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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 Author’s Copyright © All rights reserved.
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Author’s Copyright © 2014. All rights reserved.
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 Author’s Copyright © All rights reserved.
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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! Author’s Copyright © All rights reserved.
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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. Author’s Copyright © All rights reserved.
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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 Author’s Copyright © All rights reserved.
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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 Author’s Copyright © All rights reserved.
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Concept of population modeling
– fit one subject in the perspective of all the other subjects –
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Author’s Copyright © 2014. All rights reserved.
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. Author’s Copyright © All rights reserved.
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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! Author’s Copyright © All rights reserved.
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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. Author’s Copyright © All rights reserved.
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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 Author’s Copyright © All rights reserved.
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Tasks of Population PK/PD Software
Optimizing individual doses Simulation Estimation Data processing & Plotting Optimal design Author’s Copyright © All rights reserved.
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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. Author’s Copyright © All rights reserved.
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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. Author’s Copyright © All rights reserved.
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Simulate the antibiotic concentrations for dosage regimens in mice or humans
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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). Author’s Copyright © All rights reserved.
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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.)
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The average patient? Sörgel F. Chemotherapie Journal (2003)
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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. Author’s Copyright © All rights reserved.
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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. Author’s Copyright © All rights reserved.
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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. Author’s Copyright © All rights reserved.
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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). Author’s Copyright © All rights reserved.
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Mechanism-based modeling / systems pharmacology Evaluating proposed mechanisms of action, resistance and synergy Design mechanistically optimized monotherapy and combination dosage regimens.
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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:
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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.
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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. Author’s Copyright © All rights reserved.
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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) Author’s Copyright © All rights reserved.
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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) Author’s Copyright © All rights reserved.
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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) Author’s Copyright © All rights reserved.
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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:
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Achieve therapeutic target goals most precisely in an individual patient Account for MIC / pathogen, renal function, other diseases, etc.
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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:
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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. Author’s Copyright © All rights reserved.
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Optimal Dose Selection programs for antibiotics
Roberts JA et al., Lancet Infect Dis 2014; 14:
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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.
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Backup slides
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Exposure response and exposure toxicity relationships
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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 Author’s Copyright © All rights reserved.
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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:
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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:
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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:
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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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Author’s Copyright © 2014. All rights reserved.
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.
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