Introduction to population pharmacokinetics, Bayesian theory, and analysis of population pharmacokinetics data.

1. POPULATION
PHARMACOKINETICS
Dr. Ramesh Bhandari
Asst. Professor,
Department of Pharmacy Practice
KLE College of Pharmacy, Belagavi

2. Dr. Ramesh Bhandari
Population Pharmacokinetics
ALL HUMANS ARE ALIKE
TRUE ONLY AS A SPECIES
DIFFERENCE EXISTS –
including their response to the
drugs

3. Dr. Ramesh Bhandari
Population Pharmacokinetics
Research has uncovered significant
differences among different populations
in:
 Rate of drug metabolism
 Responses to drugs
 Side effects of drugs

4. Dr. Ramesh Bhandari
Population Pharmacokinetics
Genetic Variations of different
racial and ethnic groups
Difference in proteins encoding
Difference in drug metabolism
Sub Therapeutic/toxic levels
Dosage adjustment is needed particularly for
Narrow therapeutic Index drugs.

5. Dr. Ramesh Bhandari
Population Pharmacokinetics
 Examples of different responses of drugs among
different population groups.
 CYP2C19*2 & *3 is the phenotype for poor
metabolizer.
 CYP2C19*17 type results in ultra metabolizing
capacity.
 Approx. 15% of Japanese, 5% of the Chinese, and
5% of the Australian populations are classified as
poor metabolizer.

6. Dr. Ramesh Bhandari
Population Pharmacokinetics
 According to FDA, Population Pharmacokinetic 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”.
 Population pharmacokinetics (Pop PK) is the study
of variability in plasma drug concentrations
between and within patient populations receiving
therapeutic doses of a drug.

7. Dr. Ramesh Bhandari
Population PK Approach Vs
Classical PK Approach
 Traditional pharmacokinetic studies are usually
performed on healthy volunteers or highly selected
patients, and the average behaviour of a group (i.e,
the mean plasma concentration–time profile) is the
main focus of interest.
 Pop PK examines the relationship of the
demographic, genetic, pathophysiological,
environmental, and other drug related factors that
contribute to the variability observed in safety and
efficacy of the drug.

8. Dr. Ramesh Bhandari
Population PK Approach Vs
Classical PK Approach
Drug
concentration
Time
Drug
concentration
Time
Drug
concentration
Time
Classical Approach
Pop PK Approach

9. Dr. Ramesh Bhandari
Advantages of Population
pharmacokinetics
 Provides better understanding of the dose-response
relationship among the target population.
 Sample population mimics the real target
population at large.
 Multiple factors may be studied in one population
PK study.
 Diversity of patient characteristics and larger
sample sizes.
 Prior dose adjustment can be made using
Population PK data.

10. Introduction to Bayesian
Theory

11. Dr. Ramesh Bhandari
BAYESIAN THEORY
 Bayesian theory was originally developed to improve
forecast accuracy by combining subjective prediction
with improvement from newly collected data.
 In the diagnosis of disease, the physician may make a
preliminary diagnosis based on symptoms and
physical examination. Later, the results of laboratory
tests are received. The clinician then makes a new
diagnostic forecast based on both sets of information.
 Bayesian theory provides a method to weigh the prior
information (eg, physical diagnosis) and new
information (eg, results from laboratory tests) to
estimate a new probability for predicting the disease.

12. Dr. Ramesh Bhandari
BAYESIAN THEORY
 In developing a drug dosage regimen, we assess the
patient’s medical history and then use average or
population pharmacokinetic parameters appropriate
for the patient’s condition to calculate the initial dose.
 After the initial dose, plasma or serum drug
concentrations are obtained from the patient that
provide new information to assess the adequacy of the
dosage.
 The dosing approach of combining old information
with new involves a “feedback” process and is, to
some degree, inherent in many dosing methods
involving some parameter readjustment when new
serum drug concentrations become known.

13. Dr. Ramesh Bhandari
BAYESIAN THEORY
 The advantage of the Bayesian approach is the
improvement in estimating the patient’s
pharmacokinetic parameters based on Bayesian
probability versus an ordinary least-squares-based
program.
 An example comparing the Bayesian method with
an alternative method for parameter estimation
from some simulated theophylline data will be
shown in the next section.
 The method is particularly useful when only a few
blood samples are available

14. Dr. Ramesh Bhandari
BAYESIAN THEORY
 Bayesian probability theory when applied to dosing of a drug
involves a given pharmacokinetic parameter (P) and plasma or
serum drug concentration (C), as shown in Equation 22.11. The
probability of a patient with a given pharmacokinetic
parameter P, taking into account the measured concentration, is
Prob (P/C):
Prob (P│C) = Prob (P) . Prob (C │P)
Prob (C)
Prob (P) = Probability of the patients parameter within the assumed
population distribution
Prob (C │P) = Probability of measured concentration within the
population
Prob (C) = unconditional probability of the observed concentration

15. Dr. Ramesh Bhandari
BAYESIAN THEORY
Problem:
After diagnosing a patient, the physician gave the patient a
probability of 0.4 of having a disease. The physician then ordered a
clinical laboratory test. A positive laboratory test value had a
probability of 0.8 of positively identifying the disease in patients
with the disease (true positive) and a probability of 0.1 of positive
identification of the disease in subjects without the disease (false
positive). From the prior information (physician’s diagnosis) and
current patient-specific data (laboratory test), what is the posterior
probability of the patient having the disease using the Bayesian
method?

16. Dr. Ramesh Bhandari
Problem solving:
Population
Disease
Test +ve
Test -ve
No
Disease
Test +ve
Test -ve
Prob (D│+) = Prob (D) . Prob (+│D)
Prob (+)

17. ADAPTIVE METHOD
OR DOSING WITH
FEEDBACK

18. Dr. Ramesh Bhandari
 In dosing drugs with narrow therapeutic ratios, an
initial dose is calculated based on mean population
pharmacokinetic parameters.
 After dosing, plasma drug concentrations are obtained
from the patient. As more blood samples are drawn
from the patient, the calculated individualized patient
pharmacokinetic parameters become increasingly
more reliable.
 This type of approach has been referred to as adaptive
or Bayesian adaptive method with feedback when a
special extended least-squares algorithm is used.

19. Dr. Ramesh Bhandari
 Many ordinary least-squares (OLS) computer
software packages are available to clinical practice for
parameter and dosage calculation.
 Some software packages record medical history and
provide adjustments for weight, age, and in some
cases, disease factors.
 Abbottbase Pharmacokinetic Systems (1986 and
1992) is an example of patient oriented software that
records patient information and dosing history based
on 24-hour clock time.
 An adaptive-type algorithm is used to estimate
pharmacokinetic parameters.

20. Dr. Ramesh Bhandari
 The average population clearance and volume of
distribution of drugs are used for initial estimates, and
the program computes patient-specific Cl and VD as
serum drug concentrations are entered.
 The program accounts for renal dysfunction based on
creatinine clearance, which is estimated from serum
creatinine concentration using the Cockroft–Gault
equation.
 The software package allows specific parameter
estimation for digoxin, theophylline, and
aminoglycosides, although other drugs can also be
analyzed manually.

21. Dr. Ramesh Bhandari
 Many least-squares (LS) and weighted least squares
(WLS) algorithms are available for estimating patient
pharmacokinetic parameters.
 Their common objective involves estimating the
parameters with minimum bias and good
prediction, often as evaluated by mean predictive
error.
 The advantage of the Bayesian method is the ability
to input known information into the program, so
that the search for the real pharmacokinetic parameter
is more efficient and, perhaps, more precise.

22. Dr. Ramesh Bhandari
 Bayesian Approach with OLS Method:
Ci= f(P,ti) ℇi
OBJOLS =
𝑖=1
𝑛 𝐶𝑖
−𝐶ˆ𝑖
2
σi
2

23. Dr. Ramesh Bhandari
The Bayes Estimator
 When the pharmacokinetic parameter, P, is estimated from a
set of plasma drug concentration data (Ci ) having several
potential sources of error with different variance, the OLS
method for parameter estimation is no longer adequate (it
yields trivial estimates).
 The intersubject variation, intrasubject variance, and
random error must be minimized properly to allow efficient
parameter estimation.
 The weighted least-squares function was suggested by
Sheiner and Beal.
 The equation represents the least-squares estimation of the
concentration by minimizing deviation squares, and deviation
of population parameter squares.

24. Dr. Ramesh Bhandari
The Bayes Estimator
 Following equation is called the Bayes estimator.
This approach is frequently referred to as extended
least-squares (ELS).
 Intrasubject Ci = f(P,Xi) + ℇi
 Intersubject Pk = P ˆk + nk
 OBJ BAYES = 𝑖=1
𝑛 𝐶𝑖
−𝐶ˆ𝑖
2
σi
2 + 𝑘=1
𝑆 𝑃 𝑘
−𝑃ˆ 𝑘
2
ω𝑘
2

25. ANALYSIS OF POPULATION
PHARMACOKINETIC DATA

26. Dr. Ramesh Bhandari
Traditional Pharmacokinetic
Studies
 involve taking multiple blood samples periodically over time
 in a few individual patients, and
 characterizing basic pharmacokinetic parameters such as k,
VD, and Cl.
 Because the studies are generally well designed, there are
fewer parameters than data points.
 Traditional pharmacokinetic parameter estimation is very
accurate, provided that enough samples can be taken for the
individual patient.
 The disadvantage is that only a few relatively homogeneous
healthy subjects are included in pharmacokinetic studies, from
which dosing in different patients must be projected.

27. Dr. Ramesh Bhandari
Traditional Pharmacokinetic
Studies
 In the clinical setting, patients are usually less
homogeneous; patients vary in sex, age, and body weight.
 They may have concomitant disease and may be receiving
multiple drug treatments.
 Even the diet, lifestyle, ethnicity, and geographic location
can differ from a selected group of “normal” subjects.
 Further, it is often not possible to take multiple samples from
the same subject, and, therefore, no data are available to
reflect intra-subject difference,
 So that iterative procedures for finding the maximum
likelihood estimate can be complex and unpredictable due
to incomplete or missing data.

28. Dr. Ramesh Bhandari
Traditional Pharmacokinetic
Studies
 However, the vital information needed about the
pharmacokinetics of drugs in patients at different stages of
their disease with various therapies can only be obtained from
the same population, or from a collection of pooled blood
samples.
 The advantages of population pharmacokinetic analysis using
pooled data were reviewed by Sheiner and Ludden (1992)
and included a summary of population pharmacokinetics for
dozens of drugs.
 Pharmacokinetic analysis of pooled data of plasma drug
concentration from a large group of subjects may reveal much
information about the disposition of a drug in a population.

29. Dr. Ramesh Bhandari
Traditional Pharmacokinetic
Studies
 Unlike data from an individual subject collected over
time, inter- and intra-subject variations must be
considered.
 Both pharmacokinetic and non-pharmacokinetic
factors, such as age, weight, sex, and creatinine
concentration, should be examined in the model to
determine the relevance to the estimation of
pharmacokinetic parameters.

30. Dr. Ramesh Bhandari
Non-Linear Mixed Effect Model
(NONMEM)
The nonlinear mixed-effect model
(NONMEM) is so called because the model uses
both fixed and random factors to describe the
data.
The Known, observable properties of
individuals that cause the PK parameters to vary
across the population are called fixed effects.
Fixed factors such as patient weight, age,
gender, and creatinine clearance are assumed to
have no error.

31. Dr. Ramesh Bhandari
Non-Linear Mixed Effect Model
(NONMEM)
Whereas, random factors include inter- and
intra-individual differences.
Random effects can’t be predicted in
advance.

32. Dr. Ramesh Bhandari
Non-Linear Mixed Effect Model
(NONMEM)
 NONMEM is a statistical program written in
Fortran that allows Bayesian pharmacokinetic
parameters to be estimated using an efficient
algorithm called the first-order (FO) method.
 The parameters may now be estimated also with a
first order conditional estimate (FOCE) algorithm.
 In addition, to pharmacokinetic parameters, many
examples of population plasma data have been
analyzed to determine population factors.

33. Dr. Ramesh Bhandari
Non-Linear Mixed Effect Model
(NONMEM)
NONMEM fits plasma drug concentration
data for all subjects in the groups
simultaneously and estimates the population
parameter and its variance.
The parameter may be clearance and/or VD.
The model may also test for other fixed
effects on the drug due to factors such as
age, weight, and creatinine clearance.

34. Dr. Ramesh Bhandari
Non-Linear Mixed Effect Model
(NONMEM)
 The model describes the observed plasma drug
concentration (Ci ) in terms of a model with:
1. Pk = fixed effect parameters, which include
pharmacokinetic parameters or patient factor parameters.
For example, P1 is Cl, P2 is the multiplicative coefficient
including creatinine factor, and P3 is the multiplicative
coefficient for weight.
2. Random effect parameters, including (a) the variance of
the structural (kinetic) parameter, Pk, or inter-subject
variability within the population, ω2 ; and (b) the residual
intra-subject variance or variance due to measurement
errors, fluctuations in individual parameter values, and all
other errors not accounted for by the other parameters.

35. Dr. Ramesh Bhandari
Population Pharmacokinetic Data
Analysis
1) Standard two stage (STS) method
2) First Order Method

36. Dr. Ramesh Bhandari
1) Standard two stage (STS)
method
 Estimates parameters from the plasma drug
concentration data for an individual subject during
the first stage.
 The estimates from all subjects are then combined to
obtain an estimate of the parameters for the
population.
 The method is useful because unknown factors that
affect the response in one patient will not carry
over and bias parameter estimates of the others.
 The method works well when sufficient drug
concentration–time data are available.

37. Dr. Ramesh Bhandari
2) First Order Method
 less well understood
 The estimation procedure is based on minimization of an
extended least-squares criterion, which was defined through an
FO Taylor series expansion of the response vector about the
fixed effects and which utilized a Newton–Raphson-like
algorithm.
 This method attempts to fit the data and partition the
unpredictable differences between theoretical and observed
values into random error terms.
 When this model includes concomitant effects, it is called a
mixed-effect statistical model.
 The advantage of the FO model is that it is applicable even
when the amount of time–concentration data obtained from
each individual is small, provided that the total number of
individuals is sufficiently large.

38. Thank you