Subpopulation

Dear NMusers: I am trying to fit a dataset with 13 dose levels. The highest dose is about 10 times of the lowest dose. Each patient receive one dose and were sampled intensively up to 7 days. The results of individual PK analysis shown linear kinetics for some of the patients and nonlinear kinetics for the other patients. I have tried to fit all of them together. But my advisor wants me to fit linear patients and nonlinear patients separately to get a better look of fitting. Additionally, all the nonlinear patients are from higher dose levels. But not all the patients in higher dose levels shown nonlinear kinetics. So my question is which way is more appropriate in this case? Should I fit them all together or separately? Could these two types of patients be considered as subpopulations? Any comment or suggestion will be highly appreciated. Best regards, Huali

Huali - If the goal of making a very arbitrary decision as to which patient exhibits linear versus nonlinear PK is to "get a better look" then that is fine. It may reveal an underlying relationship in the data. So for example, you may wish to plot the resulting post-hoc values of clearances and volumes versus dose to understand what sort of nonlinearity is present. Does the apparent nonlinearity produce higher or lower than expected exposures? Is it a clearance or absorption issue? however, the danger in such an approach is that you are making very subjective decisions as to what is and is not nonlinear. With the limited info you have provided I can only make general assertions. However, such an exercise should only be used as an intermediate, exploratory tool to understand what is truly occurring with this drug which will then permit building a more optimal model that encompasses all the data. If the drug is subject to polymorphic metabolism, or some precipitant of a drug interaction is present then one might consider patients as subpopulations using either known values of covariates or a mixture model. However, more likely is that there is some underlying continuous distribution of Km in your population and that some fraction of your high dose patients have a low enough Km and have achieved high enough concentrations so as to exhibit an obviously nonlinear profile. A similar distribution of bioavailability might explain data moving in the opposite direction. With data as rich as you have described in your posting, it seems like you should have a very good chance of identifying the underlying properties that have produced your observations. Jeff ______________________________________________________ "Huali Wu" <hualiw Sent by: owner-nmusers 12-Aug-2008 12:14 To nmusers cc Subject [NMusers] Subpopulation Dear NMusers: I am trying to fit a dataset with 13 dose levels. The highest dose is about 10 times of the lowest dose. Each patient receive one dose and were sampled intensively up to 7 days. The results of individual PK analysis shown linear kinetics for some of the patients and nonlinear kinetics for the other patients. I have tried to fit all of them together. But my advisor wants me to fit linear patients and nonlinear patients separately to get a better look of fitting. Additionally, all the nonlinear patients are from higher dose levels. But not all the patients in higher dose levels shown nonlinear kinetics. So my question is which way is more appropriate in this case? Should I fit them all together or separately? Could these two types of patients be considered as subpopulations? Any comment or suggestion will be highly appreciated. Best regards, Huali

Huali - If the goal of making a very arbitrary decision as to which patient exhibits linear versus nonlinear PK is to "get a better look" then that is fine. It may reveal an underlying relationship in the data. So for example, you may wish to plot the resulting post-hoc values of clearances and volumes versus dose to understand what sort of nonlinearity is present. Does the apparent nonlinearity produce higher or lower than expected exposures? Is it a clearance or absorption issue? however, the danger in such an approach is that you are making very subjective decisions as to what is and is not nonlinear. With the limited info you have provided I can only make general assertions. However, such an exercise should only be used as an intermediate, exploratory tool to understand what is truly occurring with this drug which will then permit building a more optimal model that encompasses all the data. If the drug is subject to polymorphic metabolism, or some precipitant of a drug interaction is present then one might consider patients as subpopulations using either known values of covariates or a mixture model. However, more likely is that there is some underlying continuous distribution of Km in your population and that some fraction of your high dose patients have a low enough Km and have achieved high enough concentrations so as to exhibit an obviously nonlinear profile. A similar distribution of bioavailability might explain data moving in the opposite direction. With data as rich as you have described in your posting, it seems like you should have a very good chance of identifying the underlying properties that have produced your observations. Jeff ______________________________________________________ "Huali Wu" <[EMAIL PROTECTED]> Sent by: [EMAIL PROTECTED] 12-Aug-2008 12:14 To [email protected] cc Subject [NMusers] Subpopulation Dear NMusers: I am trying to fit a dataset with 13 dose levels. The highest dose is about 10 times of the lowest dose. Each patient receive one dose and were sampled intensively up to 7 days. The results of individual PK analysis shown linear kinetics for some of the patients and nonlinear kinetics for the other patients. I have tried to fit all of them together. But my advisor wants me to fit linear patients and nonlinear patients separately to get a better look of fitting. Additionally, all the nonlinear patients are from higher dose levels. But not all the patients in higher dose levels shown nonlinear kinetics. So my question is which way is more appropriate in this case? Should I fit them all together or separately? Could these two types of patients be considered as subpopulations? Any comment or suggestion will be highly appreciated. Best regards, Huali

Dear Huali, The best is to derive one model for all data. If you are pressed with time it may be sufficient to describe the data in the dose range which is clinically relevant (if known). Possibly, in this dose range there is no nonlinerarity. However, splitting the subjects based on the outcome is not a good idea. The two models you end up with will both be biased in the parameter estimates since subjects with e.g. high Km (or slow absorption/high Vmax) will be more abundant in the linear-kinetics dataset and vice versa for the nonlinear-kinetics dataset*. Additionally, without a model it is difficult to distinguish an initial nonlinearity from the absorption process, so that borderline cases may end up in the wrong dataset. The nonlinearity may only be relevant for a subpopulation of your study subjects. This can be investigated in a mixture model, in case a single distribution of parameter values can not describe your data. Before making such an attempt, try to understand the possible sources of nonlinearity in your specific case, so that the model captures this. I hope this helps! Jakob *I do not know the source of nonlinearity in the specific case, so this just to exemplify with nonlinear CL.

Huali The best solution is to fit all of your data to the more general model. In this case that is of course the non linear model (the pk linear model is a simplification of the limit where cc is very small relative to Km) Saik ----- Original Message -----

Did you try to fit a non linear model with both linear (non target specific) and non linear (target specific) clearance? At high doses, the non linear part of the clearance will allow one estimating both vm and Km. At low doses, Vm.C/(C+KM) will be reduced to Vm/Km.C which is now an additional linear clearance term. When using a population approach, not all the parameters must be identifiable for each patient unlike the traditional individual fitting procedures (like Winnonlin). Best regards; Serge Guzy Principal Scientist, XOMA (US) LLC President, CEO, POP-PHARM; Inc;