The document outlines the objectives and principles of population pharmacokinetics, emphasizing its significance in understanding variability in drug concentrations among different patient populations. It discusses the development of population pharmacokinetics, Bayesian theory, and adaptive methods used to enhance dosage strategies and pharmacokinetic parameter estimations. Furthermore, it highlights the challenges and advantages of population pharmacokinetics in drug development and clinical applications.

1. Dr. S P Srinivas Nayak,
PharmD., MSc., PGDND., (PhD)
Assistant Professor, PIPR, PU
POPULATION PHARMACOKINETICS

2. Lecture Objectives
After completion of this lecture, student will be able to:
• Explain origin and development of population pharmacokinetics
• Discuss introduction to Bayesian theory
• Discuss introduction to analysis of population pharmacokinetic data

3. Population pharmacokinetics
• 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
• Certain patient demographical, pathophysiological, and therapeutic features,
such as body weight, excretory and metabolic functions, and the presence of
other therapies, can regularly alter dose-concentration relationships
• The study participants recruited are usually healthy volunteers or are
selected very cautiously.

4. Population Pharmacokinetics
• For example, steady-state concentrations of drugs eliminated mostly by the
kidney are usually greater in patients suffering from renal failure than they
are in patients with normal renal function who receive the same drug dosage
• Population pharmacokinetics seeks to identify the measurable
pathophysiological factors that cause changes in the dose-concentration
relationship and extent of these changes so that, if such changes are
associated with clinically significant shifts in the therapeutic index, dosage
can be appropriately modified.

5. Origins and development of population pharmacokinetics
• The subjects of traditional pharmacokinetic studies are usually healthy
volunteers or highly selected patients, and the average behavior of a group
(i.e., the mean plasma concentration-time profile) has been the main focus of
interest
• Traditional pharmacokinetic studies also usually involve multiple samples
taken at fixed intervals from healthy volunteers

6. Origins and development of population
pharmacokinetics
• In contrast, population pharmacokinetic data are obtained from patients being
treated with a drug
In contrast to traditional pharmacokinetic evaluation, the population PK
approach encompasses some or all of the following features:
o The collection of relevant pharmacokinetic information in patients who are
representative of the target population to be treated with the drug

7. Origins and development of population pharmacokinetics
o The identification and measurement of variability
o The explanation of variability by identifying factors of
 Demographic
 Pathophysiological
 Environmental or
 Concomitant drug-related origin that may influence the pharmacokinetic
behavior of a drug.

8. Population pharmacokinetics
• Population kinetics is the study of variability in plasma drug concentration
between and within patient populations receiving therapeutic doses of a drug
• Traditional PK studies are usually performed on healthy volunteers or highly
selected patients, and the average behavior of a group is the main focus of
interest
• Pop K 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

9. Population pharmacokinetics
• For example, steady-state concentrations of drugs eliminated mostly by the
kidney are usually greater in patients suffering from renal failure than they
are in patients with normal renal function who receive the same drug dosage
• The resolution of the issue causing variability in patients allows for the
development of an optimum dosing strategy for a population, subgroup or
individual patient
• The importance of developing optimum dosing strategies has led to an
increase in the use of Pop K approaches in new drug development

10. Reason for doing population PK
Phase Reason for doing Pop PK
1 To estimate population parameter of a response surface model
2a To gain information on drug safety
2b How the drug will be used in subsequent stages of drug development
3 To gather additional information on drug pharmacodynamics in special population
4 Post marketing surveillance study.

11. • The magnitude of the unexplained (random) variability
is important because the efficacy and safety of a drug
may decrease as unexplainable variability increases
• In addition to inter-individual variability, the degree to
which steady-state drug concentrations in individuals
typically vary about their long-term average is also
important

12. Objectives of pop k
1. Provides estimates of pop pk parameters fixed effects
(Fixed effects: Parameters in the pharmacokinetic model
that do not vary across subject)
2. Provides estimates of variability random effects
(Random effects: Effects varying in a random way
between subjects, between occasions, or within subject)

13. a. Intersubject variability: variability between subjects; measures
the magnitude of random individual variability in relation to fixed
effects. Also referred to as inter-individual variability
b. Interoccasion variability: Random variability in individual
pharmacokinetic parameters between study occasions (day to day
variability)
c. Residual intrasubject variability: The remaining unexplained
variability in response occurring within subjects after all structural
and covariate effects have been incorporated into a model.

14. Pop pk determines significant factors
effecting inter-subject variability…
• Demographics
• Genetics
• Environmental
• Physiological
• Concomitant therapy
• Other factors

15. Advantages of pop pk
• Provides a better understanding of dose-response relationship
among the target patient population
• The sample population mimics the real target population at
large
• Evaluates entire population
• Can be used for predictions and simulations

16. Advantages of pop pk
• Computationally intensive
• Intensive and sparse sampling
• Analysis time is longer
• PK/PD modeling (relationship between drug levels and
drug effects)

17. Advantages of pop pk
• Multiple factors may be studied in one pop pk study
• Data can be used to support labeling claims, drug-conc
relationship and also to see regulatory approval of a new
use of a drug
• Data on studies of different designs, dosing regimens,
dosage and formulations can be pooled

18. Advantages of pop pk
• Provides structural model for PK/PD
• Linear and Nonlinear PK supported
• Can determine
– Clearance
– Volume of distribution
– Effect of covariates (e.g. age, weight, sex, kidney function)

19. Advantages of pop pk

20. Disadvantages
• Less rapid
• Less user-friendly software
• More expertise required for analysis, complex
methodology
• Analysis limited by imagination
• Usually patients are not homogenous

21. Disadvantages
• relatively large numbers of patients are required (typically
>40)
• complex pharmacostatistical analyses
• requires collection, compilation and verification of large
amounts of data
• model building may be tedious, labour intensive and
time-consuming

22. Disadvantages
• • model diagnostics are often complex and time-
consuming
• difficulties with handling missing data (e.g. all covariates
in all patients)

23. Recent studies
• A recent survey of 206 new drug applications and supplements
reviewed by the Office of Clinical Pharmacology and
Biopharmaceutics of the FDA in fiscal years 1995 and 1996
showed that almost one-quarter (i.e., 47) of the submissions
contained population PK and/or pharmacodynamic reports
• Because of early integration of population PK studies with clinical
studies, the population PK approach provided useful safety,
efficacy, and dosage optimization information for the drug label in
83 percent of the 47 submissions.

24. Clinical outcomes
 Population pharmacokinetic methods are an emerging and important part of drug
development including preclinical studies, clinical trials and postmarketing
surveillance.
 There are excellent reviews from the pharmaceutical industry and regulatory
perspectives, and web-based guidelines from regulatory agencies.
 Studies have involved research and clinical applications in a wide variety of patients
and conditions including diabetes, clotting disorders, malignancy, serious infection,
apnoea of prematurity, pregnancy, organ transplantation, self-poisoning and arthritis.
 Clinically, it has the potential to help the selection of the optimum dose for an
individual patient.

25. Clinical outcomes
 Like all mathematical models, a population pharmacokinetic model only provides
estimates of the true (but unknown) pharmacokinetic parameter values.
 Fitting a model to the data results in some uncertainty in the true value of the
estimated parameter, therefore plasma concentrations predicted by a model also have
a degree of uncertainty attached to them.
• There is an oft-quoted adage that ‘all models are wrong, but some are useful’.
Population analyses have numerous useful clinical applications, especially in patients
who otherwise may be difficult to recruit for a traditional pharmacokinetic study, for
example young children or patients in intensive care.

26. INTRODUCTION TO 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

27. • 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
• 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

28. • Because of inter- and intra-subject variability, the pharmacokinetic
parameters of an individual patient must be estimated from limited data in the
presence of
 Unknown random error (assays, etc)
 Known covariates and
 Variables such as clearance, weight, and disease factor, etc, and possible
structural (kinetic model) error

29. • From knowledge of mean population pharmacokinetic parameters and their
variability, Bayesian methods often employ a special approach and allow
improved estimation of patient pharmacokinetic parameters when there is a
lot of variation in data
Bayesian probability theory :
• Prob(P/C) = Prob(P).Prob(C/P) / Prob(C)
• Prob(P) = the probability of patients parameter within the assumed population
distribution
• Prob(C/P) = the probability of measured concentration within the population
• Prob(C) = the probability of observed concentration

30. Adaptive method
• 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

31. Adaptive method
• This type of approach has been referred to as adaptive, or Bayesian adaptive
method with feedback
• Many ordinary least-squares computer software packages are available to
clinical practice for parameter and dosage calculation

32. Adaptive method
• An adaptive-type algorithm is used to estimate pharmacokinetic parameters
• The average population clearance and volume of distribution of drugs are
used for initial estimates and the program computes patient-
specific Cl and V D as serum drug concentrations are entered

33. Adaptive method
• 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

34. Adaptive method
• For example, a drug is administered by intravenous infusion at a rate, R, to a
patient. The drug is infused over t hours (t may be 0.5 to 2 hours for a typical
infusion)
• The patient's clearance, Cl T, may be estimated from plasma drug concentration
taken at a known time according to a one-compartment-model equation

35. Analysis of population PK Data
Analysis of population PK Data
• The nonlinear mixed effect model (or NONMEM) is so called because the
model uses both fixed and random factors to describe data
• Fixed factors such as patient weight, age, gender are assumed to have no
error, whereas random factors include inter- and intra individual differences

36. • 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

37. • 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 V D
• The model may also test for other fixed effects on the drug due to factors
such as age, weight, and creatinine concentration

38. • There are generally two reliable and practical approaches to population
pharmacokinetic data analysis
• One approach is the standard two-stage (STS) method, which 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

39. • A second approach, the first-order (FO) method, is also used but is perhaps
less well understood
• The estimation procedure is based on minimization of an extended least-
squares criterion which utilizes a Newton-Raphson-like algorithm

40. Summary
• Bayesian theory was originally developed to improve forecast accuracy by
combining subjective prediction with improvement from newly collected data
• 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
• The nonlinear mixed effect model (or NONMEM) is so called because the
model uses both fixed and random factors to describe data

41. • Population pharmacokinetics
• Origins and development of population pharmacokinetics
• Introduction to Bayesian theory
• Adaptive method
• Analysis of population PK data

42. THANK YOU