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Hi,
I have seen many PK publications where they say data is within two fold or three fold difference and
so the predicted data is acceptable. My question is what is the scientific basis of this statement?
Is two fold difference really an acceptable number? Appreciate any input on this.
Thanks
Thomasapy
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Dear Thomasapy:
A very good question! I agree with you that I would be very skeptical of such a statement. Do
you have a particular example in mind? However, many drugs do have quite a wide therapeutic window,
and these may be the ones they are talking about. Penicillin is probably one such example. However,
many other drugs such antibiotics can and often do have much narrower ranges of effect, and will
need individualized selection of target effect and/or serum concentration goals, and individualized
dosage regimens tailored to body weight, renal function, hepatic metabolism, to hit these chosen
target goals with maximum precision.
I remember a meeting of the IATDM-CT in DC in Sept 01, (the week of 9/11), when somebody got up
and talked about a new drug for transplant patients.. This drug was SO GOOD, he said, that it did
not need TDM, as the standard deviation of its apparent volume of distribution was only 25%! This
got my attention, and when he had finished, I said that if the SD was 25%, then 2 SD down was 50%,
and 2 SD up was 150 %, and did he really believe what he said? , I asked him if that really could
be, that a 3 fold difference inn Vd and/or serum concentration was really bioequivalent. The room
got very quiet and he didn't really say much. This may be another example of what concerns you. It
certainly concerned me.
Let's talk some more about precision in drug dosage.
Many PK/PD model systems are called parametric. That is, they assume that the model parameter
distributions are either normal, lognormal, or bimodal, for example. Their model parameters are
estimated as means and variances. The action taken (the dosage regimen) is taken based only on the
central tendencies of those assumed distributions, rather than on the entire distributions
themselves. In this case, there is no way to estimate and maximize the precision with which a dosage
regimen hits its desired target. The great majority of PK/PD population models are of this type.
In contrast, nonparametric (NP) population PK/PD models make no assumptions at all about the
shape. Instead of only estimating parameter means and covariances, they estimate the entire model
parameter distributions. These distributions are discrete, not continuous. Each distribution
consists of many discrete support points, up to 1 per subject studied in the population. Each point
has an estimate of each model parameter value, and an estimate of the probability of that support
point in the population.. These probabilities all sum to 1.0.
Now you can develop a maximally precise dosage regimen as follows, using multiple model (MM)
dosage design, as follows. A candidate dosage regimen is given to each support point. Each point
generates a profile of future serum concentrations into the future. At the time for which you have
chosen your target goal to be achieved, one can now compare the predictions generated by each
support point and compare them with the desired target. The distance of each prediction from the
target is squared and multiplied by the probability of each support point. This computes the
weighted squared error with which that regimen fails to hit the target. This process continues
until the dosage regimen is found which minimized that weighted squared error cost function. In this
way one now has developed the maximally precise regimen to give that patient.
This process does not come from the PK/PD community. Instead, it comes from the aerospace
community, which uses such strategies for flight control and spacecraft guidance systems. This is
why our Laboratory of Applied {Pharmacokinetics uses NP population models and couples this with
multiple model dosage design.
We try to use optimally designed protocols for monitoring patients with TDM, and we use Bayesian
analysis in a different way from most others. Instead of trying to compute the most likely maximum
aposteriori probability (MAP) point for each parameter, using conventional MAP Bayesian strategies,
we compute the entire most likely Bayesian posterior joint parameter density for each model
parameter. Those points in the original population model that predict the patient's TDM serum
concentrations well become much more probable. Those that do not become much less probable. In this
way the patient's Bayesian posterior joint density is found. This then is used to develop the
subsequent dosage regimen for that patient to hit most precisely whatever is selected as the next
target goal for that patient.
Yes, there are many drugs that have narrow windows for target goals. Also, in such situations,
it is also important to evaluate each patient's clinical sensitivity to the drug in question and to
select a target goal that may not be in the general therapeutic range, but which is an
individualized clinically selected target goal for that particular patient, based on your clinical
appraisal of the patient and his need for the drug and the expected risk of toxicity which you as a
clinician feel is the best overall for that patient. Then you turn to the software to develop the
MM dosage regimen to hit your individualized target with maximum precision.
Our USC Bestdose clinical software is designed to do just that. It is available, along with our
research Pmetrics package, for evaluation over our web site www.lapk.urg. Also there are many
references available there. Some others are:
1. Tatarinova T, Neely M, Bartroff J, van Guilder M, Yamada W, Bayard D, Jelliffe R, Leary R,
Chubatiuk A, Schumitzky A: Two general methods for population pharmacokinetic modeling:
non-parametric adaptive grid and non-parametric Bayesian. J Pharmacokinet Pharmacodyn. 2013
Apr;40(2):189-99. doi: 10.1007/s10928-013-9302-8. Epub 2013 Feb 13.
2. 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.
3. Jelliffe R: Some Comments and Suggestions Concerning Population Pharmacokinetic Modeling,
Especially of Digoxin, and its relation to Clinical Therapy. Therap. Drug Monit. 34: 368-377, 2012.
4. Walsh T, Goutelle S, Jelliffe R, Golden J, Little E, De Voe C, Mickiene D, and Conte J:
Intrapulmonary Pharmacokinetics and Pharmacodynamics of Micafungin in Adult Lung Transplant
Patients. Antimicrobial Agents and Chemotherapy, 54: 3451- 3459, 2010.
5. 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.
6. Neely M, Rushing T, Kovacs A, Jelliffe R, and Hoffman J: Voriconazole Pharmacokinetics and
Pharmacodynamics in Children. Clin. Inf. Dis. 50: 27-36, 2010.
7. Neely M, and Jelliffe R: Practical Therapeutic Drug Management in HIV-Infected Patients: Use
of Population Pharmacokinetic Models Supplemented by Individualized Bayesian Dose Optimization. J
Clin Pharmacol. 48: 1081-1091, 2008.
8. Macdonald I, Staatz C, Jelliffe R, and Thomson A: Evaluation and Comparison of Simple
Multiple Model, Richer Data Multiple Model, and Sequential Interacting Multiple Model (IMM) Bayesian
Analyses of Gentamicin and Vancomycin Data Collected From Patients Undergoing Cardiothoracic
Surgery. Ther. Drug Monit. 30:67–74, 2008.
9. Bondareva I, Jelliffe R, Gusev E, Guekht A, Melikyan E, and Belousov Y: Population
Pharmacokinetic Modeling of Carbamazepine in Epileptic Elderly Patients: Implications for Dosage. J.
Clin. Pharmacol. Therap., 31: 211-221, 2006.
10. 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.
11. Zhu M, Burman W, Starke J, Stambaugh J, Steiner P, Bulpitt A, Auclair B, Beerning S, Jelliffe
R, Jaresko G, and Peloquin C: Pharmacokinetics of Ethambutol in Children and Adults with
Tuberculosis. Int. J. Tuberc. Lung Dis. 8: 1360-1367, 2004.
12. Bayard D, and Jelliffe R: A Bayesian Approach to Tracking Patients having Changing
Pharmacokinetic Parameters. J. Pharmacokin. Pharmacodyn. 31 (1): 75-107, 2004.
13. Bondareva I, Jelliffe R, Sokolov A, and Tischenkova I: Nonparametric Population Modeling of
Valproate Pharmacokinetics in Epileptic Patients using Routine Serum Monitoring Data: Implications
for Dosage. Journal of Clinical Pharmacy and Therapeutics, 29: 1-16, 2004.
14. Bondareva I, Jelliffe R, Sokolov A, and Tischenkova I: Nonparametric Population Modeling of
Valproate Pharmacokinetics in Epileptic Patients using Routine Serum Monitoring Data: Implications
for Dosage. Journal of Clinical Pharmacy and Therapeutics, 29: 1-16, 2004.
15. Martin P, Bleyzac N, Souillet G, Galambrun C, Bertrand Y, Maire P, Jelliffe R, and Aulagner
G: Relationship between CsA trough blood concentration and severity of acute graft-versus-host
disease after paediatric stem cell transplantation from matched sibling or unrelated donors.
Bone Marrow Transplantation 32: 777-784, 2003.
16. Jelliffe R: Estimation of Creatinine Clearance in Patients with Unstable Renal Function,
without a Urine Specimen. Am. J. Nephrology, 22: 320-324, 2002.
17. Bleyzac N, Souillet G, Magron P, Janoly A, Martin P, Bertrand Y, Galambrun C, Dai Q, Maire P,
Jelliffe R, and Aulagner G: Improved clinical outcome of paediatric marrow recipients using a test
dose and Bayesian pharmacokinetic individualization of busulfan dosage regimens. Bone Marrow
Transplantation, 28: 743-751, 2001.
18. Bondareva I, Sokolov A, Tischenkova I, and Jelliffe R: Population Pharmacokinetic Modelling
of Carbamazepine by using the Iterative Bayesian (IT2B) and the Nonparametric EM (NPEM) algorithms:
Implications for Dosage. J. Clin. Pharm. Ther. 26: 213-223, 2001.
19. Milman M, Jiang F, and Jelliffe R: Creating Discrete Joint Densities from Continuous ones:
the Moment-Matching, Maximum Entropy Approach. Computers in Biol. Medicine, 31: 197-214, 2001.
20. Jelliffe R: Goal-Oriented, Model-Based Drug Regimens: Setting Individualized Goals for each
Patient. Therap. Drug Monit. 22: 325-329, 2000.
21. 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.
22. Corvaisier S, Maire P, Bouvier d'Yvoire M, Barbaut X, Bleyzac N, and Jelliffe R: Comparisons
between Antimicrobial Pharmacodynamic Indices and Bacterial Killing as Described by Using the Zhi
Model. Antimicrobial Agents and Chemotherapy 42: 1731-1737, 1998.
23. Jelliffe R, Schumitzky A, Bayard D, Milman M, Van Guilder M, Wang X, Jiang F, Barbaut X, and
Maire P: Model-Based, Goal-Oriented, Individualized Drug Therapy: Linkage of Population Modeling,
New "Multiple Model" Dosage Design, Bayesian Feedback, and Individualized Target Goals. Clin.
Pharmacokinet. 34: 57-77, 1998.
24. Maire P, Barbaut X, Vergnaud JM, El Brouzi M, Confesson M, Pivot C, Chuzeville M, Ivanoff N,
Brazier JL, and Jelliffe RW: Computation of Drug Concentrations in Endocardial Vegetations in
Patients during Antibiotic Therapy. Int. J. Bio-Med. Comput. 36: 77 -85. 1994.
25. Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis P, Barbaut X, and
Tahani B: Individualizing Drug Dosage Regimens: Roles of Population Pharmacokinetic and Dynamic
Models, Bayesian Fitting, and Adaptive Control. Therapeutic Drug Monitoring, 15: 380-393, 1993.
I know this is a long reply, and maybe more than you wanted. But I agree strongly with you that
precision is most important. This is why, for over many years now, we have taken this approach of
NP pop modeling, MM dosage design, and maximally precise open loop stochastic Bayesian adaptive
control. The evidence simply shows that parametric population PK/PD models and MAP Bayesian adaptive
control will never be aware of the issue of evaluating precision and will be totally incapable of
evaluating and maximizing it with dosage regimens.
Very best regards,
Roger Jelliffe
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