# RE: Getting rid of correlation issues between CL and volume parameters

From: Matt Hutmacher <matt.hutmacher>
Date: Tue, 26 Nov 2013 09:41:17 -0500

Hi Jacob, and everyone,

Sorry to be unclear and if I have added any confusion. My derivation =
was for the oral/SC administration (into a depot compartment) case with =
no IV data and with no extra CL/V correlation. If there were extra =
correlation, the OMEGA matrix would look like

V11+VFF VFF+COV(eta1,eta2) VFF+COV(eta1,eta3) =
VFF+COV(eta1,eta4)
VFF+COV(eta2,eta1) V22+VFF VFF+COV(eta2,eta3) =
VFF+COV(eta2,eta4)
VFF+COV(eta3,eta1) VFF+COV(eta3,eta2) V33+VFF VFF =
VFF+COV(eta3,eta4)
VFF+COV(eta4,eta1) VFF+COV(eta4,eta2) VFF+COV(eta4,eta3) V44+VFF

which would not be identifiable without the IV data. In my opinion, if =
there is no IV data, the F is really just conceptual. It is a a way of =
thinking about certain covariates that affect both CL and V etc in an =
identical way. Parameterization using covariates (which I do often) and =
an eta on F is just a trick (in the no-IV data case) to get the OMEGA =
matrix as previously defined and to avoid having to specify eg, =
CL=THETA(1)/(1+THETA(2)*FOOD) V=THETA(3)/(1+THETA(2)*FOOD), in the =
model (which is equivalent). In this case, I am concerned about adding =
the extra eta on F to constrain the OMEGA matrix because of the whole =
identifiability issue. Plots would certainly be affected (there really =
aren't 3 etas in the non-IV data case). In there is no =
extra-correlation, and F is inducing a high degree of correlation, one =
might consider putting the eta's on V, K, K12 and K21. The variability =
of F would be lumped into V, and this would cancel from the K's allowing =
a diagonal matrix (note that one would need to be careful how one =
parameterized this and it does not preclude evaluating and estimating =
fixed effects on CL, V, etc.)

Best,
Matt

(I have trimmed some of the earliest emails from this note to ensure =
delivery).

-----Original Message-----
From: owner-nmusers
On Behalf Of Ribbing, Jakob
Sent: Tuesday, November 26, 2013 05:46
To: Mueller-Plock, Nele; Leonid Gibiansky; 'nmusers'
Cc: Ribbing, Jakob
Subject: RE: [NMusers] Getting rid of correlation issues between CL and =
volume parameters

Hi Nele,

I believe Matt's point was more to the situation where any remaining =
correlation between CL and V random components can not be accounted for =
by covariates, so that both eta on F and block2 on CL and V is used?

If eta on F and covariates takes care of the correlation between CL and =
V: I would say that you may get even more informative diagnostics with =
this implementation.
For example, if you have not yet taken dose/formulation into account and =
this affects only F, it would come out as a clearer trend on the eta1 =
(relative F). This would help in interpretation (but I would highlight =
Nick's earlier point that eta on F may capture other nonlinearities that =
are shared between CL and V; like degree of protein binding for a =
low-extraction drug).

Best

Jakob

-----Original Message-----
From: owner-nmusers
On Behalf Of Mueller-Plock, Nele
Sent: 26 November 2013 08:21
To: Leonid Gibiansky; 'nmusers'
Subject: RE: [NMusers] Getting rid of correlation issues between CL and =
volume parameters

Dear all,

Thanks for picking up this discussion, and bringing in so many points of =
view.
When I started the discussion I had in mind the physiological viewpoint, =
from which we know that if there is between-subject variability in F1, =
this must result in a correlation between volume and CL parameters. From =
the discussions I would conclude that the group would favor to account =
for this correlation via inclusion of ETA on F1 and then a coding of
FF1=EXP(ETA(1))
CL=THETA()*EXP(ETA())/FF1
V=THETA()*EXP(ETA())/FF1

whereas this does not mean that there is no additional correlation =
between the parameters which needs to be accounted for in the =
off-diagonal OMEGA BLOCK structure? Also, I am afraid I was not able to =
completely follow Matt's argumentation, but would also be interested to =