RE: Getting rid of correlation issues between CL and volume parameters
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).
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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 hear if implementing the code
above might lead to misleading plots.
Thanks and best
Nele