# RE: Dilemma with PPK parameters

From: Ken Kowalski <ken.kowalski>
Date: Fri, 5 Feb 2010 14:01:31 -0500

Hi All,

I think we are getting off the point. What Varsha was asking is how can =
the CL reported as L/kg/hr be so different between the two treatment =
groups while the volume of distribution and half-life could be so =
similar when fitting a one compartment model? I think the answer to =
this question is in the parameterization of CL and Vd with WT. Varsha =
parameterized CL and Vd as

TVCL = THETA(1) + THETA (3) * WT

TVVD = THETA(2) + THETA (4) * WT

and the estimate of CL reported in units of L/kg/hr was obtained from =
the estimate of THETA(3). However, if the WT relationship is not =
proportional to WT for the control group, and is relatively invariant =
over the range of WT, then fitting this linear model in WT could give =
rise to a large (non-zero) value of THETA(1) and a small value of =
THETA(3). Comparing THETA(3) between treatment groups as the difference =
in CL only makes sense if THETA(1)=0. Thus, with the above model, we =
should not interpet THETA(3) as the total CL in L/kg/hr unless =
THETA(1)=0.

The typical individual halflife is

K=TVCL/TVVD

THALF = LN(2)/K

which involves THETA(1) through THETA(4) whereas what Varsha was =
reporting as a difference in CL were the estimates of THETA(3) from =
fitting each treatment separately. So one could obtain different =
estimates of THETA(1) and THETA(3) between the two treatment groups =
while obtaining similar estimates of TVCL for a given value of WT. In =
other words, it is possible that TVCL and TVVD are similar between the =
two treatment groups (which would lead to similar halflives) and yet =
different estimates of THETA(3) for the two treatment groups.

Best regards,

Ken

Kenneth G. Kowalski

President & CEO

A2PG - Ann Arbor Pharmacometrics Group, Inc.

110 E. Miller Ave., Garden Suite

Ann Arbor, MI 48104

Work: 734-274-8255

Cell: 248-207-5082

Fax: 734-913-0230

ken.kowalski

From: owner-nmusers
On Behalf Of Serge Guzy
Sent: Friday, February 05, 2010 1:22 PM
To: Ulrika Simonsson; varsham
Subject: RE: [NMusers] Dilemma with PPK parameters

Dear Ulrika.

I of course do agree with you about the relationships. My issue was: =
What is the relationship if any when the true model is let say a two =
compartmental model but you are using the one compartmental model with =
only one half life?

While the relationship Cl=V.K still handle (assuming linear kinetics), =
I do not think a similar simple relationship applies always between =
Clearance and this single half-life since your model is misspecified and =
the half-life you get is some sort of hybrid estimate. You then maximize =
the likelihood using any optimization procedure and will then get an =
estimate of this hybrid parameter by suing the formula T=0.693/K.

My point was that may be model misspecification could explain the =
Clearance issues addressed by our colleague.

Best

Serge Guzy, PhD

President, CEO; POP_PHARM; Inc.

From: Ulrika Simonsson [mailto:ulrika.simonsson
Sent: Friday, February 05, 2010 10:07 AM
To: Serge Guzy; varsham
Subject: RE: [NMusers] Dilemma with PPK parameters

Dear all,

Just a short note:

There is still a relationship between CL and half-lives for a =
two-compartmental model although not as simple as for a one =
compartmental model.

For a two-compartmental model you can derive the two half-lives =
(t1/2alpha and t1/2 beta) through either estimates of macro (CL, V2, V3, =
Q) or micro constants (K10,K21,K12) through (2 comp iv model):

K10=CL/V1

K12=Q/V1

K21=Q/V2

SUM=K10+K12+K21

ROOT=SQRT(SUM*SUM-4*K21*K10)

Alpha=0.5*(SUM+ROOT)

Beta=0.5*(SUM-ROOT)

t1/2alpha=LN(2)/Alpha

t1/2beta=LN(2)/Beta

Best regards,

Ulrika

Ulrika Simonsson, PhD

Assoc Prof of Pharmacometrics

Uppsala Pharmacometrics

Department of Pharmaceutical Biosciences

Uppsala University

BMC, Box 591, 751 24 Uppsala

Sweden

From: owner-nmusers
On Behalf Of Serge Guzy
Sent: den 5 februari 2010 18:17
To: varsham
Subject: Re: [NMusers] Dilemma with PPK parameters

I did not see the data but could you envisage that you have may be model =
misspecification. Half life relationship to clearance applies for =
example to the one compartmental model assumption. What if you have =
multiple half lives? I would not expect a simple relationship between a =
model using one half life with clearance when the true model has =
multiple one.
As far as I know the non compartmental relationship applies to clerance =
with volume and elimination rate and assumes linear kinetics.
Best
Serge guzy,PhD
President,CEO,POPPHARM

----- Original Message -----
From: owner-nmusers
To: nmusers
Sent: Fri Feb 05 05:58:01 2010
Subject: [NMusers] Dilemma with PPK parameters

Dear Group:
I am seeking some help to logically explain the difference in CL of a =
drug between 2 groups who received the same drug for the same indication =
but one group had induced hypothermia (treatment-N=24) while the =
other did not (control-N=115).

The half life for control- 111hrs and treatment 129 hrs (roughly)- not =
statistically different.
However, the parameters:

Control Group Treatment group

CL- 0.000105 L/kg/hr (suspect) CL- 0.00467 L/kg/hr

Vd -0.733 L/kg Vd 0.876 L/Kg

I used the same model for both groups and the half life calc was part of =
the model. I have run the model for both multiple times using various =
theta values. each time the minimization is complete. The bootstrap for =
treatment group gives reasonably good agreement. The bootstrap for =
control parameters match well for Cl (0.000273 L/kg/hr) but not for Vd =
(0.416 L/kg).

Given the relationship between Vd and CL how is this possible? How can =
the half life be so close when there is such a huge difference in CL for =
both groups? Where am I going wrong?

Would appreciate any help anyone can provide.

Thanks!!

Varsha Mehta, MS(CRDSA), Pharm.D., FCCP
Clinical Associate Professor
Pharmacy, Pediatrics and Communicable Diseases
Clinical Pharmacist Neonatal Critical Care
University of Michigan
(O) 734-936-8985
(F) 734-936-6946
varsham

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Received on Fri Feb 05 2010 - 14:01:31 EST

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