population pharmacokinetics

Population Pharmacokinetics

Mr. T.S. Mohamed Saleem M.Pharm., Ph.D

Assistant Professor & Head

Introduction

26-11-2014T.S.M. Saleem-Department of

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Pharmacokinetic studies based on a traditional intensive design model areusually conducted using carefully selected

volunteer subjects,

a controlled experimental design, and

collection of multiple blood samples.

After measurement of drug and metabolite concentrations in all samples,pharmacokinetic models are applied to determine parameters such as

elimination half-life,

volume of distribution, and

clearance.

During the new drug development process, a series of pharmacokineticstudies are conducted to determine the influence of major disease states orexperimental conditions hypothesized to affect drug disposition.

Such factors might includeage, gender, body weight, ethnicity,

hepatic and renal disease,

coadministration of food, and

various drug interactions.

Introduction (Cont……)


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Classical pharmacokinetic studies can quantitate the

effects of anticipated influences on drug disposition

under controlled circumstances, but cannot identify

the unexpected factors affecting pharmacokinetics.

A number of examples of altered drug

pharmacokinetics became apparent in the patient

care setting only in the postmarketing phase of

extensive clinical use.

Examples include the

digoxin-quinidine interaction,

altered drug metabolism due to cimetidine, and

the ketoconazole-terfenadine interaction.

Population Pharmacokinetic method


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Population pharmacokinetic methodology has developed as anapproach to detect and quantify unexpected influences on drugpharmacokinetics.

Population pharmacokinetic studies, in contrast to classical ortraditional pharmacokinetic studies, focus on the central tendency ofa pharmacokinetic parameter across an entire population, andidentify deviations from that central tendency in a subgroup ofindividual patients.

Analysis of clinical data using a population approach allowspharmacokinetic parameters to be determined directly in patientpopulations of interest and allows evaluation of the influence ofvarious patient characteristics on pharmacokinetics.

Because the number of blood samples that need to be collected persubject is small, this approach is often suitable for patient groupsunable to participate in traditional pharmacokinetic studies requiringmultiple blood samples (e.g.,)

neonates,

children,

critically ill patients, or

individuals who are not able to provide informed consent

Methylphenidate Pharmacokinetics

A study of methylphenidate (MP) pharmacokinetics

in children. Study design may not be appropriate for

ethical and practical reasons.

Participating subjects were 273 children aged 5 to 18

years having a primary diagnosis of attention

deficit/hyperactivity disorder (ADHD).

They had been receiving MP at a fixed dosage level

for at least 4 weeks, and were under treatment for at

least 3 months.


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Children meeting the eligibility criteria had an initial

screening visit, at which one parent or a legal

guardian provided written informed consent, and the

child provided assent.

Demographic characteristics were recorded,

including the dosage of MP, the usual times for

individual doses, and the duration of treatment.


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The second visit, which followed shortly, was a bloodsampling day.

The time and size of the last MP dose, and of anyother medication received that day or during the prior2 weeks, were recorded.

A 5-mL whole blood sample was obtained byvenipuncture.

This sample was immediately centrifuged, and a 2-mL aliquot of plasma was removed for subsequentdetermination of MP concentrations by a liquidchromatography/mass spectroscopy/massspectroscopy (LC/MS/MS) assay.


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Analysis of data

The identified independent variables were age, sex,

body weight, size of each dose, and time of sample

relative to the most recent dose.

The pharmacokinetic model was a one-compartment

model with first-order absorption and first-order

elimination, under the assumption that all subjects

were at steady state (Fig. 1).


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The overall model was specifically modified for each of the 273

subjects to incorporate the individually applicable independent

variables, as well as the dosage schedule (b.i.d. or t.i.d.).

Individual values of continuous variables (t time sample taken

relative to the first dose; C plasma MP concentration) were fitted to a

single set of iterated variables using unweighted nonlinear

regression (Fig.1).

When the time between first and second doses, or between second

and third doses, was not available, the mean value was assigned

based on cases in which the data were available.

For the b.i.d. dosage, the mean interval was 4.3 hours. For the t.i.d.

dosage, the mean intervals were 4.1 and 3.7 hours, respectively. As

is customary, clearance was assumed to be proportional to body

weight.


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Results

The total daily dose of MP was significantly lower insubjects receiving MP b.i.d. (n 109) compared tosubjects on a t.i.d. schedule (n 164);

the mean total daily dosages in the two groups were 25and 39.3 mg, respectively (p .001).

Within each group, clinician choices of total dailydosages were influenced by body weight, as mean totaldaily dose increased significantly with higher bodyweights.

However, the association of body weight with meanplasma concentration was not significant for the b.i.d.dosage group, and of only borderline significance (.05 p.1) for the t.i.d group.

This finding is consistent with the underlying assumptionthat clearance is proportional to body weight.


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Age was significantly correlated with body weight (r 0.54, p.001) and with height (r 2 0.77).

Height and body weight also were significantly correlated (r0.77).

An acceptable estimate of absorption rate constant could bederived only for the b.i.d. dosing data. The iterated parameterestimate was 1.192/h, corresponding to an absorption half-lifeof 34.9 minutes.

The iterated estimates were 0.154/h for elimination rateconstant, corresponding to an elimination halflife of 4.5 hours(relative standard error: 23%).

For clearance, the estimate was 90.7 mL/min/kg (relativestandard error: 9%). The overall r-square was 0.43 (Fig. 38.2).

There were no evident differences in pharmacokineticsattributable to gender.

Figure 2 shows predicted plasma MP concentration curves forb.i.d. and t.i.d. dosage schedules, based on the populationestimates.


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Implication

Pharmacokinetically based approaches to the

treatment of ADHD with MP are not clearly

established.

The mean prescribed per dose amount for the whole

study population was 0.335 mg/kg per dose (range

0.044-0.568), and 36% of the children received

between 0.25 and 0.35 mg/kg per dose.

The mean total daily dose was 0.98 mg/kg/day for

the entire sample, and increased significantly in

association with larger body weight.


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The pharmacokinetic model explained 43% of the

variability in plasma MP concentrations during typical

naturalistic therapy.

The model fit equally well for both genders.

Assuming that clearance is proportional to body

weight in the context of intercorrelated age and

weight allows age, weight, and daily dosage to be

used to predict plasma concentrations of MP during

clinical use in children.

These findings support the value of prescribing MP

on a weight adjusted basis.


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Our typical population value of elimination half-lifewas 4.5 hours, with a confidence interval of 3.1 to8.1 hours.

This estimate somewhat exceeds the usual range ofhalf-life values reported in single-dose kinetic studiesof MP.

This could reflect the relatively small number ofplasma samples from the terminal phase of theplasma concentration curve, upon which reliableestimates of beta are dependent.

MP kinetics may also have a previouslyunrecognized dose-dependent component, in whichestimated values of half-life are larger at steady statethan following a single dose.


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The single-sample approach described in this study

allows relatively noninvasive assessment of

pharmacokinetic parameters in a group of children

and adolescents under naturalistic circumstances of

usual clinical use, when blood sampling is not

otherwise clinically indicated.

This approach in general can be applied to other

special populations such as neonates, the elderly, or

individuals with serious medical disease.


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General Methods for Population

Pharmacokinetic Modeling

Non-Parametric Adaptive Grid

and

Non-Parametric Bayesian


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Population pharmacokinetic (PK) modeling involvesestimating an unknown population distribution basedon data from a collection of nonlinear models.

A drug is given to a population of subjects. In eachsubject, the drug’s behavior is stochasticallydescribed by an unknown subject-specific parametervector ∂.

This vector ∂ varies significantly (often genetically)between subjects, which accounts for the variabilityof the drug response in the population.

The mathematical problem is to determine thepopulation parameter distribution F (∂) based on theclinical data

According to FDA


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“Knowledge of the relationship among concentration,

response, and physiology is essential to the design

of dosing strategies for rational therapeutics.

Defining the optimum dosing strategy for a

population, subgroup, or individual patient requires

resolution of the variability issues.”


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Traditional Population

Population Healthy volounteers

Highly selected

patients

Target patient population

(Pediatrics, elderly, AIDS)

Study size Small Large or integrated

(observational or

experimental)

Sampling data Dense (typically 1 to 6 time

points) following drug

administration.

Sparse, few samples for

many patients

Inter-individual Variability Minimized through

restrictive criteria

Demographics

Pathophysiological

Concomitant medications

Relationships of

concentration,

PK/PD

Limited Extensive, make

predictions

about future events -

steady

state concentrations and

efficacy. guide dosage

adjustments. determine

therapeutic window. guide

dosage for safety


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E.g.: A simple Pk model

Ri = infusion rate

Cl = drug clearance

k =elimination rate constant

= measurement error, intra-individual error

Dru

g C

onc

Time N(0,)

kteCl

RiCp 1


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Dru

g C

on

c

Time

ss

kt

ss

kt

Cp

RiCl

eCpCp

eCl

RiCp

1

1


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PK Model Objectives

1. Provide Estimates of Population PK

Parameters (CL, V) - Fixed Effects

2. Provide Estimates of Variability - Random

Effects

Intersubject Variability

Interoccasion Variability (Day to Day Variability)

Residual Variability (Intrasubject Variability,

Measurement Error, Model Misspecification)


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PK Model Objectives

3. Identify Factors that are Important

Determinants of Intersubject Variability

Demographic: Age, Body Weight or Surface Area,

gender, race

Genetic: CYP2D6, CYP2C19

Environmental: Smoking, Diet

Physiological/Pathophysiological: Renal (Creatinine

Clearance) or Hepatic impairment, Disease State

Concomitant Drugs

Other Factors: Meals, Circadian Variation, Formulations


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PK model Advantages

Sparse Sampling Strategy (2-3

concentrations/subject)Routine Sampling in Phase II/III Studies

Special Populations (Pediatrics, Elderly)

Large Number of Patients Fewer restrictions on inclusion/exclusion criteria

Unbalanced DesignDifferent number of samples/subject

Target Patient PopulationRepresentative of the Population to be Treated


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Population PK modeling approaches can be

classified statistically as either parametric or

nonparametric.

Each can be divided into maximum likelihood or

Bayesian methods.

parametric maximum likelihood (PML)

nonparametric maximum likelihood (NPML)

Parametric maximum likelihood (PML)


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Oldest and most traditional.

The parameters come from a known, specified probabilitydistribution (the population distribution) with certain unknownpopulation parameters

(e.g. normal distribution with unknown mean vector µ andunknown covariance matrix ∑).

The first and most widely used software for this approach hasbeen the NONMEM (NONlinear Mixed Effects Modeling)program developed by Sheiner and Beal .

There are other parametric maximum likelihood programscurrently available, such as Monolix and ADAPT.

The ADAPT software also allows for parametric mixtures ofnormal distributions.

Asymptotic confidence intervals can be obtained about thesepopulation parameters. Here “asymptotic” means as thenumber of subjects in the population becomes large.

Nonparametric maximum likelihood (NPML)


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The nonparametric maximum likelihood (NPML)

approach was initially developed by Lindsay and

Mallet.

It directly estimates the entire joint distribution. This

permits discovery of unanticipated, often genetically

determined, nonnormal and multimodal

subpopulations, such as fast and slow metabolizers.

The NPML approach is statistically consistent . This

means that as the number of subjects gets large, the

estimate of F given the data converges to the true F.

NP Adaptive Grid (NPAG) algorithm


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This method calculates the maximum likelihood

estimate of the population distribution with respect to

all distributions.

Compared with most parametric population modeling

methods, NPAG calculates exact, rather than

approximate likelihoods, and it easily discovers

unexpected sub-groups and outliers

NP Bayesian (NPB) algorithm


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The NPB algorithm provides a Bayesian estimate of

this totally unknown population distribution, including

rigorous (not asymptotic) credibility intervals around

all parameter estimates for any sample size.

THE POPULATION PK/PD MODEL


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Consider a sequence of experiments where each

one consists of a dosage regimen and a set of

measurements at several time points on one of N

individual subjects.

Yi are the observed measurements, e.g. serum

concentrations, PD effects.

The population analysis problem is to estimate

based on the data

DATA AND INFORMATION REQUIRED FOR

POPULATION PK ANALYSIS


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1. Data Input

2. Prior Knowledge and Information

Data input


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Accurate dosing information and history such as

dose formulation, dosage.

Plasma/blood concentrations from a validated assay

(sparse or dense)

Pharmacodynamic measurements and safety

profiles (e.g., ECG, side effects)

Covariate data – demographics, lab values,

concomitant meds, metabolizer status, disease,

fasting.

Accurate capture of time/date associated with above

items

Prior Knowledge and Information


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Previous PK information: pharmacokinetic modeling

compartmental model,

parameter estimates,

relative proportion of inter-patient to intrapatient and/or

residual.

summary statistics.

Impact of patient covariates

age,

body weight,

medical conditions.

For example, creatinine clearance and drug clearance,

much of the drug is eliminated by the kidney without

being metabolized (unchanged) or much of the drug

undergoes metabolism.

Conclusions


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Population modeling is most likely to add value when areasonable a priori expectation exists that inter-subjectkinetic variation may warrant altered dosing for somesubgroups in the target population.

The population PK approach can be used to estimatepopulation parameters of a response surface model inphase 1 and late phase 2b of clinical drug development,where information is gathered on how the drug will beused in subsequent stages of drug development.

The population PK approach can increase the efficiencyand specificity of drug development by suggesting moreinformative designs and analyses of experiments.

In phase 1 and, perhaps, much of phase 2b, wherepatients are sampled extensively, complex methods ofdata analysis may not be needed.

Conclusions (Conti………..)


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The population PK approach can also be used in early

phase 2a and phase 3 of drug development to gain

information on drug safety (efficacy) and to gather

additional information on drug pharmacokinetics in

special populations, such as the elderly.

This approach can also be useful in post-marketing

surveillance (phase 4) studies. Studies performed during

phases 3 and 4 of clinical drug development lend

themselves to the use of a full population

pharmacokinetic sampling study design (few blood

samples drawn from several subjects at various time

points.

This sampling design can provide important information

during new drug evaluation, regulatory decision making,

and drug labeling.


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population pharmacokinetics

Health & Medicine

pharmacokinetic models

measurement of drug

altered drug metabolism

number of blood samples

entire population

population pharmacokineticsmr

mohamed saleem

andvarious drug interactions