloads

best

Serge



#10 serge guzy

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Posted 14 September 2016 - 10:25 AM

Not sure LLi you got the project. I am trying again.

Serge

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#11 raghava choudary

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Posted 14 September 2016 - 01:35 PM

If the assumption is that the IV has bioavailability of 1 and that PO must be <1 (which is almost if not always the case), then yes, the ilogit function will make sure you stay between 0 and 1. Now, if you have random effects, you must define the logit of the bioavailability being normally distributed, not lognormally distributed as y=ilogit(x) is between 0 and 1 only if x between -infinity and plus infinity. If x is positive like lognormal defines it, then ilogit(x) will be between 0.5 and 1.

 

y=ilogit(x), therefore logit(y)=logit(ilogit(x))=x. ilogit is your bioavailability F, therefore logit(F)=x and x must be normally distributed

 

Dear Raghava

Your data set and the model had issues that are not easy to handle.

I will try to explain  all what I did.

1: You had many "0" observations. I deleted those. It is never  agood idea to keep "0" observed values

2: If you look at your Oral data, you will see many animals exhibit double absorption. Without taking that into account, there iwll be a serious misfit

3: We have oral and IV data but putting the same animal with both IV and Oral as a cross over design created problems as same animal data could not explained with the model under corss over. I put different ID for IV and Oral animals

4: i added non linear kinetics

5: The model is quite complex but the fit is relatively good.

Look at the lst model I made and the plot just above the last model that show you  the obs vs IPRED. The CWRES are not too bad.

This is the best I can do with your data.

Hope it helps.

Best Regards

Serge

Dear serge,

 

Thank you for the detailed explanation.

 

In the attached project, The final estimate of flogit and logit fraction are 0.0152 and 0.190 using FOCE-ELS where as with QRPEM the estimates are 5.305 and 0.648 respectively. Can logit fraction be more than 1 ?

 

best regards,

 

Raghav



#12 raghava choudary

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Posted 14 September 2016 - 01:41 PM

Dear Serge,

 

Thank you for the reply,

 

I will go through the project and get back to you if i have any queries or doubts.

 

Meanwhile, we have generated the Vmax and Km for the compound in rat liver microsomes / hepatocytes and would like to use those values for simulating rat PK profile. Will this work with this compound. Any thoughts?

 

Regards,

 

Raghav,

Dear Serge,

 

I did similar exercise with IVSC data in the attached project with emphasis on bioavailability. 

 

I get the bioavailability value of more than 3 when i use inverse logarithm function.

 

Please guide

 

Raghav

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#13 serge guzy

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Posted 14 September 2016 - 02:02 PM

Dear Serge,

 

I did similar exercise with IVSC data in the attached project with emphasis on bioavailability. 

 

I get the bioavailability value of more than 3 when i use inverse logarithm function.

 

Please guide

 

Raghav

Dear Raghav

In the attached project, you did not make any transformation for bioavailability. Therefore there is no inverse transformation to perform.

Best Regards

Serge



#14 LLLi

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Posted 14 September 2016 - 02:23 PM

Dear Serge,

 

Thank you! I got the project and thank you for the detailed explanation. 

 

So from your information, can I say that for any dataset in which C0 is not zero we need add the initial condition into the model and this can only be done by using textual model? 

 

If I simultaneously fit two sets of data (eg iv and po, and both datasets contain non-zero C0) I need add the following statement in my code?

 sequence {
      Aa = C0po*V
      A1 = C0iv*V
   }
 

Thank  you!
LLLi


Edited by LLLi, 14 September 2016 - 02:39 PM.


#15 serge guzy

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Posted 14 September 2016 - 02:47 PM

Dear Serge,

 

Thank you! I got the project and thank you for the detailed explanation. 

 

So from your information, can I say that for any dataset in which C0 is not zero we need add the initial condition into the model and this can only be done by using textual model? 

 

If I simultaneously fit two sets of data (eg iv and po, and both datasets contain non-zero C0) I need add the following statement in my code?

 sequence {
      Aa = C0po*V
      A1 = C0iv*V
   }
 

Thank  you!
LLLi

Dear LLLi

The answer is usually no. C0 refers to the Plasma concentration not been zero, I guess because of endogenous level.

If you give the dose both IV and Oral, then the question to ask is if you have non zero level in both oral and IV compartment. You do not observe level in the oral compartment and if you have some amount non zero before you give the oral dose, then the initial conditions would be

 

sequence{Aa=Aabase

A1=C0iv*V}

 

Aabase and C0iv are either known or estimated by the program

 

If you have only non zero level in Plasma , then the sequence statement is as before.

 

It will never be as you mentioned unless C0 is the same in oral and IV but again we never measure oral level.

best

Serge



#16 LLLi

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Posted 15 September 2016 - 01:32 PM

Dear Serge,

 

Thank you!

 

I have a question. If we have several subjects, say 10, and these subjects have different initial condition (C0), how to write the sequence statement? Do we need to write 10 statements for 10 subjects?

 

Thank you!

LLLi


Edited by LLLi, 15 September 2016 - 01:58 PM.


#17 serge guzy

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Posted 15 September 2016 - 02:14 PM

Dear Serge,

 

Thank you!

 

I have a question. If we have several subjects, say 10, and these subjects have different initial condition (C0), how to write the sequence statement? Do we need to write 10 statements for 10 subjects?

 

Thank you!

LLLi

Dear LLLi

You put C0 in your data set as a covariate for each patient and you read the covariate as C0 like you would do with weight.

In the code itself you write

covariate(C0)

 

In your data set, you add the column called C0 with for each individual the value of C0. You put that value as the first record for each patient. There is no need to write for each record C0 as it is only one value per patient.

You can use covariate(C0) or fcovariate(C0). It does not matter because it does not change with time for each patient.

Hope it is clear.

best Regards

SERGE







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