- On 11 Sep 2013 at 10:08:40, Thomas Nadakal (thomasapy.-at-.yahoo.com) sent the message

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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 - On 11 Sep 2013 at 20:55:59, Roger Jelliffe (jelliffe.aaa.usc.edu) sent the message

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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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