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Individualizing Dosage Regimens: Learning about our pa8ents op8mally while trea8ng them at the same 8me, achieving maximum
precision throughout. Roger W. Jelliffe, M.D.
Professor of Medicine Emeritus, Founder and Director Emeritus,
Laboratory of Applied Pharmacokinetics, USC Keck School of Medicine
Children’s Hospital of Los Angeles Los Angeles, CA, USA
[email protected] www.lapk.org
Our Lab
Fearless Founder Alan Schumitzky
Mike Van Guilder Aida Bustad Dave Bayard
Michael Neely – Hot new blood!
Supported in part by NIH grants EB005803, GM 068968, and HD070886
Tasks to be done for each pa8ent
• 1 – First, learn op8mally about the drug • 2 – Then, op8mize the ini8al dosage regimen • 3 – Then, learn about the drug in that
pa8ent op8mally while you must treat him/her at the same 8me
• 4 – Con8nue learning and trea8ng op8mally throughout the course of treatment.
• 5 – There are tools for each part of this task.
Tool #1 - Nonparametric (NP-UPD) PK/PD models
• The most likely (ML) popula8on parameter distribu8ons, given the data, “CAN BE FOUND” in a discrete collec8on of support points, up to 1 point per subject.
• Each NP model parameter support point contains an es8mate of each model parameter value, and of the probability of that collec8on of values in the popula8on.
• No assump8ons need to be made about the shape of the distribu8ons in the popula8on. They use UNCONSTRAINED parameter distribu8ons (UPD).
What is the IDEAL Popula8on Model?
• The correct structural PK/PD Model. • The collec8on of each subject’s exactly known parameter values for that model.
• Therefore, mul8ple discrete individual models, one model from each subject.
• Usual con8nuous sta8s8cal summaries can also be obtained, but usually will lose info.
• NP -‐ UPD models best approach this una_ainable ideal.
An NP-‐UPD Popula8on Model, made by Mallet
Tool # 2 - Multiple Model (MM) dosage design
Select your pa8ent’s specific therapeu8c target goal – not a window.
Use all mul8ple models in NP pop model (the blue slide). Give a candidate dosage regimen to each model. Predict future results from each model, each predic8on weighted by its probability.
Compute WEIGHTED SQUARED ERROR of the predic8ons overall failure to hit the target.
Find the regimen having LEAST weighted squared error in target goal achievement. The most precise regimen.
It uses the en8re distribu8on of each parameter, not just a single value summary of some assumed distribu8on.
5/1/15 8
Con8nuous IV Vanco. Predic8ons when regimen based on CPD parameter means is given to all support points
5/1/15 9
Vanco, con8nuous IV. Predic8ons when MM regimen is given to all support points
No8ce that… The dose itself is a most important tool to minimize pa8ent variability in response.
This is at least as important as having addi8onal covariate informa8on.
With parametric models you will never be aware of this issue, and never be able to do it.
Jelliffe R: Goal-‐Oriented, Model-‐Based Drug Regimens: SePng Individualized Goals for
each PaTent. Therap. Drug Monit. 22: 325-‐329, 2000. Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target
Goals most Precisely using Nonparametric Compartmental Models and "MulTple Model" Design of Dosage Regimens. Therap. Drug Monit. 22: 346-‐353, 2000.
Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric PopulaTon Methods: Their ComparaTve Performance in Analysing a Clinical Data Set and Two Monte Carlo SimulaTon Studies. Clin. Pharmacokinet., 45: 365-‐383, 2006.
Tool # 3 - Correct description of assay errors Describe Assay Errors by 1/variance, NOT CV%.
• Get es8mate of SD for every TDM serum level going through the lab assay system.
• Variance = SD2
• 1/Variance = correct Weight. • Assay Error Polynomial (AEP):
SD = A0C0 + A1C1 + A2C2 + A3C3 • Store it in the solware. • No need to censor low data any more • No LLOQ! This is an illusion from using CV%. 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 PopulaTon PharmacokineTc and Dynamic Models, Bayesian FiPng, and AdapTve Control. TherapeuTc Drug Monitoring, 15: 380-‐393, 1993.
21.15
10.33 9.9663
14.323
0.56708
0.423024 0.413376
0.7973
1.7188
0
0.2
0.4
0.6
0.8
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1.2
1.4
1.6
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0 2 4 8 12
Concentration (ug/ml)
SD
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25
CV
%
CV%
SD
Tool # 4 – Estimate CCr from changing SCr
0.4W(C2 – C1) = P – Cavg x CCr x 1440 (Daily change = Produc8on – Excre8on)
• Where P is daily crea8nine produc8on (see ar8cle) C1 and C2 are SCr in mg/100ml, W is weight (in hundreds of grams), and CCr is crea8nine clearance (in hundreds of ml/min).
Then adjust for 1.73 M2 BSA Jelliffe R: Es8ma8on of Crea8nine Clearance in Pa8ents with Unstable
Renal Func8on, without a Urine Specimen. Am. J. Nephrology, 22: 3200-‐3204, 2002.
Es8ma8on errors in CCr
CV of serum crea8nine = ± 5% CV of urine crea8nine = ± 8%
Then if collect 24 hr urine with CV = ± 5%, 52=25 twice = 50, plus 82=64, = 114.
SQRT 114 ~ 11 So the classical CCr has a CV = ± 11%,
or 95% conf limits of ± 22%
Es8mated vs Measured CCr
Tool # 5 - MM Optimal TDM protocols
Do NOT wait, and do not get only steady state trough levels! Start right with the very first dose! Consider 1 sample for each model parameter to be es8mated. Use, for example, D-‐op8mal design strategies. There is an
op8mal 8me to sample for each model parameter value, given a certain dosage regimen format.
Olen, get a peak and a sample at about 1/3 the peak. Be_er, consider the new MM-‐op8mal design, op8mizing the
8mes to maximize precision of dosing to desired target conc, or AUC, for example.
Do NOT waste money, effort, and pa8ent care with poor designs. The TDM community can do a MUCH BETTER job here.
5/1/15 USC LAPK 17
Best 8me to sample
For a constant assay error, the greatest change in serum conc when volume of dist changes is at the true peak, not later. Samples near the peak are most informa8ve about Vd.
Example of D-‐OpTmal Design: Finding Volume Vd from a First-‐Order Response
5/1/15 USC LAPK 18
The greatest change in serum conc from a change in the Kel is when the serum conc is 36% of the original peak value. Samples near 1.44 half-‐8mes are most informa8ve about Kel.
Example of D-‐OpTmal Design: Finding Kel from First-‐Order Response
Best 8me to sample
Mul8ple Model Op8mal Design
– Optimizing experimental design this way is fundamentally different from optimizing experimental design to estimate patient’s parameters, as in D-optimal design, etc.
0.020.04
0.060.08
0.10.12
1.5
2
2.50
0.005
0.01
0.015
0.02
Vs
10 Model Prior
Kel
Prob
MM Prior
VK
1 - Randomly sample a population model support point. 2 - Give it a simulated dose and some simulated observations, at a specific set of candidate sampling times, with assay noise. 3 - Get the MAP Bayesian posterior estimate. 4 – See if that MAP estimate corresponds to the original point (correct classification) or some other point (incorrect). 5 – Repeat steps 1-4 many times. See the percent of times the classification is correct. 6 – Do this for many candidate designs. 7 - Find the sampling design that minimizes the percent incorrect classification.
20
• Model Response Separation r(t) is the separation between two model responses at a given time t
• Defines natural statistic for discriminating between two models • Bayes Risk of mis-classification is shown in gray area
Model Response Separation r(t)
0 2 4 6 8 100
0.2
0.4
0.6
0.8
1Model Responses
Time
Model 1 ReponseModel 2 Response
r(t) = response separation
-1 -0.5 0 0.5 1 1.50
0.5
1
1.5
2Two-Model Classification Problem
r(t)=response separation
Bayes Risk
• Bayes Risk (gray area) decreases as response separation r(t) increases
• Models are best discriminated by sampling at a time t that maximizes r(t)
Pull Gaussians apart to minimize gray area
21 21
ED EID API MMOpt Invariant under regular linear reparametrization*
Yes Yes
Yes
Yes
Invariant under regular nonlinear reparametrization*
No No
Yes Yes
Allows taking fewer than p samples, p= # of parameters
No
No
No
Yes
Can handle heterogeneous model structures
No
No
No
Yes
Gives known optimal solution to 2-model example*
No
No
No
Yes
Captures main elements of minimizing Bayes risk
No
No
No
Yes
Comparison Table
*Proved in Bayard et. al., PODE 2013 [23]
22
Weighted MMOpt
Optimal Dosing
Parameter Estimation
Metric Estimation
23 23
Model Parameters # K V
1 0.090088 113.7451
2 0.111611 93.4326
3 0.066074 90.2832
4 0.108604 89.2334
5 0.103047 112.1093
6 0.033965 94.3847
7 0.100859 109.8633
8 0.023174 111.7920
9 0.087041 108.6670
10 0.095996 100.3418
PK Population Model with 10 Multiple Model Points - First-Order PK Model
0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
3.5All subject responses
Time (hr)
Conc
entra
tion
0 5 10 15 200
50
100
150
200
250
300
350
400Dose Input
Time (hr)
Units
Dose input = 300 units for 1 hour, starting at time 0
Model Responses • Grid points 15 min apart • MMOpt optimized over time grid
24
Unweighted MMOpt for PK Es8ma8on • Summary of optimal 1,2 and 3 sample designs applied to PK Estimation
• 1 Sample Design: MMOpt performance equals Bayesian optimal design (both have Bayes Risk of 0.5474).
• MMOpt performance improves on EDopt design for 2 and 3 sample designs – 2 Sample Design: Bayes Risk of 0.29 versus 0.33 – 3 Sample Design: Bayes Risk of 0.23 versus 0.26
• All results are statistically significant to p<0.0001
25
Weighted MMOpt for AUC Control
26
Weighted MMOpt for AUC Control (Cont’d) • Summary of optimal 1,2 and 3 sample designs applied to AUC control
• 1 Sample Design: weighted MMOpt performance approximates that of the weighted Bayesian optimal design (RMS error of 3.62 versus 3.77 AUC units)
• MMOpt performance improves on EDopt design for 2 and 3 sample designs – 2 Sample Design: RMS error of 2.11 versus 2.62 (units of AUC) – 3 Sample Design: RMS error of 1.70 versus 2.42 (units of AUC)
• All results are statistically significant to p<0.0001
Tool # 6 - NP Bayesian adaptive control tools
Previous data = past experience = popula8on model. 1 – Pop model is the Bayesian Prior (prior to now) –
es8mates probability of model parameters based on past experience.
2 -‐ New data from pa8ent. Recompute param distribu8ons based on past + new.
3 -‐ This is the Bayesian posterior – the individualized pt model.
An Ini8al Gentamicin Predic8on based on popula8on model prior: goal = 12 ug/ml
95 Percentile Distance
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Gevng Individualized Bayesian Models in Pa8ents – 4 ways
1. MM Bayesian posteriors 2. MAP Bayesian Posteriors 3. Hybrid Bayesian posteriors. 4. Interac8ng MM (IMM) Sequen8al
Bayesian Posteriors.
Es8mates with MM posterior
Hybrid Bayesian posterior • Start with MAP Bayesian. It reaches out, but not fully (shrinkage). Pop prior holds it back.
• Add new support points nearby, inside and mostly outside, to AUGMENT the pop model for the coming new pa8ent data.
• Then do MM Bayesian on ALL the support points.
• Can also use for pa8ents without a popula8on model.
Pa8ent on digoxin and quinidine -‐ Hybrid Bayesian posterior plot
Pa8ent on digoxin and quinidine -‐ Hybrid Bayesian Posterior Joint Density
Interac8ng Mul8ple Model (IMM) Sequen8al Bayesian analysis.
• All other fivng methods assume fixed parameter values throughout the data analysis.
• IMM lets param distribu8ons change with each new data point to get sequen8al Bayesian posterior distribu8ons.
• IMM tracks Gent and Vanco behavior best in ICU pa8ents.
• Bayard D, and Jelliffe R: A Bayesian Approach to Tracking PaTents having Changing PharmacokineTc Parameters. J. Pharmacokin. Pharmacodyn. 31 (1): 75-‐107, 2004.
• Macdonald I, Staatz C, Jelliffe R, and Thomson A: EvaluaTon and Comparison of Simple MulTple Model, Richer Data MulTple Model, and SequenTal InteracTng MulTple Model (IMM) Bayesian Analyses of Gentamicin and Vancomycin Data Collected From PaTents Undergoing Cardiothoracic Surgery. Ther. Drug Monit. 30:67–74, 2008.
By avoiding clearance and using Vs and Ks instead, the 2 separate issues of fluid balance and drug eliminaTon can be managed best.
TDM up to now has been mostly for achieving general serum concentra8on
guidelines. • But now, what about seeing each pa8ent as a unique individual?
• Pa8ents vary greatly in their sensi8vity to serum concentra8ons.
• Also, digoxin clinical effect does not correlate with serum concentra8ons, but with peripheral, nonserum compartment, concentra8ons.
Serum digoxin concentrations in nontoxic and toxic patients found by Doherty [1]. Note great overlap between therapeutic and toxic concentrations, and the fact that approximately half the patients with serum levels of 3.0 ng/ml or more were NOT toxic. Also note that the incidence of toxicity is very low for levels up to 1.0 ng/ml, moderate (though significant) for levels of 1.0 to 2.0, more above 2.0, but still only about 50% for levels of 3.0 ng/ml or greater.
Management of digoxin therapy
• Two compartment NP pop model. • Clinical effect correlates with peripheral compartment concentra8ons, not with central (serum) concentra8ons.
• Plan regimens either for trough serum concentra8ons (usually 0.7 ng/ml) or peak peripheral concentra8ons (usually 7 ng/gm, 7 hrs aler an oral dose).
• But pa8ents with aur fib, flu_er olen need 9-‐18 ng/gm to convert and stay converted.
Bauman et al: Am.J.Cardiovascular Drugs 2006; 6:
Literature data
• Study Digoxin /Placebo Periph conc. P • Falk et al 9/18 v 8/18 8.0 NS • DAAF 60/117 v 56/122 9.23 NS • Jordaens et al 9/19 v 8/20 11.25 NS
Conversion to RSR • Hou et al 17/24 (71%) 9.0 <0.05 • Weiner et al 40/47 (85%) 13.9 <<0.005
(Clinical PharmacokineTcs (DOI) 10.1007/s40262-‐014-‐0141-‐6)
New onset AF – SCr = 0.8, Serum concentra8ons over 8me
New onset AF – SCr = 0.8, Peripheral concentra8ons over 8me
New onset AF – 96 F SCr = 8, CCr = 3.7 Serum concentra8ons over 8me
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New onset AF – 96 F SCr = 8, CCr = 3.7 Peripheral concentra8ons over 8me
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Problems with educa8on in drug therapy
• No one teaches meaningful PK in med schools anywhere
• No one knows anything about dosage individualiza8on
• Their only informa8on comes from the drug companies
• Poor illiterate med schools! • Poor illiterate docs! • Poor poorly treated pa8ents! • Rich and richer drug companies! • Rich and richer lawyers!
Problems with drug marke8ng
Suppressing their own science for marke8ng!
• They have the data for each pa8ent -‐ • Outcome, and An8platelet effect. • They can easily find the an8platelet effect associated with best outcome, least bleeding.
• They can set a target an8platelet effect, • And dose each pa8ent to achieve it! • Why do they adver8se that this is NOT NEEDED?? Why?? Think about it!
• WE BADLY NEED INDIVIDUALIZED DOSAGE.