A New Platform for Combining the ‘Bottom-Up’ PBPK Paradigm and POPPK Data Analysis

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A New Platform for Combining the ‘Bottom-Up’ PBPK Paradigm and POPPK Data Analysis

  1. 1. A New Platform for Combining the ‘Bottom-Up’ PBPK Paradigm and POPPK Data Analysis Masoud Jamei Senior Scientific Advisor, Head of M&S Honorary Lecturer, University of Sheffield M.Jamei@Simcyp.com PKUK, 25-27 Nov 2009, UK IN CONFIDENCE © 2001-2009
  2. 2. Acknowledgement: The Team Current: Geoff Tucker, Amin Rostami-Hodjegan, Mohsen Aarabi, Khalid Abduljalil, Malidi Ahamadi, Lisa Almond, Steve Andrews, Adrian Barnett, Zoe Barter, Kim Crewe, Helen Cubitt, Duncan Edwards, Kevin Feng, Cyrus Ghobadi, Matt Harwood, Phil Hayward, Masoud Jamei, Trevor Johnson, James Kay, Kristin Lacy, Susan Lundie, Steve Marciniak, Claire Millington, Himanshu Mishra, Chris Musther, Helen Musther, Sibylle Neuhoff, Sebastian Polak, Camilla Rosenbaum, Karen Rowland-Yeo, Farzaneh Salem, David Turner, Kris Wragg Previous: Aurel Allabi, Mark Baker, Kohn Boussery, Hege Christensen, Gemma Dickinson, Eleanor Howgate, Jim Grannell, Shin-Ichi Inoue, Hisakazu Ohtani, Mahmut Ozdemir, Helen Perrett, Maciej Swat, Linh Van, Hua Wang, Jiansong Yang & .... Many others IN CONFIDENCE © 2001-2009
  3. 3. Grants Received by Simcyp IN CONFIDENCE © 2001-2009
  4. 4. Assessing vs Anticipating Covariate Effects Top-Down: Sparse Samples Analysis Clinical Studies Bottom-Up: Systems Biology/Pharmacology/Pharmacokinetics IN CONFIDENCE © 2001-2009
  5. 5. Data-Driven (Top-Down) Approach (Ide et al. 2009) 1 C=Cie-kit 2 Empirical Compartmental Semi/Physiological IN CONFIDENCE © 2001-2009
  6. 6. Data-Driven (Top-Down) Approach A primary objective of population pharmacokinetic (POPPK) studies is to estimate the inter-individual variability in PK parameters and identify the covariates that may account for the variability. (JPP 2004) The power of selecting a true covariate decreases with increasing correlation to any false covariate. If the goal is hypothesis testing, the practical implication is that one cannot fully discriminate between true and false between two highly correlated covariates, other than for very strong covariates or large data sets. IN CONFIDENCE © 2001-2009
  7. 7. Trends in Covariate Analyses in POPPK Studies Contribution to new knowledge or confirmation of existing information? Aim: Assessing the relationship between the knowledge of human physiology and biology (system pharmacology) and the reported covariate in POPPK studies. A total of 140 papers from 5 journals were reviewed and they were classified as ‘Old’ (1990-1997) and ‘Recent’ (2006-2007) studies. 60 old recent No of Papers 40 20 0 not graphs univariate posthoc 2 criteria prior other described knowledge The difference in the objective function was the most commonly used criterion for inclusion of a covariate in the final model of old studies. Multiple criteria including DOF, graphs, likelihood ratio and clinical relevance were used in recent studies. Chetty and Rostami (PKUK 2008) IN CONFIDENCE © 2001-2009
  8. 8. Trends in Covariate Analyses in POPPK Studies Commonly Used Covariates • Covariates that were commonly Sex included in the final model in both old and recent categories were Age demographic factors, hepatic and Weight kidney function, drug dosing and BSA interactions. BMI • Extensive information already Dose exists on the impact of these Dosing regimen factors on drug disposition. Formulation • Covariate analyses may benefit from a priori identification of CLcr influential variables using virtual Concurrent medication populations. Hepatic/Renal function Plasma albumin Smoking Chetty and Rostami (PKUK 2008) IN CONFIDENCE © 2001-2009
  9. 9. Bottom-Up: Systems Pharmacology Approach Using PBPK Modelling. Bioavailability: release, dissolution, stability, permeability, efflux and/or uptake transport, gut wall and hepatic first pass metabolism, ... Metabolism: unbound fraction, efflux and or uptake transport, enzyme abundace, blood flow, HSA, Heamatocrite, induction, inhibition, ... Distribution: unbound fraction, blood flow, efflux and/or uptake transport, organ size, HSA, ... PBPK Models IN CONFIDENCE © 2001-2009
  10. 10. Combining Physiological and Drug-dependent Data Drug Data Systems Trial Data Design Mechanistic IVIVE & PBPK Population Pharmacokinetics & Covariates of ADME (Jamei et al., 2009) IN CONFIDENCE © 2001-2009
  11. 11. POPPK and Covariate Effects CL = Typical parameter estimate x (Body weight/13) 3/4 x [1 - 0.0542 x (Cholesterol - 5.4)] x [1 - 0.00732 x (Haematocrit - 31)] x [1 + 0.000214 x (Serum creatinine - 524)] The typical values refer to a patient with a body weight of 13 kg, cholesterol of 5.4 mmol l-1, serum creatinine of 524 mmol l-1 and a haematocrit of 31%. IN CONFIDENCE © 2001-2009
  12. 12. The Complexity of Covariates Genotypes (Distribution in Population) Renal Function Plasma Body Ethnicity Disease Proteins Fat Serum & Creatinine Haematocrit Sex Age (Distribution in Population) (Distribution in Population) Height Brain Body Volume Heart Surface Volume Area Weight MPPGL HPGL Cardiac Cardiac Liver Output Index Enzyme & Volume Transporter Liver Intrinsic Abundance (Updated after Jamei et al., 2009) Weight Clearance IN CONFIDENCE © 2001-2009
  13. 13. Liver Well-Stirred Model QH . fu/B:P.Uptake.CLuint CLH = QH + fu/B:P.Uptake.CLuint fu/B:P . Uptake = Culiver/Ctotal (blood) Culiver/Ctotal (blood)>fu/B:P if drug is substrate for uptake transporters Culiver/Ctotal (blood)<fu/B:P if drug is substrate for efflux transporters IN CONFIDENCE © 2001-2009
  14. 14. Liver Blood Flow & fu/B:P 4.5 Proportion of cardiac output Cardiac Index 4 22% and 7% for portal vein and arterial liver (L/min/m2) blood supply, respectively) 3.5 3 Cardiac output based on BSA and 2.5 age (2.5, 4, 3 and 2.4 L/min/m2 for 1, 10, 20 and 2 80 years of age, respectively) 0 20 40 60 80 100 Age (years) CB/Cp = (CRBC:CP)*HC + (1- HC) fu fu/B:P= Min (CB/Cp) = 1- Heamatocrit CB/Cp Max (CB/Cp) = ∞ Covariation of Hc: Age: - Children Sex: - Female Individual Attributes: - Athletes Environment: - High Altitude IN CONFIDENCE © 2001-2009
  15. 15. Top-Down vs Bottom-Up 1.5 LV = 0.722 x BSA1.176 LV = 1.38 x (BW/70kg)0.75 1.2 Liver Volume (L) 0.9 0.6 Fanta et al – “Developmental PK of ciclosporin: A population pharmacokinetic study in paediatric 0.3 transplant patients Br J Clin Pharmacol 64:772, 2007 (with Corrections) 0 10 20 30 40 50 60 70 Body Weight (kg) IN CONFIDENCE © 2001-2009
  16. 16. Top-Down vs Bottom-Up [1 - 0.00732 x 100*(HC - 0.31)] Clpo  fu/[(CRBC/Cp)*HC + (1- HC)] CLpo  fu/B:P.CLuint fu = 0.037 and CRBC/Cp = 1.8 fu/B:P = 0 0.0296 (at HC = 0.31) [[0.037/[1.8*HC + (1- HC)] ]/ 0.0296] 1.4 1.2 Relative Change in CL 1 0.8 0.6 CL Multiplier (Top-Down) 0.4 CL Multiplier (Bottom-Up) 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Heamatocrit (Jamei et al., 2009) IN CONFIDENCE © 2001-2009
  17. 17. Parameter Estimation Module Tune design parameters to fit observations Simcyp simulation Trial and Error Parameter Estimation (PE) Module IN CONFIDENCE © 2001-2009
  18. 18. Overall Settings Parameter Estimation Module Overview DVs Models Design Parameters Parameter Estimation Module Predicted Parameters IN CONFIDENCE © 2001-2009
  19. 19. PK Profiles Template Route of administration can be oral or intravenous (bolus and/or infusion). Dosing regimen can be single or multiple dosing and irregular dosing for different individuals is also supported. The number of observation and their related sampling times for individuals can independently be entered. The observations and dosing times can be entered in any order for any of subjects. The subjects covariates (if any) are only needed once. IN CONFIDENCE © 2001-2009
  20. 20. Some of Available Models Minimal and full PBPK models Lung PO Small Intestine Gut Metabolism Adipose ka Bone Portal Vein Brain Heart QPV QPV Venous Arterial Kidney Blood Blood QHA Muscle QH Skin Liver Systemic IV Compartment Liver Hepatic Clearance Renal Spleen Clearance Portal Vein Gut IV Dose PO Dose IN CONFIDENCE © 2001-2009
  21. 21. Some of Available Models Permeability-limited Liver Model - Hepatobiliary Transporters Capillary blood KP-on KtP-off P +ve P KP-off pH=7.4 KtEW-in KtEW-out KtP-off pH=7.4 +ve P KtP-on +ve EW Sinusoidal OATP1B1 OATP1B3 MRP3 KtIW-in KtIW-outOCT1 membrane Tight junction KtNP-on P-gp +ve KtNP-off KtAP-on KtAP-off NP MRP2 KtNL-on KtNL-off Bile Ktel +ve BCRP AP -ve NL pH=7 IW EW: Extracellular Water NL: Neutral Lipids AP: Acidic Phospholipids Canalicular membrane IW: Intracellular Water NP: Neutral Phospholipids IN CONFIDENCE © 2001-2009
  22. 22. Some of Available Models One-compartment absorption, Compartmental Absorption and Transit, and Advanced Dissolution, Absorption and Metabolism (ADAM) models. Small Intestine Lumen Stomach Duodenum Jejunum I & II Ileum I Ileum II Ileum III Ileum IV 1 2 3 4 5 6 7 Faeces Enterocytes Metabolism PBPK Distribution Model Portal Vein Liver IN CONFIDENCE © 2001-2009
  23. 23. Some of Available Models Enterohepatic Recirculation (EHR) including gallbladder emptying Figure from Roberts et al. 2002 IN CONFIDENCE © 2001-2009
  24. 24. Some of Available Models Up to 4 compounds and two of their metabolites in addition to their auto and mutual interactions (inhibition/induction). Lung Adipose Bone Enterocytes Gut Metabolism of metabolite Qvilli Brain Venous Blood Portal Vein Heart Arterial Blood Kidney QPV QPV Muscle QHA Skin QH Systemic Liver Compartment Liver Spleen Hepatic Metabolism Renal Clearance Portal of metabolite of metabolite Vein Gut IV Gut Metabolism PO Hepatic Metabolism IN CONFIDENCE © 2001-2009
  25. 25. Design Parameters Virtually any parameter can be selected. It can be population-dependent parameters or drug-dependent parameters. Up to 10 parameters can simultaneously be fitted. The initial values and ranges are provisionally assigned but can be changed by users. Currently, uniform, normal and log-normal distribution of parameters are included. Covariates are inherently included! IN CONFIDENCE © 2001-2009
  26. 26. Optimisation Algorithms  Direct/random search methods (Hooke-Jeeves, Nelder- Mead, …);  Genetic Algorithms (GA);  Combined Algorithms: Begin with a global optimisation method (GA) and then switch to a local optimisation method; e.g., HJ or NM. IN CONFIDENCE © 2001-2009
  27. 27. Optimisation Algorithms - Nelder-Mead (Simplex) Nelder-Mead (1965) method which is also called downhill simplex is a commonly used nonlinear optimisation algorithm. Nelder-Mead includes the following steps: • Reflection; • Expansion; • Contraction; • Reduction; http://optlab-server.sce.carleton.ca/POAnimations2007/NonLinear7.html IN CONFIDENCE © 2001-2009
  28. 28. Local vs Global Minimum Objective Function Value (OFV) Initial value Another Initial value Local minima Design Parameter, e.g. CL Global minimum 28 IN CONFIDENCE © 2001-2009
  29. 29. Objective Function Landscapes 4 2 20 Log OFV 0 15 Log OFV -2 10 -4 0 0 5 -6 1 0 1 0 1 2 0 2 2 1 3 3 2 3 Vss (L) 4 3 5 4 Vss (L) 4 5 4 i n in yi  f (, t i ) 2  y i  f (, t i )  2  i 1 yi2 i 1 IN CONFIDENCE © 2001-2009
  30. 30. Genetic Algorithms (GAs) GAs are based on Darwin's theory of evolution and mimic biological evolution (Survival of the Fittest).  Stochastic search and optimisation technique  Search in a ‘collection’ of potential solutions  Work with a representation of the design parameters  Guided by objective function, not derivatives  Uses probabilistic transition rules Holland (1975) ; Goldberg (1983, 1989) IN CONFIDENCE © 2001-2009
  31. 31. GAs Stages  Assessing candidate solutions according to the defined objective function and assign fitness based on the ability or utility of the candidate solutions.  Selecting candidate solutions based on a probabilistic function of their fitness. Fitnessi Re - Production Probabilit y i  n  Fitness i 1 i  After adjusting fitness values, candidates are selected for mating.  Then genetic operations, e.g. cross-over and mutation are applied. IN CONFIDENCE © 2001-2009
  32. 32. Genetic Algorithms Stages Evaluate Candidates Randomly Assigned Set of Candidate Candidates Parameters Select a New Set of Rank Candidates Candidates Recombination and Reproduce New Mutation Candidates IN CONFIDENCE © 2001-2009
  33. 33. Maximum Likelihood (ML) Approach Maximising the probability of obtaining a particular set of data, given a chosen probability distribution model. This can be done by maximising the so called log-likelihood function: N  L()   log(  pi (Yi |  i ,  2 ) p( i |  , )d i ) i 1 The optimal ML estimate can be found from:  ( yk  f ( X ki , ik )) 2 1 2    M OML (i )     ln   k 1   2 2  IN CONFIDENCE © 2001-2009
  34. 34. Maximum a Posterior (MAP) Approach MAP estimation is a Bayesian approach in the sense that it can exploit additional information on the supplied experimental data. Consequently if the user has prior knowledge regarding the parameters then the MAP should in theory provide more accurate estimations of the design parameters than the Maximum Likelihood which only requires experimental measurements. MAP differs from ML in that it uses prior distribution of parameters p(θ):  ( yi  f (, t i )) 2  P  ( j   j ) 2    N O MAP ()     ln (b 0  b1f (, t i ) b 2 ) 2     ln( j ) 2 i 1  ( b 0  b1f (, t i ) )  j  j b2 2 2    Where β={b0, b1, b2} vector defines the variance model: Additive β={b0, 0, 1} Proportional β={0, b1, 1} Combined β={b0, b1, 1} IN CONFIDENCE © 2001-2009
  35. 35. Expectation-Maximisation (EM) Algorithm In order to determine the ML or MAP estimations we need to use an optimisation algorithm. The Expectation-Maximisation (EM) algorithm is one of the most popular algorithms for the iterative calculation of the likelihood estimates. The EM algorithm was first introduced by Dempster et al (Dempster, Laird et al. 1977) and was applied to a variety of incomplete-data problems and has two steps which are the E-step and the M-step. E-step: Determining the conditional expectation using Monte Carlo (MC) sampling and updating MC pool for each individual after each iteration. M-step: Maximise this expectation with respect to θ and updating population parameters and variance model parameters. IN CONFIDENCE © 2001-2009
  36. 36. PE Reports There are six sheets: PE Input Sheet, Summary, Individual and Pop fit, Observed Vs Predicted, Residual Errors and Parameters Trend (Ind). IN CONFIDENCE © 2001-2009
  37. 37. Future Vision An ideal modelling platform would be one that could incorporate strengths of population analysis (top-down) and PBPK (bottom-up) ; ... Middle-out! Adoption of middle out approach; break the preclinical/clinical PK model divide. Bring PBPK models into all phases of clinical drug development. Now increasingly possible with the availability of commercially supported software. Complete learning by Phase II. Refine preclinical PK parameters with early experimental human/patient (Phase 0, I & II) data. Phase III: Confirming phase. Increasingly ask whether observed concentration-time data are within expectations, instead of ‘hunting’ for PK covariates and relationships. Look for similar developments emerging in PD. Move to a better model-based drug development paradigm. Slide adapted with permission from Malcolm Rowland IN CONFIDENCE © 2001-2009

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