1. Population PK/PD modelling: Software Choices
ESCMID Postgraduate Technical Workshop
Advanced Antimicrobial Pharmacokinetic and Pharmacodynamic Modelling & Simulation
Population PK/PD modelling: Software Choices
Monday, October 6th, 2014 Liverpool, UK
Jürgen B Bulitta, PhD Senior Research Fellow Monash University, Melbourne, Australia
Adjunct Assistant Professor SUNY Buffalo, NY, USA
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Outline
“The right task”
Software tools for
Non-compartmental analysis
Exposure-response & exposure-toxicity relationships
Simulation of PK and PK/PD profiles
Estimation of PK and PK/PD model parameters
Optimal dosing of a patient population (Monte Carlo simulation)
Optimal dosing of individual patients
Optimal clinical trial design
Clinical trial simulation
Concluding remarks
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3. Most appropriate tool for the required task
Define and discuss the objective(s)
Evaluate the time available Gain a thorough understanding of the data Discuss / select relevant approaches  May need to revisit the approach / time
Select the most suitable software tool and data analytical approach.
Secondary, as long as one of suitable tools is chosen and used by a skilled person. Plausibility checks!
A model without a task is not very useful.
Often, several tools can yield suitable results.
There is no single tool which does it all!
Communication of approach & results is critical!
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4. Relevant tasks for anti-infective PK/PD
Determine Cmax, AUC, T>MIC, clearance (CL), volume (Vd), and other parameters via non-compartmental analysis (NCA).
Fit an exposure-response (or exposure-toxicity) relationship correlating fAUC/MIC with bacterial counts at 24 h, for example.
Simulate antibiotic concentrations for dosage regimens in mice or humans.
Develop a population PK or PK/PD model to:
Propose optimized empiric dosage regimens for a patient population via Monte Carlo simulations.
Identify covariates that affect dosing (e.g. renal function, body size).
Evaluate proposed mechanisms of action, resistance, and synergy.  To design mechanistically optimized (combination) dosage regimens.
Achieve therapeutic target goals most precisely in an individual patient. Account for MIC / pathogen, renal function, other diseases, etc.
Propose a clinical trial design that provides safe and effective regimens and optimally informs a PK or PK/PD model for patients.
Evaluate the robustness of a clinical trial design.
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5. Tasks and Tools Optimal dosing NCA (Cmax, AUC, T>MIC
Exposure response
Safety model / relationship
Simulation of drug concentrations
(Population) PK model
(Population) PD model
Predict effect and safety for in vitro and animal models, and ultimately patients
Optimal dosing
Robust Clinical Trial design
Optimal trial design  PK/PD model
Individual patient
Patient population
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6. Optimal dosing NONMEM, ADAPT, S-ADAPT, Pmetrics/USC*PACK, Monolix,
Phoenix/NLME, WinBUGS, SAS, Matlab, R-packages, others
WinNonlin, Kinetica, others
NCA (Cmax, AUC, T>MIC
Any (!) estimation tool
Exposure response
Safety model / relationship
(Population) PK model
(Population) PD model
Berkeley Madonna
Any tool for sim. / est.
Skill level:
Basic
Intermediate
Advanced
Simulation of drug concentrations
Predict effect and safety for in vitro and animal models, and ultimately patients
PFIM, WinPOPT, POPT, PopDes, POPED, etc.
Clinical Trial Simulator
Optimal dosing
BestDose ID-ODS DoseMe TCI Works MWPharm
First-dose CADDy
WinAUIC
Optimal trial design  PK/PD model
Berkeley Madonna, MicLab Any population tool
Individual patient
Patient population
Robust Clinical Trial design
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7. Concept of population modeling
– fit one subject in the perspective of all the other subjects –

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Least squares method
Observations
Fitted line
Offsets
 Minimize sum of squares of the offsets y o o o o o o o
Option to weight residuals (e.g. by 1/x)  weighted least squares o x
This method is NOT used for population PK/PD estimation.
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9. Standard-two-stage method
Naïve averaging
Naïve pooling
Time (h)
CL = 12 L/h
V = 36 L
CL = 8 L/h
V = 41 L
Standard-two-stage method
CL = 10 L/h
V = 40 L
Concentration (mg/L)
“Fit each subject separately”
Descriptive statistics, Average  SD
CL = 10.0  2.00 L/h
V = 39.0  2.65 L
Standard-two-state method
usually yields reasonable estimates for average PK parameters, if data are rich
usually yields biased (too large) estimates for the between subject variability
Time (h)
Time (h)
CLAv = 9.5 L/h
VAv = 39 L
CLPooling = 9.7 L/h
VPooling = 40 L
Naïve averaging and naïve pooling
All observations considered to come from one subject
No individual CL and V estimates
Ignore between subject variability (BSV)
cannot use actual sampling / dosing times
Naïve averaging
Average or median is computed
actively reduces available observations
Naïve pooling
One ID per dose level
Preferable to averaging
Only yields fairly unbiased estimates, if BSV is small (maybe: %CV <15%)
Directly estimated parameters
Calculated from parameter estimates.
These are not population methods!
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10. Borrowing of information
Sparse data
Considering all relevant values of CL and V can be done by sampling e.g combinations of CL and V for patient i and then calculating the individual subject objective function (Li).
IV bolus dose, 1-compartment model
How well does the curve generated from one set of θ fit the observations?
How likely is it to obtain the current set of parameters (θ) given the parameter variability model.
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11. Applications of population PK/PD models
Model structure
Observations (“data”)
Simulations, Optimal design
New experimental data
Re-estimate
Accept or Reject or Revise
Qualify (validate)
Optimizing individual doses
Estimation
Parameter estimates
Expert knowledge
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12. Tasks of Population PK/PD Software
Optimizing individual doses
Simulation
Estimation
Data processing & Plotting
Optimal design
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13. Tasks of Population PK/PD Software
Optimizing indiv. Doses: BestDose, ID-ODS, DoseMe TCI Works, MWPharm
First-dose, CADDy
WinAUIC
Simulation
Estimation
Berkeley Madonna, Model Maker, acslXtreme, Stella, Gepasi, and all estimation programs
NONMEM, ADAPT V, S-ADAPT, Pmetrics/NPAG, WinNonlin, Phoenix/NLME, PDx‑MC‑PEM,SAAM II, many more
Data processing & Plotting
Any programming language, Perl, Python, Visual Basic, Matlab, S-Plus, R, SAS, etc.
R, S-Plus, WinNonlin, Matlab, EXCEL, SigmaPlot, etc.
Optimal design
ADAPT, S-ADAPT, PFIM, WinPOPT, POPT, PKStaMP, PopDes, POPED, Clinical Trial Simulator
Review of population optimal design software: Mentré F et al. PAGE 2007.
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14. Estimation approaches
No good reason to use these algo-rithms (Sheiner & Beal, JPB 1981; 9:635-51).
(Naïve averaging or Naïve pooling)
Estimation
(Standard-two- stage approach)
FO method (e.g. in NONMEM) is now outdated by at least 2 generations of algorithms or >15 years.
Two Stage Hierarchical Population Methods (Adapt V, S-Adapt, NONMEM, Pmetrics/NPAG, Monolix, PEM, Phoenix/NLME, SAS, R)
Three Stage Hierarchical Population Methods (BUGS, S-Adapt, Monolix, NONMEM, Pmetrics, others)
Not recommended to get initial estimates via naïve methods or an outdated population algorithm:  risk of local minima.
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15. Simulate the antibiotic concentrations for dosage regimens in mice or humans

16. Rise to steady-state after multiple dosing
Simulations without between patient variability (also called deterministic simulations)
Rise to steady-state after multiple dosing
Linear 2-compart-ment model at different doses
Km = 0.1 mg/L
Michaelis- Menten elimination
Almost any PK/PD and other software package (incl. Excel®) will do this task.
Time to implement the model (i.e. coding and debugging) guaranteed to be longer than computation time (usually ~msec).
Robust differential equation solver critical.
Ability to plot multiple / all variables highly important to better understand a model.
Berkeley Madonna very powerful for this task (and easily usable by beginners).
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17. Propose optimized empiric dosage regimens for a patient population via Monte Carlo simulations. Identify covariates that affect dosing (e.g. renal function, body size, etc.)

18. The average patient?
Sörgel F. Chemotherapie Journal (2003)

19. Between Subject Variability
PK Model for 1 patient
PK model for a population of patients
Variability in PK parameters
One set of PK parameters for Clearance (CL), volume of distribution (V), and absorption rate constant (ka).
Absorption rate constant ka not shown.
Bulitta JB, PhD Thesis, 2006.
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20. Derivation of PKPD susceptibility breakpoints
Population PK model
Calculate fT>MIC for each patient and for all relevant MICs
Fraction of patients
fT>MIC (h) for MIC of 2 mg/L
Simulate 10,000 virtual patients
Target: fT>MIC  40% of 24h = 9.6h
PKPD breakpoint: 1 mg/L
Probability of target attainment
Bulitta JB, PhD Thesis, 2006.
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21. Types of parameter variability models
Parametric distribution one sub-population comprising the entire population
Mixture of parametric distributions representing several sub-populations
Number of sub-populations needs to be user-specified. Software: ADAPT V, S-ADAPT, NONMEM, Monolix, others.
Non-parametric every patient can be its own sub- population
Available in Pmetrics / USC*PACK (NPEM, NPAG) and in NPML.
NONMEM, ADAPT, S-ADAPT, Monolix, Phoenix/NLME, WinBUGS, SAS, Matlab, R-packages, Pmetrics / USC*PACK, others.
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22. Software for population PK modelling and Monte Carlo simulations
Simulation and Estimation
NONMEM, ADAPT V, S-ADAPT, BUGS, Pmetrics/NPAG, Phoenix/NLME, R, others
Berkeley Madonna, acslXtreme, Crystal Ball, others
Specialized tool in antimicrobial PK/PD:
MicLab (Medimatics)
Important software characteristics:
Can the software handle correlation between PK parameters (e.g. CL and V)?
Availability of post-processing tools to summarize the results (e.g. Perl or R scripts).
Is the simulation tool robust (e.g. differential equation solver; capabilities to assure / enforce positive semi-definite covariance matrix).
Ability to simulate with a prior distribution (Full Bayesian approach, 3-stage method).
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23. Mechanism-based modeling / systems pharmacology Evaluating proposed mechanisms of action, resistance and synergy  Design mechanistically optimized monotherapy and combination dosage regimens.

24. Mechanism-based modeling of antibiotic action and resistance
Resistance often limits access to target site.
Time course & mechanisms of activity and resistance.
Efflux pumps,
Beta-lactamase activity
Error-prone replication
Bulitta JB et al. Curr Pharm Biotechnol, 2011:

25. Rationally Optimizing Combination Chemotherapy
DRUG A
DRUG B
Receptor 1
Receptor 2
Killing via pathway A
Killing via pathway B
Bacterial killing
Genotypically susceptible bacteria
Genotypically intermediate bacteria
Receptor 3
Phenotypically resistant non-replicating persisters
Eradicate
Enhances killing
Phenotypic resistance mechanism(s)
Inhibit (upregulation)
Genotypically ‘resistant’ cells Pre-existing vs. de novo formation
Mutation
Spontaneous or error-prone mutation
Mechanism-based modeling integrates time course & probabilities
Authors’ copyright © 2011, all rights reserved.

26. Systems pharmacology Mechanism-based PK/PD modeling
Software:
S-ADAPT, ADAPT V, NONMEM, Pmetrics,
Monolix
Estimation and simulation
Important software characteristics:
Robustness and efficiency of estimation algorithm  models with many (often >20) parameters to be simultaneously estimated.
Pre- and post-processing tools (e.g. SADAPT-TRAN, NM-TRAN, AMGET [for ADAPT V]) extremely important.
Automated code enhancing & debugging enables beginner and intermediate users to perform such modeling and often accelerates model coding >10-fold.
Robust computational tool (differential equation solver, other features)
Customization of result plots highly important.
Parallelized estimation.
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27. Exact calculation of the integral of one simplified function approximating the log-likelihood
True probability distribution characterizing the uncertainty of clearance for the ith patient
This scenario with one support point applies to the LAPLACIAN method (FOCE relies on more approximations than LAPLACIAN; FO method far worse)
Function with a precisely known integral
BUT: It is unknown how well the simplified function approximates the log-likelihood!
Density
mode
Model Parameter (e.g. clearance)
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28. Approximating the true log-likelihood as precisely as needed
True probability distribution for clearance of patient i
Use a sampling function to randomly draw points on the x-axis. The probability of a point drawn at a position is determined by the sampling function (also called proposal density).
Density
Model Parameter (e.g. clearance)
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29. Approximating the true log-likelihood as precisely as needed
True probability distribution for clearance of patient i
For each randomly drawn point of the sampling function, calculate the exact value of the true density.
 Interpolate between support points.
Important sampling algorithm approximates the true log-likelihood as closely as needed.
Density
~zero density at this tail
Model Parameter (e.g. clearance)
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30. Prospective ‘validation’ based on external in vivo data
Model predictions at 106 CFU/mL inoculum
Log10 (CFU/mL)
A: 30 min
B: 5 h
Time (h)
fT>MIC
40%
60%
93%
75%
100%
Time > MIC
Bacteriostasis target ~35% fT>MIC
Near-maximal cell killing target ~65% fT>MIC
Log10 CFU per lung at 24 h
CFU: Colony-forming unit.
Craig WA. Clin Infect Dis 1998, 26:1-12.
Andes D & Craig WA. IJAA 2002; 19:261-8.
Neutropenic mouse lung infection model (at 24 h)
 The model quantitatively predicted the
PKPD target values for cephalosporins.
Bulitta JB, et al. Current Pharmaceutical Biotechnology 2011; 12:
Targets in patients: Ambrose PG et al. CID 2007, 44:

31. Achieve therapeutic target goals most precisely in an individual patient Account for MIC / pathogen, renal function, other diseases, etc.

32. Different Bayesian updating methods to individualize PK parameters in an unstable critically ill patient
Available in Pmetrics, Best Dose
Michael Neely, Roger Jelliffe et al.
Bulitta JB et al. Curr Pharm Biotechnol, 2011:

33. Optimized dosing of individual patients
Simulated concentrations
Clearance distribution
Concentration (mg/L)
Time (h)
Dose optimization based on “typical patient”
Loading dose + Continuous inf
Dose optimization based on full non-parametric distribution (Multiple-Model Dosage Design)
Hit target most precisely!
Typical patient
Target
Concentration (mg/L)
Time (h)
MAP Bayesian individualization
Observation +/- SE
Time (h)
Concentration (mg/L)
Real data from Dr Roger Jelliffe.
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34. Optimal Dose Selection programs for antibiotics
Roberts JA et al., Lancet Infect Dis 2014; 14:

35. Software choices for antimicrobial PK/PD
Carefully defining the objective should always be the first step.
A variety of powerful software tools are available and accessible also to beginner and intermediate users. No single tool does it all.
Very significant improvements in software usability, efficiency and robustness of algorithms were achieved over the last years.
Model estimation time is usually no longer a real limitation, even for complex models with >30 parameters. (Parallelized estimation!) In the future, a semi-automated code generator will be very helpful.
Performing a Monte Carlo simulation to optimize empiric dosage regimens is very helpful. However, this is NOT the same as selecting an optimal dosage regimen for an individual patient.
Softwares for optimal dosing of individual patients are available and are being enhanced for different devices (incl. smart phones).
Communication / explanation of results by a skilled modeler is critical.

36. Backup slides

37. Exposure response and exposure toxicity relationships

38. Non-compartmental analysis
Many software packages:
Commercial software:
Phoenix / WinNonlin
Kinetica
EquivTest
Matlab/SimBiology PKSolutions (Excel based)
Topfit
Free software:
Bear
PK for R
S-ADAPT
WinNonlin industry standard (documentation excellent; FDA CFR Part 11)
Calculate / obtain: Cmax, AUC, T>MIC, CL, Vd, etc.
Pharm PK archives & Wikipedia
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39. Exposure response – continuous outcome data
Cefotaxime vs K. pneumoniae in neutropenic lung infection model (after 24 hours of therapy)
Cmax / MIC
AUC / MIC
Time > MIC
Log10 CFU per lung at 24 h
Software tools:
Many nonlinear regression tools.
Suggestions:
ADAPT (maximum likelihood, free, user-friendly).
WinNonlin (as commercial package).
Many other tools equally capable.
Modeling approach:
Amount of data Usually significant
Type of output data Continuous
Signal Often strong
Time-course data No (or not used)
Between subject variability Yes (but not used in analysis)
Recommended algorithm Maximum likelihood or
(Weighted least squares)
Craig WA. Clin Infect Dis 1998, 26:1-12. Pictures from: Drusano GL. Nat Rev Microbiol 2004; 2:

40. Exposure response – Dichotomous (Yes/No data)
AUC
Probability of cure or toxicity
Afibrile on day 7
Nephotoxicity for Q24h dosing
Nephotoxicity for Q12h dosing
MIC: 4 mg/L
MIC: 1 mg/L
MIC: 0.25 mg/L
Software tools:
Statistical packages for logistic regression and CART analysis.
Parametric hazard models to describe time-dependent risks (eg. of death or adverse events).
Suggestions:
Systat for logistic regression.
(Other tools equally capable.)
Population modelling tools for parametric hazard models:
NONMEM, S-ADAPT, Monolix, etc.
Modeling approach:
Amount of data Less (especially for tox.)
Type of output data Dichotomous (e.g. Live/Dead, Yes/No)
Signal Often weaker
Time-course of risk No (or usually not used)
Between subject variability Yes (but not used in analysis) Recommended algorithm Maximum likelihood or Bayesian algorithms
Drusano & Louie. Antimicrob Agents Chemother 2011; 55:

41. Optimize empiric dosage regimens via Monte Carlo simulation
Individual patient’s PK and MIC are unknown.
Can incorporate influential covariates (e.g. renal impairment).
Bulitta JB et al. Curr Pharm Biotechnol, 2011:

42. Achieve Target Goals Pmetrics www.lapk.org Population PK model
Sequential Multiple-Model (MM) Bayesian updating
Pmetrics
Individual patient data
Population PK model
Interacting Multiple-Model (MM) approach.
Here, PK parameters can change over time (unstable patients!)
Individual patient data
Unstable patients!
Slide kindly provided by Dr. Roger Jelliffe.

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Authors’ Disclosure
I have never received any funding or any other financial incentive from a software company and am not associated with any commercial software package.
I am the creator and developer of the free, open-source SADAPT-TRAN tool and am a passionate user of Berkeley Madonna. I have been an active user of a Pharsight Academic Excellence License for several years since 1999.
I have received collaborative research grants from Pfizer, Trius, Cempra, CSL, Cubist, Novartis, and Boryung. None of this collaborative work is related to this presentation.
Author’s Copyright © All rights reserved.