Population Pharmacokinetics

Population Pharmacokinetics

• Focuses on inter-individual variabilities which influence drug pharmacokinetics or a dosage schedule
• These differences arise from demographics, pathophysiology, age, disease (renal or hepatic malfunction), and the use of multiple drugs
• Used to determine a suitable dosage for a group, minimizing negative effects related to individual physiological variations potentially impacting the therapeutic index
• Polymorphism of metabolic enzymes can cause changes in a dosage schedule
• Enables assessment of elements responsible for variance within a particular group and allows for focused therapeutic drug monitoring
• Can be conducted using both sparse and dense data samples
• Data is analysed using computer algorithms such as NONMEM and P-PHARM
• Focuses on population PK approaches, the utilization of population PK in medication development, the application of various data analysis softwares, and instances of research performed over the previous 7 years

Key terms

• Population Pharamcokinetics (PK)
• Demographical variability
• NONMEM
• P-PHARM

Traditional vs. Population Pharmacokinetics

Rationale for Population PK Analysis

• Key objective involves determining the impact of covariates, such as age, weight, lab values, concomitant drugs, and other illnesses, on drugs PK or PK / PD
• Establishes the best dosage plan for optimizing effectiveness or safety of medications with limited therapeutic ranges
• Aids in selecting dosage options for key trials, defining labels, and planning future research on hepatic status and drug interactions
• Assesses inter-patient variability and random residual variability, including intra-patient measurement error
• Supports the creation of a preclinical and clinical PK plan for submission to the NDA (New Drug Application)
• Offers Bayesian priors to aid forecasting in randomized concentration
• Controlled Trials and enhances the precision of patient dosage plans
• Aides in clarifying why trials failed or had limited success, utilizing PK or PK/PD correlations

Uses of Population Analysis

• Used throughout all medication development phases, particularly in clinical phase III
• Preclinical Research
• Phase 1 Research:
  • Biopharmaceutical research
  • Dosage range finding research
  • Studies of specific populations
  • Research on medication interactions
• Phase 2 and 3 Research:
  • The effectiveness and safety of a New Chemical Entity are generally determined during phase 3 research within a specific patient group
• Long-term safety and post-market monitoring for medication safety and effectiveness

Elements Affecting Pharmacokinetics

• Most medications exhibit some degree of pharmacokinetic variability
• This variability is described through fixed and random effects

Fixed Effects Elements

• These elements relate patient PK parameters to characteristics, including:
  • Age, weight, height, and sex
  • Pathophysiology like kidney or liver malfunction
  • Other elements like drugs, dose, time course and patient compliance

Random Effects Elements

• Unidentifiable due to recording mistakes, unidentified pathophysiology, and analytical differences
  • Inter-individual random effects
  • Differences between subjects
  • Intra-individual/inter-occasion random effects
  • Reflect changes within a subject
  • Residual error
  • Measurement inaccuracies and model deficiencies

Covariates

• Influence the result and can clarify variability in model parameters

Population PK Analysis Methodologies

• Includes population model of population analysis within a framework
• Parameter estimation has different methods
• Depending on strategy, population study methodology is divided into:
  • Parametric
  • Non-parametric

Population PK Analysis - Parametric Approach

• Assumes that parameters conform to normal Gaussian or log-normal distribution
• Produces:
  • Mean
  • Standard Deviation (SD)
  • Correlation between covariates

Population PK Analysis - Non-Parametric strategy

• Discrete distribution without dependence on assumption

Statistical Methods for Population Analysis

• Naive Pooled Data
  • Combines all data as if it originated from a single reference person, suitable for modelling through classical strategies
  • Used to assess concentration-time profiles for PK parameters
  • Cannot assess set impacts or differentiate individual variances
• Two-Stage Strategy
  • Uses classical fitting via non-linear least squares regression in data-rich situations
  • Computes summary statistics by multiple regression analysis using individual parameter estimates
  • Likely to overestimate random effects despite unbiased mean estimates
• Bayesian Estimation
  • Estimates parameters for an individual using the prior odds of parameters across a subject population and relevant individual data
  • Needs estimates of prior parameters
  • Fit is depend on priors

Modelling Non-Linear Mixed Effects

• Used when not all subjects are extensively measured
• Applies single-stage strategy
• Considers population study sample
• Provides evaluations of population features

Modelling Non-Linear Mixed Effects - Features

• Population PK approach using one stage examination that estimates parameters such as mean parameters, set impact parameters, inter-individual variability, and random residual error
• Estimates population parameters from a complete set of individual concentration values
• 3 Sub-models:
  • Structural sub-models
    • Describes overall trend
  • Statistical Sub-model
    • Counts for variability
  • Covariate sub-model
    • Expresses relationships between covariates using set impact parameters

Parameter Estimations - Multiple Estimation Methods

(1) First-Order Method (FO)

• Assesses common value for each parameter (or coefficient), along with variance-covariance, and variance for the random error
• Individual ηs are NOT estimated (2) POSTHOC Estimation:
• Uses empirical Bayes methodologies (3) First-Order Conditional Estimation
• Linerisation is carried out in the area of conditional estimates (4) Laplacian Conditional Estimation
• Second-order estimation
• Suitable for highly nonlinear models (5) HYBRID Estimation
• Applies FOCE to estimate ηs, with designated exceptions using the FO method, potentially speeding up the full FOCE process

Population Pharmacokinetic Analysis - Software Methodologies

• Assesses the impact of categorization through software
• Many software packages include first-order estimation, alongside advanced linearization techniques

Software Methodologies - NONMEM

• The most used program to analyse population PK and PD data
• Implements maximum likelihood method
• Evaluation is performed using 1 of 2 expansion methods about conditional estimates of inter-individual random impacts or a second-order expansion about conditional estimates

Software Methodologies - NLME

• Uses generalized least squares (GLS) procedure in the S-PLUS software
• This series carries out expansion surrounding conditional estimates of random impacts
• GLS estimates set impact parameters and then random impact

Software Methodologies - NLINMIX

• Uses SAS macro, using generalized estimating equations (GEE)
• It uses expansion about zero or conditional estimates of random impacts
• Results include estimates, standard errors, and test statistics

Software Methodologies - MIXNLIN

• Executes 4 algorithms by SAS-based program:
  • Estimated generalised least squares
  • Iteratively reweighted generalised least squares
  • Pseudo maximum likelihood
  • Pseudo restricted maximum likelihood
• Compared to maximum likelihood, it is less efficient but computationally simpler

Software Methodologies - P-PHARM

• Uses parametric expectation-maximization (EM)
• Includes population mean and estimates along with error variance via linearization surrounding empirical Bayes approximates of random impacts

Software Methodologies - WINNONMIX

• Offers 2 algorithms:
  • The Lindstrom and Bates linearization technique calculates maximum likelihood or restricted maximum likelihood, fit or missing data
  • Two-stage estimation method applies to rich data sets
• Characteristics:
  • PK-PD modeling
  • Library of models and Fortran programming
  • Spreadsheet/workbook data management, including formula support, functions, importing/exporting, missing values, etc
  • Plots of data and overlay plots
  • Dynamic memory for comprehensive datasets and models
  • Statistics on input and output
  • Effects modelling
  • Sparse and Rich Data set algorithms
  • Fitting optimization using maximum likelihood or restricted maximum likelihood
  • Goodness-of-fit statistics, including diagnostic and goodness of fit statistics

Significance in Clinical Treatment

• Meloxicam plasma concentrations in RA patients were examined using nonlinear mixed effect modelling (NONMEM)
  • The researchers evaluated effects of age, weight, gender, and related treatments
• Males and females 18-80 years with RA, in 3-week trials
  • Meloxicam once-daily for 3 weeks or 6 months at doses from 7.5-60mg
  • Assessment of plasma samples from 586 patients using NONMEM
  • Data was described by one-compartment model
  • CI (95%) in males was 0.377 1 h-1 (0.0304-0.449), and 0.347 1 h-1 (0.274-0.419) in females
  • Analysis using WinBUGS
  • Showed age and gender both affected clearance
  • Small influence of age for dose adjustment of less than 10%
  • Drug interactions found
    • Sulphasalazine and glucocorticoids both altered meloxicam clearance (+19% and 12%, respectively)
• The population meloxicam showed similar the data from phase I trials, while the significance of uncommon interactions should be considered
  • Renal failure may alter how body handles the drugs and influence clinical effects

Significance in Clinical Treatment - Eleonora L. Swart (2005)

• Population PK of lorazepam/midazolam in critical patients with acute Kidney Failure with continuous venovenous hemofiltration (CVVH)
• Involved twenty critical patients with acute renal failure on CVVH
• Given lorazepam (n=10) or midazolam (n=10) through continuous infusion
• Renal failure affects body's drug process and influences drug effect
  • CVVH carries out ultrafiltration at 2 L/h w/ pre-dilution or post dilution
  • 180 mL/min blood flows with 1.9m2 cellulose triacetate membrane filter
  • Rates of Lorazepam/midazolam are 0.32-4 mg/h and 1-14 mg/h
  • Each patient measured to ICU stay over 48 hours with periodic ultrafiltrate samples
• Samples of urine during 24-hour intervals if produced, which was taken when the ultrafiltrate fluid bag was replaced
• During lorazepam/midazolam infusion blood was withdrawn and collected at t=0 and when ultrafiltrate fluid bag was replaced for 48 hours
• Samples were assessed to find multiple blood volumes and metabolites using high-performance liquid chromatography and drug concentrations.
  • Determined the one-compartment PK
  • Assessment used NONMEM to find K
  • Total-body clearance was 6.4 L/h; 376 L was volume of distribution
  • The rate of filtration was 0.31 L/h which is approximately 5% Average degree of plasma protein binding was 82.9 % for lorazepam at 0.16 sieving coefficient
    • 39.5% was Degree of plasma protein binding of lorazepam glucuronide during 0.48 sieving
  • the single compartment model was described using the pharmacokinetics of midazolam.
    • In this case 8.5 L/h being total-body clearance and 157 being volume distribution
    • 0.055 L/h or nearly 0.7 % being the rate of clearance by ultrafiltration.
• From these trials the test indicated neither lorazepam nor midazolam is efficiently removed by CVVH which helps rid glucuronide metabolites

Significance in Clinical Treatment - Panhard L (2005)

• Designed research to determine inter and intra-individual differences in nelvinavir and its M8 metabolite
• COPHAR 1-ANRS 102 studies in patients with with the HIV virus
  • Blood samples were taken from first day and second at 1-3 months with nelfinavir and M8
  • Used a one-compartment model with additional compartment with first order rate-constant
    • V/F for mean in 309
    • Absorption rate-constant at 0.4 h-1
• Significant impacts of comedication found for both nelfinavir and M8 which was used to describe therapeutic drug monitoring.

Significance in Clinical Treatment - Lamivudine (LMV), Stavudine (STV) and Zidovudine (ZDV)

• Panhard X (2007) researched the individual PK variability of LMV, STV, ZDV
  • Tested patients blood serum for nucleoside analogues (NA) in COPHAR1-ANRS102 trial
  • Found to be one-compartment model
  • Variability was observed using a mix of combination with NFV versus IDV

Significance in Clinical Treatment - Polymorphism & Igor Locatelli (2010)

• Polymorphism in genes leads to prolonged/terminated action
• Studied a population PK of the influence of CYP2D6 genotype on riserpidone metabolism
• Research tested the metabolism of riserpidone to determine the CYP2D6 genotype
  • This resulted in Caucasian serum being tested using serum of creatinine clearance (Clcr)
• Revealed some new discoveries about the PK of enantiomers which can greatly influence the affects of the body by CYP2D6