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Pop PK Analysis in Juvenile Rats: Preclinical Case Study 04-Sep-2008 Mark L.J. Reimer, PhD Senior Director, Preclinical Development mreimer@pharsight.com © Pharsight Corporation All Rights Reserved

Pop PK Analysis in Juvenile Rats: Preclinical Case Study

04-Sep-2008

Mark L.J. Reimer, PhD

Senior Director, Preclinical Development

mreimer@pharsight.com

Overview

1. Project Background

• Challenge

• Approach

2. Building the Model

• Base Population PK Model

• Search for covariates

• Forward addition

• Backward deletion

• Final model equations and parameters

3. Optimal Sampling Strategy

• Partial derivative approach

• Modeling & simulation

• Evaluation of sparse sampling strategies

4. Conclusions and Acknowledgements

slide 2

Project Background

Large molecule biological

• Recombinant protein in preclinical (ADME/T) development

• Selective to targets implicated in genetic metabolic disorder

Challenge

• 13-week repeat dose tox study in juvenile rats

• Daily IV dosing @ 3 non-zero dose levels

• N=9 per sex per dose in TK arm

• Blood samples collected on Day 1, 28, 56, and 91

• What are the optimum (minimum) number of rats and sampling

times needed in order to reliably assess exposure in TK arm?

Approach

• Develop a population PK model based on existing rich and sparse

IV data collected in previous studies

• Propose an optimal sampling strategy (OSS)

• Perform Bayesian analysis on sparse sample set to evaluate

exposure in 13-week tox study (in progress)

slide 3

Rich Sampling vs. Sparse Sampling Strategies

Rich Sampling (TK Study)

Concentration

Exposure

Time (h)

Sparse Sampling (Tox Study)

Concentration

Exposure

Time (h)

If we know the population statistics (mean and variance) as

developed from the rich sampling TK studies, we can use the

model to fit sparse serum concentration data and derive the

entire drug exposure from as little as a single time point.

slide 4

Building the Model

Existing PK data

Data from three existing studies are merged

• Study 1 (MD; sparse; one tp 24h post dose every week)

• Study 2 (SD & MD; sparse; 7 tp over 72h; Day 1 & 28)

• Study 3 (SD; rich; 10 tp over 72h)

1000

800

600

Linear

10 3.0 9

9

7

5

4

3

2

10 2.0 9

7

5

4

3

2

Semi-Log

DV

400

DV

10 1.0 9

7

5

4

3

2

200

0

10 0.0 9

7

5

4

3

2

0 10 20 30 40 50 60 70

TIME

10 -1.0

10 30 50 70

TIME

slide 6

Model Selection

Based on prior knowledge and overall plasma concentration

vs. time curve relationships, a two-compartment IV bolus

model was selected

Blood sample

IV Bolus

Vc

Q

Vp

CL

slide 7

NONMEM Analysis

The dataset was analyzed using NONMEM v6 (non-linear mixedeffects

modeling) software (with Wings For NONMEM v6)

Three different error models were tested:

Proportional : Y = a*F MOF = 2591

Additive: Y = b + F MOF = 4162

Proportional + Additive: Y = F + F*a + b MOF = 2536

MOF = Minimum Objective Function

(a measure of the goodness-of-fit to the data)

slide 8

Structural Model Goodness-of-Fit Plots

Observed Concentration (ng/mL)

0 200 400 600 800

Population Weighted Residual

-5 0 5

Population Weighted Residual

-5 0 5

0 200 400 600 800 1000

0 20 40 60

Population Predicted Concentration (ng/mL)

T ime Post Dose (h)

Observed Concentration (ng/mL)

0 200 400 600 800

Individual Weighted Residual

-10 -5 0 5 10

Individual Weighted Residual

-6 -4 -2 0 2 4 6

0 200 400 600 800

0 20 40 60

Individual Predicted Concentration (ng/mL)

T ime Post Dose (h)

slide 9

Covariate Addition

An allometric scaling model was used to assess the effect of body

weight (BW) on the PK parameters

CL BW = CL*(BW/0.250) b

● This covariate was successively added to the PK parameters to

determine if the net result was a better fit of the observed data

● A covariate effect on the PK parameter was retained when there

was a significant improvement in goodness-of-fit (i.e. a decrease in

the absolute MOF value)

slide 10

Covariate Search: Forward Addition

∆MOF ≥ 4 for statistical significance

Structure

MOF

∆MOF

BASE

+BW on CL

+BW on Q

2536

2179

2474

357

+BW on Vc

2742

+BW on Vp

2572

BW on CL (b=1)

+BW on Q

+BW on Vc

2179

2010

2146

169

+BW on Vp

2055

BW on CL, Q

2010

slide 11

+BW on Vc

+BW on Vp

BW on CL, Q, Vp

+BW on Vc

2009

1965

45

1965

1940

25

Covariate Search: Backward Deletion

∆MOF ≤ 10 for statistical significance

Structure

MOF

∆MOF

FULL

-BW on CL

-BW on Q

-BW on Vc

-BW on Vp

1940

2379

1997

2009

1965

439

57

69

25

X

No covariates can be removed without a significant

deterioration in goodness-of-fit (i.e. increase in MOF value),

therefore the full model includes an effect of BW on all four

basic PK parameters

The final model was relaxed (b on CL was unconstrained) and

the data was refit (MOF = 1902)

slide 12

Final Model Equations

2 COMPARTMENT IV BOLUS

PK

Primary Parameters

TVCL=THETA(1)*(BW/0.25)**THETA(7) TYPICAL VALUE OF CL (L/h)

CL=TVCL*EXP(ETA(1)) ;CL (POP+VAR) (L/H)

TVQ=THETA(2)*(BW/0.25)**THETA(8) TYPICAL VALUE OF Q (L/h)

Q=TVQ*EXP(ETA(2)) ;Q (POP+VAR) (L)

TVV1=THETA(3)*(BW/0.25)**THETA(10) TYPICAL VALUE OF Vc (L)

V1=TVV1*EXP(ETA(3)) ;Vc (POP+VAR) (L)

TVV2=THETA(4)*(BW/0.25)**THETA(9) TYPICAL VALUE OF Vp (L)

V2=TVV2*EXP(ETA(4)) ;Vp (POP+VAR) (L)

Scaling Parameters

S1=V1/1 Dose in mg conc in mg/L

slide 13

Final Model Equations

Secondary Parameters

K=CL/V1

AUC=AMT/CL

Cmax=AMT/V1

Vss=V1+V2

HLe=LOG(2)*Vss/CL

Elimination rate (1/h)

Post hoc AUC (mg*h/L)

Post hoc Cmax (mg/L)

Post hoc Vss (L)

Post hoc Effective t1/2 (h)

$ERROR

IPRE=F

PROP=IPRE*THETA(5)

ADD=THETA(6)

SD=SQRT(PROP*PROP+ADD*ADD)

Y = IPRE+SD*ERR(1)

IRES=DV-IPRE

IWRE=IRES/SD

DEFINITION OF IPRED

DEFINITION OF PROPORTIONAL ERROR

DEFINITION OF ADDITIONAL ERROR

DEFINITION OF SD

DEFINITION OF OBSERVED VALUE

DEFINITION OF RESIDUAL

DEFINITION OF WEIGHED RES

slide 14

Final Model Equations

Population Estimates

THETA (0.001, 0.04) TVCL

THETA (0.001, 0.1) TVQ

THETA (0.001, 0.1) TVV1

THETA (0.001, 0.5) TVV2

Variability Estimates

OMEGA 0.3 ETACL

OMEGA 0.3 ETAQ

OMEGA 0.3 ETAV1

OMEGA 0.3 ETAV2

Error Estimates

THETA (0.01,0.3) ERRCV

THETA (0.01,0.3) ERRSD

Allometric exponent

THETA (1) expb

THETA (1) expc

THETA (1) expd

THETA (1) expe

SIGMA 1 FIX EPS1

ESTIMATION METHOD=1 INTERACTION

MAXEVAL=9900 PRINT=10 POSTHOC

COVARIANCE PRINT=E

slide 15

0 20 40 60

T ime Post Dose (h)

0 20 40 60

Full Model Goodness-of-Fit Plots

Observed Concentration (ng/mL)

0 200 400 600 800

Population Weighted Residual

-5 0 5

Population Weighted Residual

0 100 200 300 400 500

Population Predicted Concentration (ng/mL)

T ime Post Dose (h)

Population Predicted Concentration (ng/mL)

Observed Concentration (ng/mL)

0 200 400 600 800

Individual Weighted Residual

-6 -4 -2 0 2 4 6

Individual Weighted Residual

-5 0 5

0 200 400 600 800

Individual Predicted Concentration (ng/mL)

slide 16

-6 -4 -2 0 2 4 6

Final Model Parameters

Parameter

Value

%Rel SE

%BSV

PK

CL (L/h)

0.0163

4.17

26.4

Q (L/h)

0.0195

15.6

60.2

Vc (L)

0.0299

9.87

37.1

Vp (L)

0.15

10.7

23.1

Allometric Exponent

CL

1.27

3.57

Q

1.33

12.4

Vc

0.794

12.1

Vp

1.35

6.3

Residual Error

Proportional (%)

17.2

19.1

Additive (mg/L)

0.118

20.3

slide 17

Individual Predicted vs. Actual Concentrations

25

1000

Linear Plot of Concentration vs. Time for Animal 397

Semi-Log Plot of Concentration vs. Time for Animal 397

Concentration (mg/L)

20

15

10

Model

Observed

Concentration (mg/L)

100

10

1

Model

Observed

5

0.1

0

0.01

0 6 12 18 24 30 36 42 48 54 60 66 72

Time (h)

Example of the fit of the model to the rich (10-time point) TK

data for a single animal. Predicted values lie above and below

observed, but there is no obvious bias.

slide 18

Optimal Sampling Strategy (OSS)

Partial Derivatives in WinNonlin® (WNL)

• As part of its modeling features, WinNonlin® (Pharsight Corporation)

allows plotting of various partial derivatives which can be used to

optimize sampling time points

•The sensitivity of concentration values to a particular PK parameter

increases as that parameter's partial derivative deviates from zero

•Sampling in regions of greater sensitivity should result in more

precise estimates for the PK parameter evaluation

•The NONMEM population model was inputted into WNL and the partial

derivatives for a rich sampling scenario were obtained

●

Time points included: 0, 0.083, 0.25, 0.5, 0.75, 1, 2, 3, 4… 72 h

slide 20

Partial Derivatives Results

Vc

CL

Vp

Q

0.083h (Vc)

slide 21

0.5h (Q, Vp)

1h (Q, Vp, Vc, CL)

5h (Vc, Vp)

Optimal Sample Size Model Validation

STEP 1: Simulate a rich “true” dataset following SD (Day 1) and MD

(Day 28, 56 and 91) using the model

STEP 2: Determine “true” PK parameters (AUC, C max

, t ½

) derived from

rich sampling using the model

STEP 3: Evaluate predictive performance (degradation of PK

parameter estimates) of the model by comparing the PK evaluated in

STEP 2 (theoretical parameters) vs. a sparse simulated dataset (fitted

parameters).

The same simulated source data is used throughout. In STEP 2, rich

data (13 time points) from the simulations are used. In STEP 3, sparse

data (1-3 time points; based on the WNL partial derivative analysis)

are used. The post hoc estimates from the model derived from the

candidate sparse time points are compared to the “true” parameters.

slide 22

Simulations

Actual sampling occasions, dose levels and dosing regimen from

the 13-week tox study design were used.

BW increases with respect to sampling occasions (Day 1 SD to Day

91 MD) were simulated based on reference growth curve data. An

E max (with baseline) model was used:

For males:

For females:

⎛ (682-58) ⋅ Day

BW (g) = 58+ ⎜

⎝ Day + 64.2

3.41

3.41 3.41

⎞

⎟

⎠

⎛ (293-53) ⋅Day

BW (g) = 53+ ⎜

⎝ Day + 52.1

3.44

3.44 3.44

⎞

⎟

⎠

A variance component (BSV of 1%) was also added to account for

inter-individual variation. This was assumed to remain relatively

unchanged over time.

slide 23

Model Performance Evaluation

N

−1

[ * ∑( i

)]

i=

1

MPE = N pe

Bias

N

1

−1 ∑

2 2

i

i=

1

RMSE% = [ N * ( pe ) ]

Precision

pe = [( AUC ) − ( AUC )]/( AUC )

predicted truevalue truevalue

slide 24

Sparse Sampling Strategy Evaluation for SD (Day 1)

Precision remains relatively similar across sampling scenarios.

Sampling 9 animals @ 0.5 h post dose offers the lowest overall bias in terms of

AUC and half life.

Sampling 3 animals @ 0.083, 0.5 and 1 h post dose offers low bias in all

parameters, with slightly higher precision, when compared to the single point

approach.

slide 25

Sparse Sampling Strategy Evaluation for MD

For multiple doses, although the single 0.5 h time point gives lower absolute

numbers, both approaches have overall similar bias and precision.

The same sampling approach as selected in Day 1 can be used.

slide 26

Conclusions

•Building the Model

● A population PK model was developed based on prior PK/TK knowledge

● The effect of BW on PK parameters (CL, V c

, V p

, and Q) was established

•Optimal Sampling Strategy

● Sampling 3 animals @ 0.083, 0.5, and 1 h is recommended on Day 1

● Sampling 9 animals @ 0.5 h would also lead to acceptable estimates

● A single point sampling strategy was adopted for both SD and MD

•Next Steps

● Pending interim results from 13-week tox study, sparse sampling strategy

will be re-evaluated and model adjusted (if required)

slide 28

Simulating the future based on past results

• There is a growing use of in silico tools at both the preclinical and

clinical ends of the drug discovery and delivery process

• Population PK modeling & simulation can help to optimize preclinical

sampling strategies, especially when faced with practical sampling

challenges

● “Trial & Error” approaches are too expensive

• Cross-functional interaction between Pharsight’s preclinical and

clinical teams to arrive at optimal study design

• Acknowledgements

● Dr. Martin Beliveau, Associate Scientist, Reporting and Analysis Service

slide 29

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