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I have two questions:
A) I am going through the metrum institute videos about population PK PD analysis. In Lab 2
spfreload=1), the instructor uses a tool called solver to perform iterations to determine the least
objective function value. The instructor is using a Mac (open office). How can I get that tool or
add-in in excel?
B) In the weighted least square example discussed in the video, the weighting used is (1/observed
concentration). What are the other common weighting strategies? Is there any specific reason to
prefer one weighting strategy over the other?
Manushree Bharadwaj, BVSc, PhD Candidate
Graduate Teaching Assistant
Department of Physiological Sciences
Center for Veterinary Health Sciences
Oklahoma State University
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From: William Wolowich
Solver is an add-in that you need to activate in excel. It is part of the analysis pack, you might
have to download it from the microsoft site if it doesn't show up in your add ins list.
Weighting for regression is mostly empiric. Other common schemes include 1/obs^2, 1/predicted, and
1/ predicted^2. The last two are iterative.
From: Nick Holford
If you look at this web page:
and find the section on "Error Models and Objective Functions" there is a link to:
On that web page you will find a description of how to install the Excel solver (from Excel) (look
at the Excel section of the web page).
If you follow the instructions for using the solver (on this web page) you can find examples which
show how different weighting schemes affect parameter estimation. You may also wish to look at
which gives some additional explanation about objective functions and weighting.
From: Roger Jelliffe
A – What is probably happening is that the differential equations must be solved numerically. This
is done by differential equation solvers - integration routines to solve the differential
equations. Why are you using something in Excel? I am not clear.
As to population analysis, 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.
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.
Pmetrics is a freely available software package, embedded in R. The papers above compare the
strengths and weaknesses of parametric versus nonparametric approaches to population modeling.
Nonparametric approaches get more likely results because they do not constrain the model parameter
distributions into some assumed shape like normal or lognormal. The shape is determined only by the
You can get Pmetrics at www.lapk.org. Rather than minimize a least squares objective function as
your instructor appears to want to do, Pmetrics maximizes the likelihood of the results given the
data. Most likely results, not just the best fit. If you assume a normal distribution for the
population parameters, they will be the same. If you release the distributions to be free of those
constraining assumptions of normality, as with Pmetrics, then the likelihood is the better objective
Further, parametric population models will not permit maximally precise drug dosing for optimal
patient care, as they use only a single summary value for each model parameter, rather than the
entire distribution itself, as the nonparametric approach does. This is called Multiple Model (MM)
dosage design. You might look at
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.
B – The weighting is not clear. Why is he using 1/the concentration? What you want to do is to get
real. The proper way to weight the data is by the reciprocal of the variance of the measured
concentration. A lot of people weight by 1/observed conc or 1/conc squared, but the really correct
thing is to use 1/variance of the assay measurement itself – whatever it is. You might look at
almost any statistics book, and find that the proper measure of precision of a measurement whose
error has a Gaussian distribution is by the reciprocal of the variance of the assay measurement at
that value. You also might look at
Jelliffe R, Schumitzky A, Bayard D, and Neely M: Describing Assay Precision - Reciprocal of
Variance is much better than CV%. Therapeutic Drug Monitoring. 06/2015; 37(3):389-94.
Also, for more general references, you might look at
Jelliffe R: Estimation of Creatinine Clearance in Patients with Unstable Renal Function, without a
Urine Specimen. Am. J. Nephrology, 22: 320-324, 2002.
Jelliffe R: Goal-Oriented, Model-Based Drug Regimens: Setting Individualized Goals for each Patient.
Therap. Drug Monit. 22: 325-329, 2000.
Jelliffe R, Schumitzky A, Bayard D, Leary R, Botnen A, Van Guilder M, Bustad A, and Neely M: Human
Genetic variation, Population Pharmacokinetic – Dynamic Models, Bayesian feedback control, and
Maximally precise Individualized drug dosage regimens. Current Pharmacogenomics and Personalized
Medicine, 7: 249-262, 2009.
Many approaches to modeling are not oriented to any clinical application, as they mainly
serve the interests of the pharmaceutical industry. You will go to meeting after meeting, and you
will see everyone talking about this or that model of some drug, but very few are really oriented
toward being really maximally useful to anyone but the industry. It is mainly for this reason that I
stopped going to the PAGE meetings a number of years ago. Maybe I will go again sometime, but only
time will tell.
In the meantime, if you are really interested in population PK/PD modeling, I would strongly
urge you to look at Pmetrics, which is much better suited to clinical applications and to being
socially useful, in addition to being, in my view, better science – more likely results, maximally
precise dosage regimens to hit target goals best.
Hope this helps,
Very best regards,
From: Edward O'Connor
It is an add on no charge. Open options in excel and check for add ons. Select solver you might
also want analysis tool pal
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Solver is part of data analysis pack of Excel, personally I found it very useful when trying to
solve complex equations. You have to open Option---> add in ---> click on data solver and click Go
close the excel program and reopen you will see solver is added you are good to go..... Happy baby
steps into Modeling and Simulation.
Prasad NV Tata, Ph.D., FCP
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For you interest, if you wish, you can see the Solver Add-in in action assisting in my identical
Excel Win and Mac versions of PK Solutions - pharmacokinetics data analysis the easy way for
education and research.
Dr. David S. Farrier
Founder / Owner
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The following three papers may interest you as they utilize Solver in Excel:
1) Meineke, I. & Brockmöller, J. "Simulation of complex pharmacokinetic models in Microsoft Excel."
Computer Methods and Programs in Biomedicine, 88: 239-245 (2007)
The program described in this paper, "Pk-engine", allows for the simulation of various
pharmacokinetic models, but no modeling.
2) Zhang, Y. et al. "PKSolver: An add-in program for pharmacokinetic and pharmacodynamic data
analysis in Microsoft Excel." Computer Methods and Programs in Biomedicine, 99: 306-314 (2010);
3) Wu, B. & Hu, M. "A Useful Microsoft Excel Add-in Program for Pharmacokinetic Analysis."
Pharmaceutica Analytica Acta, doi:10.4172/2153-2435.S11-002 (2011) Available online at:
The program ("XlSimEst") made available by Wu and Hu, unlike "PKSolver", both accepts user-defined
models and provides standard error estimates for the fitted PK parameters.
Peter W. Mullen, PhD, FCSFS
KEMIC BIORESEARCH (www.kemic.com)
P.O. Box 878
22 Nichols Ave.
Nova Scotia, B4N 4H8
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