Transcript 10_Population Pharmacokinetics

Population Pharmacokinetics
Dr Mohammad Issa Saleh
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Population Pharmacokinetics
“The study of the sources and correlates of
variability in drug concentrations among
individuals who represent the target
population that ultimately receive relevant
doses of a drug of interest”
FDA Guidance for Industry, 1999
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Population Pharmacokinetics role
• Individualizing the dose to get optimum benefit
• Designing dosing guidelines for drug labelling
• Communicating important aspects of drug
clinical pharmacology to regulatory bodies
• Understanding the effect of competing dosing
regimens on outcomes of clinical trials
• Helps the quantitative assessment of typical
pharmacokinetic parameters, and the betweenindividual and residual variability in drug
absorption, distribution, metabolism, and
excretion
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Sources of variability
• Sources of variation that contribute to differences
between expectation and outcome are usually
categorized as inter-individual and residual in nature
• The parameter values of a particular patient will differ
from the expected values because of inter-individual
variability
• Residual variation includes intra-individual variability
(random changes in a patient’s parameter values over
time), inter-occasion variability (change in a patient’s
parameter from one occasion [period] to another), drug
concentration measurement error, and model
misspecification errors
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Two Types of Datasets to Consider
• “Rich” data - intensive sampling from each
subject. May be possible to fit each
subject’s data separately.
• “Sparse” data - only a small number of
samples obtained from each subject. Not
possible to fit each subject’s data
separately.
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PK modeling single subject

E.g.: A simple Pk
model Ri
Cp 
 1  e kt  
Cl

Ri = infusion rate
Cl = drug clearance
k =elimination rate
constant
 = measurement
error, intra-individual
error
 N(0,)
Drug Conc

Time
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Residual error
• The difference between observed
concentration and model predicted
concentration
• Residuals are usually assumed to be
independent, normally distributed with
mean zero and variance of σ2
  N(0,)
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Population Pharmacokinetics
• It seeks to obtain relevant pharmacokinetic information in
patients who are representative of the target population
to be treated with the drug
• It recognizes sources of variability, such as inter-subject,
intra-subject, and inter-occasion, as important features
that should be identified and quantified during drug
development or evaluation
• It seeks to explain variability by identifying factors of
demographic, pathophysiologic, environmental, or drugrelated origin that may influence the pharmacokinetic
behaviour of a drug
• It seeks to quantitatively estimate the magnitude of the
unexplained part of the variability in the patient
population
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Why PK parameter vary among
individuals?
• Pharmacokinetic variability is affected by several factors
such as:
– demographics (eg. gender, body weight, surface area, age, and
race etc.)
– environmental factors (eg. smoking, diet, and exposure to
pollutants etc.)
– genetic phenotype that affects the clearance of drugs (eg.
CYP2D6, 2C19, 2C9, 2A6 etc.)
– drug–drug interactions
– physiologic factors (eg. pregnancy)
– pathophysiologic factors (eg. renal and hepatic impairment)
– Other factors (eg. circadian rhythm, adherence, food effect and
the timing of meals, activity, posture)Determining the above
issues provides a outline for defining optimum dosing strategies
in a population, a subpopulation, or for the individual patient
• Determining the above issues provides a outline for
defining optimum dosing strategies in a population, a
subpopulation, or for the individual patient
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Population Pharmacokinetics:
advantages
•
•
•
•
•
Allows to use both sparsely and intensively sampled data
Helps to carry out the pharmacokinetic investigations in special populations
such as neonates, elderly, patients with AIDS, critical care patients, and
those with cancer etc., where the number of samples to be obtained per
subject is limited because of ethical and medical concerns
During drug development, relatively few samples can be obtained from
patients participating in Phase II and III studies for the determination of the
pharmacokinetics of a drug in the relevant population and for the
determination of the relationship between dose, exposure (concentration),
and response/safety
The sparse sampling approach for characterizing PopPK yields better
estimates of inter-subject variability than traditional approaches that yield
positively biased estimates of this measure of dispersion. A combination of
accurate and precise estimates of inter-subject variability and the mean
parameter value for a drug is useful for selecting an initial dose strategy for
drug therapy in a patient and dosage individualization
The analyses of sparse samples collected for PopPK analysis have been
reported to be cost-effective and provide not only an opportunity to
estimate variability, but also to identify its sources.
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Population Pharmacokinetics:
disadvantages
• A disadvantage of the PopPK approach is
that it requires skilled pharmacokineticists
and pharmacometricians who are able to
implement the mathematical and statistical
techniques used in the estimation of
PopPK parameters.
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Population Pharmacokinetics
1.
2.
3.
4.
Naïve average data approach
Naïve pooled data analysis
Two stage approach
Nonlinear mixed effects model
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Naïve average data approach
• It is common practice in preclinical and
clinical pharmacokinetics to perform
studies in which the drug administration as
well as the sampling schedules are
identical for all subjects
• For this type of analysis there are as many
data points as there are individuals at
each sampling time
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Naïve average data approach
•
Analysis of such data using the naive
averaging of data (NAD) approach
consists of the following procedure:
1. Compute the average value of the data for
each sampling time
2. A PK model is fitted to the mean-data while
estimating the best-fit PK parameter values
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Naïve pooled data analysis
• Sheiner and Beal proposed the term naive
pooled data (NPD) approach for the
method in which all data from all
individuals are considered as arising from
one unique individual
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Two-Stage Approach
•
With this approach, individual parameters are
estimated in the first stage by separately fitting
each subject’s data, then in the second stage
obtaining parameters across individuals, thus
obtaining population parameter estimates
1. „Fitting individuals
2. Averaging individuals’ PK parameters;
calculate variances
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Two-Stage Approach:
1-Fitting individuals
Drug Conc
Subject 1: Cl1, K1
Subject 2: Cl2, K2
Subject 3: Cl3, K3
Subject 4: Cl4, K4
Time
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Two-Stage Approach:
1-Fitting individuals








R
Cp 
 1  e  k1t  
Cl1
Drug Conc
R
Cp 
 1  e  k 2t  
Cl2
Time
Cp 
R
 1  e  k 3t  
Cl3
Cp 
R
 1  e  k 4t  
Cl4
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Two-Stage Approach:
2-Averaging individuals’ PK parameters; calculate
variances
Subject
Cl
K
1
Cl1
K1
2
Cl2
K2
3
Cl3
K3
4
Cl4
K4
Average
??
??
SD
??
??
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Problems with “Two-stage” analysis
1. Ethical concerns
1. 2-stage analysis requires ‘rich’ data sets (e.g., 6-10
concentration v. time samples)
2. Difficult to justify in seriously ill patients & in special
populations (pediatrics, elderly, etc.)
2. High Cost
3. Little opportunity for serendipity. Optimization of
study design removes variables, which
minimizes the likelihood of finding unexpected
relationships (e.g., effect of hepatic impairment
on CL for drug that is exclusively cleared in the
urine).
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Mixed-Effects Modeling Approach
•
Simultaneously fits “Pop PK” model to all data
collected from the study The Pop PK model is
structured to:
1. Define mean values for PK parameters (e.g,. CL, V)
and define covariates (parameters & covariates are
the “fixed-effects” of the system)
2. Account for random variation (“random effects”:
inter-individual variability [person-to-person
variability within a group], inter-occasion variability
[day-to-day variability], and residual variability
[model misspecification, assay error])
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Mixed-Effects Modeling Approach
•
Using Mixed effects modeling the
following are determined:
1. Theta (θ): Population estimate for the PK
parameter
2. Eta (η): Describes inter & intra-individual
variability. η will have a mean of zero and a
variance of ω2
3. Epsilon, Err (ε): Residual variability (assay,
etc). ε will have a mean of zero and a
variance of σ2
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Population pharmacokinetic model of digoxin in older
Chinese patients and its application in clinical practice
Xiao-dan ZHOU, Yan GAO, Zheng GUAN, Zhong-dong LI, Jun LI
Aim: To establish a population pharmacokinetic (PPK) model of digoxin in older Chinese
patients to provide a reference for individual medication in clinical practice.
Methods: Serum concentrations of digoxin and clinically related data including gender, age,
weight (WT), serum creatinine (Cr), alanine aminotransferase (ALT), aspartate
aminotransferase (AST), blood urea nitrogen (BUN), albumin (ALB), and co-administration
were retrospectively collected from 119 older patients taking digoxin orally for more than 7 d.
NONMEM software was used to get PPK parameter values, to set up a final model, and to
assess the models in clinical practice.
Results: Spironolactone (SPI), WT, and Cr markedly affected the clearance rate of digoxin.
The final model formula is Cl/F=5.9×[1– 0.412×SPI]×[1–0.0101×(WT–62.9 )]×[1–0.0012×(Cr–
126.8 )] (L/h); Ka=1.63 (h-1); Vd/F=550 (L). The population estimates for Cl/ F and Vd/F were
5.9 L/h and 550 L, respectively. The interindividual variabilities (CV) were 49.0% for Cl/F and
94.3% for Vd/F. The residual variability (SD) between observed and predicted concentrations
was 0.365 μg/L. The difference between the objective function value and the primitive
function value was less than 3.84 (P>0.05) by intra-validation. Clinical applications indicated
that the percent of difference between the predicted concentrations estimated by the PPK
final model and the observed concentrations were -4.3%−+25%. Correlation analysis
displayed that there was a linear correlation between observated and predicted values
(y=1.35x+0.39, r=0.9639, P<0.0001).
Conclusion: The PPK final model of digoxin in older Chinese patients can be established
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using the NONMEM software, which can be applied in clinical practice.
What is the interpretation of the
results?
• Population estimated parameters:
– Cl/ F = 5.9 L/h
– Vd/F = 550 L
– Ka=1.63 hr-1
K = (Cl/F)/(Vd/F)
• Population estimated concentrations:

KaFXo
Cp 
e  Kt  e  Kat
Vd ( Ka  K )

• Where Vd/F, Ka, and K are population estimated
PK parameters
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What is the interpretation of the
results?
• Individual (ith individual) estimated parameters:
– (Cl/F)i=5.9×[1– 0.412×SPI]×[1–0.0101×(WT–62.9
)]×[1–0.0012×(Cr–126.8 )]+ η
– (Vd/F)i = 550+ η
– (Ka)i=1.63+ η
• Where SPI, WT and Cr are characteristics
specific to the individual
• η is the random effects models for stochastic
variation in individual parameter values
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What is the interpretation of the
results?
• Individual estimated concentrations:

KaFXo
Cp 
e  Kt  e  Kat
Vd ( Ka  K )

• Where Vd/F, Ka, and K are individual
estimated PK parameters
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What is the interpretation of the
results?
• The observed concentration is described
as:
KaFXo
Cp 
e  Kt  e  Kat  
Vd ( Ka  K )


• Where Vd/F, Ka, and K are individual
estimated PK parameters
• ε is the residual variability
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Describe the variability?
• Interindividual variability:
η has a mean of zero and a CV% of 49.0%
for Cl/F and 94.3% for Vd/F
• Residual variability:
• ε has a mean of zero and a standard
deviation of 0.365 μg/L
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