Analysis of pk data- Pop PK analysis

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  • 1. Analysis of population PK Data Gayatri Devi R Student 5th PHARM D
  • 2. PHARMACOKINETIC DATA   intended to define the time course of drug and major metabolite concentrations in plasma and other biological fluids in order to obtain information on absorption, distribution, metabolism, and elimination. Importance??    Pharmacokinetically guided dose escalation (PGDE) studies Dose fixing in Phase II and subsequent studies. To adapt drug dosage to the individual patient (therapeutic drug monitoring)
  • 3. Relevant PK parameters          Total clearance (CL), Fraction of dose excreted unchanged in urine (fe), Volume of distribution at steady state (Vss), Volume of distribution during the terminal phase (VZ), Blood/plasma concentration ratio, Terminal half-life (t1/2 Z), Fraction of unbound drug in plasma (fu), Bioavailable fraction of dose (F), if applicable, and Absorption rate constant (ka),
  • 4. Designing a dosage regimen.. Following parameters should be known as well:  Area under the plasma concentration time curve(AUC),  Maximum concentration (Cmax),  Minimum concentration (Cmin) after repeated dosing, and Time of Cmax (tmax).  In addition, the effective and toxic concentrations should be assessed
  • 5. Population PK: from 1972 to 1977   Population pharmacokinetics is the study of the sources and correlates of variability in drug concentrations among individuals who are the target patient population receiving clinically relevant doses of a drug of interest. Pop PK seeks to identify the measurable pathophysiologic factors that cause changes in the dose-concentration relationship and the extent of these changes so that, if such changes are associated with clinically significant shifts in the therapeutic index, dosage can be appropriately modified.
  • 6. Population pharmacokinetics incl:     Assessment of global variability of the plasma drug concentration profile in a patient population. Allocation of this variability to pharmacokinetic parameters (e.g. variability of clearance, bioavailability, etc). Explanation of variability by identifying factors of demographic, pathophysiological, environmental, or concomitant drug-related origin that may influence the pharmacokinetic parameters. Quantitative estimation of the magnitude of the unexplained variability in the patient population.
  • 7. What does PK software do?       Fitting drug concentration-versus-time data to a series of pharmacokinetic models, and choosing the one that best describes the data statistically. Fitting data into a pharmacokinetic or pharmacodynamic model defined by the user Simulation Experimental design Clinical pharmacokinetic applications Computer programs for teaching
  • 8.   The application of population analysis methods to therapeutic problems has led to on-going methodological and software development which in further has established more complex applications. Commonly used softwares used for analysis of PK data:    NONEM (NONlinear Mixed Effects Modeling) * -developed by S.L.Beal and L.B. Sheiner MK MODEL – developed by National Institutes Of Health Support PROPHET system NPEM 2 ( Non Parametric Expectation Maximization), version 3- well adapted for Pop Pk
  • 9. Model setup screen of NLME
  • 10. Other softwares incl.  USCPACK PC PROGRAMS*   Consists of various Pk programs Clinical programs incl. related routines in which past therapy data for individual patients are entered into files along with parameter and dose predication programs for various drugs like:       Amikacin(amik) Gentamicin(Gent) Netilmicin(Net) Tobramycin (Tob) Bayesian General Modeling (MB) Least Squared General Modeling
  • 11. Population analysis    Synonym: repeated measures modeling, non linear mixed effects modeling, non linear hierarchical modeling. Pop PK analysis refer to a set of statistical techniques that can be used to learn about the average response in a population as well as the variability in response that arises from different sources. Population analysis is the application of a model to describe data that arise from more than one individual
  • 12. Approaches for analyzing Pop PK data  Standard two - stage approach  refers to fitting a pharmacokinetic model to the data of each individual  Afterwards summary statistics are computed for the total collection of individual parameter estimates  Using this approach, the inter individual variance tends to be overestimated. it is not applicable when the individual data are too sparse for individual model fits. 
  • 13. Contd..  Nonlinear Mixed-Effects Modelling Approach  With this type of modelling not only pharmacokinetic parameters but also inter-individual variance parameters are estimated.  The parameters are population means, shift parameters, and inter-individual and residual variance parameters  A population pharmacokinetic data analysis should include relevant covariates, e.g. age, weight, gender, creatinine clearance, co-medication, and concomitant diseases  Quantitative relationships between covariates and pharmacokinetic parameters often help predict individual PK before any individual data have been obtained.
  • 14. Considering an example….     PK model for a gentamicin-like drug that incorporates the central elements relevant to a population analysis. This drug displays one compartment model characteristics Vd =20 L and clearance (4 L Hr -1) dose admn by IV bolus. We used this PK model to simulate plasma concentration–time data for 30 patients who received a single intravenous bolus dose of 420 mg (6 mg /kg for a 70 kg individual),where each patient provided seven blood samples at times 0.25, 0.5, 1, 2, 4, 8 and 12 h following dosing.
  • 15. Observed conc-time data for 30 samples
  • 16. A population analysis was then conducted on the simulation 'dataset’.  A population model for our data will consist of three elements: (1) A model for the typical response – this is the response for a typical (average) patient, (2) a model for heterogeneity and (3) a model for uncertainty. 
  • 17. Model for typical response  This is sometimes also called a structural model. For pharmacokinetics this would be a compartmental model that describes the plasma drug concentration over time (see Figure 2A).  The pharmacokinetic model that describes our gentamicin- like drug at a specific time (t) is:
  • 18. A) The observed concentration–time data overlaid with the median predicted concentration from the PK model. (B) Observed concentration–time data overlaid with the median and 2.5th and 97.5th percentiles of the predicted concentrations from the PK model
  • 19. Model of heterogeneity    We use the term heterogeneity in population analysis to describe the variability between individuals. This is also termed Between Subject Variability (BSV) or InterIndividual Variability (IIV). This involves two distinct models:  a model developed to describe predictable reasons why individuals are different.  a model developed to quantify the remaining source of random variability Figure 2B encompass the observed plasma concentration data of our PK example.
  • 20. CLCR as an abbreviation for creatinine clearance CLNR as an abbreviation for non-renal clearance EXPLANATION:
  • 21. FIGURE 3 Individual estimates of systemic drug CL vs. creatinine clearance. The line is the regression line and the intercept represents non-renal clearance and the slope represents the fraction of drug cleared unchanged by the kidneys. The vertical difference of any individual from the regression line represents the difference of that individual from the population average and is given by c (Equation3)
  • 22. Predicted concentrations from the PK model that does not include the covariate CLCR (solid line). Predicted concentrations from a PK model that includes the covariate CLCR as a covariate on CL (dashed lines). Includingthe covariate CLCR in the model reduces the unexplained variability in the model predictions and hence improves the reliability of the model predictions
  • 23. Model for Uncertainty   This model describes why the 1st and 2nd models do not match the observations exactly. Uncertainty is also called residual error. It is assumed that uncertainty arises from (at least) four sources: (i) process error – where the dose or timing of dose or timing of blood samples are not conducted at the times that they are recorded, (ii) measurement error – where the response (e.g. concentration) is not measured exactly due to assay error, (iii) model misspecification – where the models we propose in Equations 1–3 are in reality too simple and (iv) moment to moment variability within a patient.
  • 24.  The final component to add to our analysis must account for the uncertainty in our model predictions. We need to assume (not essential but) that the uncertainty is entirely random and due to error; so by incorporating, This error represents the (residual) difference of the model prediction from the data
  • 25. Why Pop PK are performed???