Analysis of population PK Data
Gayatri Devi R
Student 5th PHARM D
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.
Pharmacokinetically guided dose escalation (PGDE) studies
Dose fixing in Phase II and subsequent studies.
To adapt drug dosage to the individual patient (therapeutic
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),
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
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
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,
Explanation of variability by identifying factors of
demographic, pathophysiological, environmental, or
concomitant drug-related origin that may influence the
Quantitative estimation of the magnitude of the
unexplained variability in the patient population.
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
Clinical pharmacokinetic applications
Computer programs for teaching
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
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
Bayesian General Modeling (MB)
Least Squared General Modeling
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
Approaches for analyzing Pop PK data
Standard two - stage approach
refers to fitting a pharmacokinetic model to the data of
Afterwards summary statistics are computed for the total
collection of individual parameter estimates
Using this approach, the inter individual variance tends to
it is not applicable when the individual data are too sparse
for individual model fits.
Nonlinear Mixed-Effects Modelling Approach
With this type of modelling not only pharmacokinetic
parameters but also inter-individual variance parameters
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.
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.
A population analysis was then conducted on the
A population model for our data will consist of three
(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.
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:
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
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
Figure 2B encompass the observed plasma concentration
data of our PK example.
CLCR as an abbreviation for creatinine clearance
CLNR as an abbreviation for non-renal clearance
Individual estimates of systemic drug
CL vs. creatinine clearance.
The line is the regression line and
the intercept represents non-renal
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
Predicted concentrations from
the PK model that does not
include the covariate CLCR (solid
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 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
(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.
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