Population Pharmacokinetics and Pharmacodynamics as a Tool ... · Leon Aarons Manchester Pharmacy...
Transcript of Population Pharmacokinetics and Pharmacodynamics as a Tool ... · Leon Aarons Manchester Pharmacy...
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Leon Aarons Manchester Pharmacy School
University of Manchester
Population Pharmacokinetics and Pharmacodynamics
as a Tool in Drug Development
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Pharmacokinetics and
Pharmacodynamics
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Clinical Pharmacokinetics
DosageRegimen
PlasmaConcentration
Site ofAction Effect
Pharmacokinetics Pharmacodynamics
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Models
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The type of model to be developed should be driven by the available information and the
goal of the simulations
Empirical models
Semi-mechanistic models
Mechanistic models
Descriptive
Explanatory Rich
“Poor”
Extrapolation in complex and
variable environment
Interpolation in simple and
stable environment
Information needed
Goal
Days Months Years
Category
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0.01
0.1
1
10
100
0 2 4 6 8 10
time
conc
entr
atio
n
1 21 2( ) t tC t C e C eλ λ− −= +
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1 2 k12
k21
k10
11 12 1 1 10 1 1 21 2 2
22 12 1 1 21 2 2
( ) ( ) ( ) ( )
( ) ( ) ( )
dC tV k V C t k V C t k V C tdt
dC tV k V C t k V C tdt
= − − +
= −
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PBPK MODEL
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,, int ,
( )( ) ( ) ( )out H
H H H A H out H H out H
dC tKp V Q C t Q C t CL Kp C t
dt= − −
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Pharmacokinetic Study Design
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Sparse Data
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Tobramycin study
Objective: to establish dosage regimen guidelines to maintain maximum efficacy (Cmax > 6 mg/L) and minimum toxicity (Cav < 4 mg/L) in a majority of patients
Patients: n 97 (after pruning)body weight (kg) 42-120age (yr) 16-85sex (M/F) 52/45creatinine clearance 10-166(ml/min)indication variety of infection
Study design: no design - routine TDMdosage - 20 to 140 mg every 8 to 24 hrnumber of concentrations per individual 1-9(median 2)duration of therapy - 14 to 520 hr
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Why? • It seeks to obtain relevant pharmacokinetic
information in patients who are representativeof the target population to be treated with thedrug
• It recognizes variability as an important featurethat should be identified and measured duringdrug development and evaluation
• It seeks to explain variability by identifyingfactors of demographic, pathophysiological,environmental or drug-related origin that mayinfluence the pharmacokinetic behavior of adrug
• It seeks to quantitatively estimate the magnitudeof the unexplained variability in the patientpopulation
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Warfarin study
Objective:to predict warfarin maintenance dose requirements toachieve a desired degree of anticoagulation based onmeasurements obtained after a sungle dose of warfarin
Data:n 48 normal subjectsweight (kg) 66-75age (yr) 20-27sex male
Study design:25mg single dose of racemic warfarin14 blood samples (0-168 hr)
Measurements:R and S warfarin (HPLC)Prothrombin time (Quick one stage)Factor VII (chromogenic method)
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Hours
Concentration (mg/L) % Activity
0 20 40 60 80 100 120 1400.0
0.2
0.4
0.6
0.8
1.0
0
20
40
60
80
100
Concentration % Activity
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PHARMACODYNAMIC MODEL
rate of change = rate of clotting - rate of clottingof clotting activity factor synthesis factor degradation
( ) ( )( )
normd
s
50,s
dCA t CA= - CA tkdt tC1 + C
γ
kd = clotting factor degradation rate constantCAnorm = normal clotting activityC50,s = drug concentration giving 50% of maximum
effectγ = slope factorCs(t) = plasma concentration of s enantiomer
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Time (hr)
FVII activity(%)
0 20 40 60 80 100 120 140 1600
20
40
60
80
100
120
140
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Prospective study
n 5 normal male volunteers
Study design 15mg single dose followed by maintenance dosing from day 3 to day 16 designed to achieve 50% of clotting factor activity
Maintenance dose DM/τ = ks•Vs•C50,s
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Dose prediction
log logˆlog logˆ
i22nparm nobs
j,i j,ik k,ii 2 2
k=1 j=1k j,i
( - y f )( - p p ) = +
cv( cv(p ) y )Φ ∑ ∑
pharmacokinetic parameters set to populationvalues
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0.0
0.2
0.4
0.6
0.8
1.0
Conc
(mg/L
)
0 4 8 12 16 Time (d)
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Approaches for population analysis
• Naïve pooled data approach
• 2-stage approach
• A fully population approach
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• Estimate parameters for the model assuming all data arise from a single individual
• Can be biased – If individuals have different amounts of data – If model very nonlinear
• No estimation of variability components • Influential factors on PK cannot be ascertained
Naïve Pooled Data Approach
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Naive pooled approach
0
5
10
15
20
25
0 1 2 3 4 5
Conc
entr
atio
n
Axis Title
Fit to all data
Estimate: CL & V
Time
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• The “traditional” approach for PK analyses • Model the PK of each subject’s data (Stage 1) • Obtain summary statistics, e.g. mean value of clearance
(Stage 2) – Between-subject variance is overestimated because estimation of
the parameters includes residual error – Assumes all individuals contribute equally – Is not helpful for identifying sources of variability (e.g. renal
function) – Essentially unusable where there are “sparse” data
Two-Stage Approach
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Two-Stage Approach
0
5
10
15
20
25
0 1 2 3 4 5
Conc
entr
atio
n
Time
Estimate: CL & V for each individual
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• Estimate the overall mean parameters and the variability between individuals as well as the residual variability
• The “standard” population analytical approach • Sparse/rich, unbalanced/unstructured data • Considers the population (rather than the individual) as the
unit for the PK analysis
• “Individuality” of the subjects is maintained
The population approach
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The population approach
0
5
10
15
20
25
0 1 2 3 4 5
Conc
entr
atio
n
Time
Prediction at population mean parameter estimates for CL & V
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The population approach
0
5
10
15
20
25
0 1 2 3 4 5
Conc
entr
atio
n
Time
Prediction at population mean parameter estimates for CL & V
Difference between population mean and individual estimate
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The population approach
0
5
10
15
20
25
0 1 2 3 4 5
Conc
entr
atio
n
Time
Prediction at population mean parameter estimates for CL & V
Difference between population mean and individual estimate
Difference between individual predicted and individual observed
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Variability
• Two levels – Variability between people (heterogeneity) – Uncertainty about the observations (residual
unexplained variability)
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Heterogeneity (Between Subject Variance [BSV])
• There are two sources of heterogeneity between patients – Predictable = BSVP – Unpredictable (random) = BSVR
• Predictable variability can arise from (examples): – differences in renal function – differences in body size and composition
• The population parameter variability (PPV) in the population is therefore the sum of these two sources:
PPV = BSVR + BSVP
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Residual unexplained variability [RUV]
• This is the variability of the observed concentration around the model predicted
• The observed will seldom equal the model predicted due to many process such as assay error
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Nonlinear mixed effects modelling
• Nonlinear: almost (if not all) PK and PKPD models are nonlinear in the parameters
• The population approach is interested in the mean parameter values (“fixed effects”) as well as the variability between and within individuals (“random effects”)
• Combining fixed and random effects is termed “mixed effects”
• Essentially all population PK studies are therefore examples of nonlinear mixed effects modelling
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Software for Population Analyses
Decreasing Market Share
Not used to any extent
• NONMEM ($$) • Monolix (free/$$) • WinBUGS (free) • SAS proc nlmixed ($$$) • Phoenix nlme (free/$$$) • S-ADAPT MC-PEM (free) • NPEM (free) • P-Pharm ($?) • NPML (dead?)
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Role of Modelling and Simulation in Phase I Drug
Development L. Aarons, M. Karlsson, F. Mentré, F. Rombout, J.-L. Steimer, A. van
Peer COST B15
Brussels January 10-11, 2000
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Essentially it is (almost) always useful • In particular if there are few observations per patient e.g.
– Outpatients or phase III studies – Intensive and emergency care – Elderly – Children, including premature infants
• When you want to learn about sources of variability • When you want to develop a model to predict future patient responses • When you want to use the model to simulate various dosing scenarios • ...
When is the population approach useful?
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Tolerability studies
1
10
100
0 5 10 15 20 25 30
Time (h)
Con
cent
ratio
n
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Unbalance and confounding
0.1
1.0
10.0
0 8 16 24
Time (h)
Con
cent
ratio
n
Subject 3Subject 6
LOQ
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Non-linear PK
0.01
0.1
1
10
100
0 50 100 150 200
Time
Conc
entra
tion
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Rich + sparse data
0.01
0.10
1.00
10.00
0 8 16 24
Time (h)
Con
cent
ratio
n
Total concentrationFree concentration
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Summary • PK/PD is model driven • PK/PD models aid the interpretation of
pharmacological data and can be used prospectively to design subsequent studies learning/confirming
• Nonlinear mixed effects modelling allows data from a variety of unbalanced, sparse designs to be analysed
• Software for nonlinear mixed effects modelling is now widely available -
even for amateurs!