Population pharmacokinetics: study of drug absorption
and disposition characteristics in a population or distinct
subset of population.
The information obtained is then summarized using
Population models address variability arising from
o Inter-individual variability
o Intra-individual variability
o Measurement errors
Start with the individuals then progress
to the population.
evaluating the individuals.
Random errors from all sources are
Goes directly to the population without
individual variability from the residual
intra-individual variability, measurement
E.g. Traditional standard two stage
Method, Naïve pooling method
E.g. Parametric method: Mixed effect
Non parametric method: NPML,
NPEM, SNP, I2S
TRADITIONAL STANDARD TWO
It is a traditional method.
It involves study of relatively small number of
individuals subjected to intense sampling.
The period of the study is short, since the individuals
are usually instutionalised.
It consists of two stages:
Stage 1: Each individuals data is analysed on a case by
case basis using weighed or extended nonlinear least
square regression to determine the individual
Stage 2: The individual pharmacokinetic parameters
are pooled to determine measures of central
tendency and variability for the population. The
association between specific pharmacokinetic
parameters and demographic characters are studied.
It provides reliable and robust estimates when extensive
numbers of samples are available for each individual.
It is a simple method.
It is a well tried and straightforward method to implement.
Many software packages are available for this method.
Statistics are straightforward and are familiar to the
It is capable of producing estimates of typical values for
members of a population that are similar to those found with
direct population approaches.
It is considered to be the golden standard in case of rich data.
Being a controlled study design, it is very expensive
and requires careful planning and implementation.
It gives unreliable results in case of sparse data.
It is difficult to study a sufficiently large number of
individuals to adequately represent the population.
There are ethical issues to obtain extensive samples
from a fragile subpopulation.
NAIVE POOLING METHOD
It is a traditional method.
In this method, the data from all individuals are
pooled and analysed simultaneously without
consideration of the individual from whom the
specific data were obtained.
It may be the only viable approach in certain
situations, for e.g. in case on animal data, where each
animal provides only one data point.
This method is generally considered the least
It is susceptible to bias.
It produces inaccurate estimates of pharmacokinetic
MIXED EFFECT MODELLING
Mixed effect modelling is a parametric method which
assumes a specific distribution of pharmacokinetic
parameters prior to estimation.
It is considered as the optimum population model
It is a direct method in which the population
parameters are determined in a single stage of
analysis applied simultaneously to the data from
This method recognises which data arise from the
same individual and which do not.
“Effects” are factors that contribute to the variability
of the measured observation.
They are of two types:
Cp = D/Vd . e –Cl/Vdt
Cp = concentration of drug in the plasma (dependent
D = dose (fixed effect)
t = time
Fixed effects are components of the structural
They do not include any unexplainable variation
either between or within individuals.
Fixed effect parameters are represented by the
Each individual in a population will have a specific
value for their pharmacokinetic parameter, which will
differ from the population typical value due to
This variability is represented by the symbol eta (?).
The manner in which an individual’s eta relates the
individual’s pharmacokinetic parameter to the
population typical value is given by the error model.
A variety of error models can be chosen, depending
upon the visual inspection of data, experience, trial
The most well-known method for applying mixed
effect method in NONMEM (non linear mixed effect
The output from NONMEM includes estimates of
mean variances and covariances of the parameters.
It is useful for sparse and randomly collected data.
It is able to derive population models when only a few
samples are available from each individual.
Individuals are still identifiable, which permits repeated
measures for individuals in spite of the data being pooled
into a single data set.
Inclusion of covariates during elimination procedure
offsets unbalanced data.
It is ideal for studying population such as very old, very
young or very sick which are difficult to study using STS.
Study design does not call for collection of samples at
specific times, resulting in imprecise estimates.
Therefore some thought should be given to the
optimal collection time.
Biased estimates have been reported especially when
data contain large amount of random error.
NON PARAMETRIC METHODS
Non parametric methods do not assume any specific
distribution of parameters about the population
values, but rather allow for many possible
In this method, the entire population distribution of
each parameter is estimated from the population
This permits visual inspection of distribution before
committing to one.
Different non parametric methods are:
Non parametric maximum likelihood [NPML]
Non parametric expectation maximization [NPEM]
Semi/ smooth non parametric method [SNP]
NON PARAMETRIC MAXIMUM
This method permits all forms of distributions
including those containing sharp changes, such as
discontinuities and kinks.
It uses maximum likelihood as estimator.
NON PARAMETRIC EXPECTATION
This method is preferred to any parametric method
when there is an unexpected multimodal or nonnormal distribution of atleast one of the nodal
It eliminates the need for initial guesses which are
required for nonlinear least square procedure.
It is preferable to traditional method in case of sparse
It uses expectation maximization as the estimator.
SEMI/ SMOOTH NON PARAMETRIC
This method places some restrictions on the type of
parametric distributions considered.
Functions that are not permitted include those
containing sharp edges and discontinuities.
ITERATIVE TWO STAGE METHOD
I2S method may be used with rich data, a mixture of
rich and sparse data or only sparse data.
To initiate the procedure an approximate prior
population model is required.
Source for these population value include
literature, naïve pooled data method, STS method
This population model is subjected to Bayesian
estimation of individual parameters for all
patients, both rich and sparse in data (stage 1).
The population parameters are recalculated with
these new individual parameters in order to form new
set of priori distribution (stage 2).
The Bayesian estimation step is performed again
using the new population model to find more
accurate estimates of individual parameters.
This is carried out until the difference between the
new and old prior distribution is essentially zero.
This method yields both individual and population
PRE APPROVAL PHASE
(drug development phase)
Development of dosage regimen.
Determination of dosage requirements in special populations
Predicting outcomes of various forms of drug administration
like multiple doses, special patient groups, and controlled
Investigating potential disease and drug interactions.
Studying drug concentration- acute toxic effect relationships.
Construction of population pharmacokinetic model.
Evaluating pharmacokinetic versus pharmacodynamics
POST APPROVAL PHASE
Application of the population average dose for an
individual, depending on the variability of
pharmacokinetic and pharmacodynamics parameters.
Dose individualisation for individuals whose
pharmacokinetic parameters are most likely to deviate
from the population typical values.
Dose individualisation for drugs with narrow therapeutic
Stochastic control of drug therapy.