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1. What method of population modeling gives you the most likely results given the data? NONMEM,
other parametric population modeling approaches, or what? Would you be surprised if it was Pmetrics?
And why is this?
2. What type of population model lets you develop dosage regimens which are specifically
designed to hit a clinically selected target goal (serum concentration, effect, etc.) with maximum
precision? And why is this?
About question #1 - Parametric population modeling approaches ASSUME that the model parameter
distributions have a certain shape. They are ASSUMED to be normal, lognormal, Poisson, etc. The
parameters estimated are those in the equation which determines the specific shape of the
distribution (mean, SD, covariances, etc.). They can also be bimodal, but the ASSUMPTION must be
made in advance of the analysis, which is then CONSTRAINED by that assumption, and because of this
constraint, will never obtain the most likely parameter distributions given the data.
On the other hand, nonparametric modeling approaches such as the NPML of Mallet and Pmetrics of
Neely et al, make no such constraints on the model parameter distributions. They use UNCONSTRAINED
PARAMETER DISTRIUTIONS (UPD’s). Because of this, they always get results that are more likely. You
might look at
Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric
Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte
Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
About question #2 – With parametric pop models, one can only take clinical action based on the
estimated CENTRAL TENDENCIES of those ASSUMED model parameter distributions. There is only one value
for each parameter. ONLY ONE dosage regimen gets evaluated. It is ASSUMED to hit the target exactly.
On the other hand, what would be the very best population model one could ever have? Somehow, one
might pick up the red phone and call GOD. HE would then tell us each subject’s EXACT model parameter
values. One can never do better than to know the exact values for each subject. The distribution
would be discrete, NOT continuous. As the number of subjects studied approaches infinity, the
distribution, with all its genetic subpopulations, would converge to the true distribution.
In contrast, if a parametric model with an ASSUMED distribution were to be used, the distribution,
with infinite subjects, would converge to the most likely ASSUMED distribution which fitted the data
the best. But that is all.
Models with UPD’s use the ENTIRE model parameter distributions, which consist of many support
points, up to one for each subject studied. With them, one can use multiple model (MM) dosage
design. It works as follows. Give a candidate regimen to each model support point. Each point
generates predictions into the future. At the time the specific target goal is desired, it is easy
to calculate the weighted squared error (each support point is weighted by its probability in the
population) of the failure of the regimen to hit the target. Then one simply finds the regimen which
minimizes the weighted squared error with which the target goal is hit. Now, we have the most
precise dosage regimen.
This is a unique strength of models with UPD’s. If one uses parametric models, one NEVER becomes
aware of this issue, and can do NOTHING to maximize the precision of any dosage regimen, as there is
no provision to do this. UPD models, yes. Parametric models, no. A reasonable reference is
Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most
Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.
Also, you might look at
Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers and
Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation
Package for R. Therap. Drug Monit. 34: 467-476, 2012.
All best wishes for the Holidays,
Roger W. Jelliffe, M.D., F.C.P., F.A.A.C.P.
Professor of Medicine Emeritus,
Founder and Director Emeritus
Laboratory of Applied Pharmacokinetics
USC School of Medicine
Consultant in Infectious Diseases,
Children’s Hospital of Los Angeles
4650 Sunset Blvd, MS 51
Los Angeles CA 90027
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