[NMusers] IOV with Mu modeling, using EM algorithms

From: Pyry Välitalo <pyry.valitalo_at_gmail.com>
Date: Thu, 16 Feb 2017 13:07:01 +0200

Dear NMusers,

Based on the NONMEM Inter-Occasion Variability (IOV) example control
stream, located at NONMEM_install_dir/examples/example7.ctl, it seems that
it is currently not possible to Mu parameterize IOV in NONMEM 7.3. The
relevant lines from example7.ctl control stream are copypasted below:

MU_2=THETA(2)
CLB=DEXP(MU_2+ETA(2))
DCL1=DEXP(ETA(3))
DCL2=DEXP(ETA(4))
DCL3=DEXP(ETA(5))
DCL=DCL1
IF(TIME.GE.5.0) DCL=DCL2
IF(TIME.GE.10.0) DCL=DCL3
CL=CLB*DCL

My question is: Does this mean that the updating procedure of IIV/IOV
parameters (omegas) does not have the EM efficiency when IOV is present? If
we had no IOV, then I think NONMEM would calculate for the update step that
THETA(2)=E(LOG(CLB))
OMEGA(2,2)=VAR(LOG(CLB))
where E() refers to computing mean and VAR() refers to computing variance.
These expressions are useful, because with these there is no need to find
the best THETA(2) or OMEGA(2,2) values with numerical optimization. It
saves computation time that just mean and variance can be taken.

Now, with the IOV model, I think the updating could be accomplished with
THETA(2)=E(LOG(CLB))
OMEGA(2,2)=VAR(LOG(CLB))
OMEGA(3,3)=VAR(LOG(CL))-OMEGA(2,2)

However, I'm not sure what actually happens inside NONMEM.
-Is the updating done like this, or does the lack of MU referencing in IOV
force the estimation process to use gradient descent for estimation of
some/all parameters?
-If gradient descent is used, how dramatically does it reduce the speed of
the estimation process?
-If MU referencing is impossible with the presence of IOV, would it then be
possible to use occasion variable OCC as the ID, and somehow convince
NONMEM not to reset the compartments when OCC changes? This way, MU
referencing could be used for the OCC variable, and IIV would be just
ignored for that run. This would be only for exploratory runs, of course.

For this discussion, let's assume that
-Adequate data exist to estimate occasion-specific random effects.
-The IOV parameters are critical for the model to be able to describe the
data nicely (e.g. large IOV in absorption)

Looking forward to hear your thoughts! Best wishes,
Pyry Välitalo
Postdoc, Leiden University, Division of Pharmacology
Senior Scientist, Orion Pharma, Drug Disposition and Pharmacometrics

Received on Thu Feb 16 2017 - 06:07:01 EST

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