pharmacology model uses slide 1 university of auckland...

Pharmacometrics

Quantitative description of pharmacology

Nick Holford

Dept Pharmacology & Clinical Pharmacology

University of Auckland, New Zealand

Slide 2

©NHG Holford, 2017, all rights reserved.

Pharmacometrics

Pharmacology

Dose Concentration Effect

Pharmacokinetics Pharmacodynamics

Science

Models

Experiment

Slide 3


Model Uses

Description

» Correlation

» Parameters

Prediction

» Interpolation

» Extrapolation

Explanation

» True science


Models for WT vs HTy = 0.4711x + 134.86

R² = 0.3801

y = 2.3553x + 63.082R² = 0.8711

0

50

100

150

200

250

0 40 80 120

HT

cmWT kgy = 35.166x0.3849

R² = 0.9187

0

50

100

150

200

250

0 40 80 120

HT

cm

WT kg

Ht=208*Wt/(Wt+16.2)

Slide 5


Model for Age vs WT

0

20

40

60

80

100

120

140

0 20 40 60 80 100

We

igh

t kg

Post natal age years

0

1

2

3

4

5

20 30 40 50

We

igh

t kg

Post Menstrual Age Weeks

Observed

Male

)/)2ln(exp(

)(/)2ln(

4max4

3

3max

2

2max

1

1max

,,

44,4

,3

,2

,1

)4321(

1)(4

)/50(13

)/50(12

)/50(11

PMATHALF

iiiii

TLAGPMATHALF

WTMAXWTi

WT

i

WT

i

WT

WTMAXi

AGEPPViAGE

WTWTiWTMAX

iWTMAX

iWTMAX

iWTMAX

eWTWTWTWTWT

eeWTFFEMTLAGPMAWT

PMATM

eWTWT

PMATM

eWTWT

PMATM

eWTFFEMWT

WT3WT3WT3

WT2WT2WT2

WT1WT1WT1

Hill2- else Hill1- then TM50PMA if



Sumpter AL, Holford NHG. Predicting weight using postmenstrual age – neonates to adults. Pediatric Anesthesia. 2011;21(3):309-15.

Slide 6


George Box

“All models are wrong

but some models are useful”


Modelling

Simulation

» Visualising model predictions

» Exploring model properties

Parameter Estimation

» Non-linear regression (often)

» Structural + Error models

Slide 8


Model Parts

Y = slope * X + intercept

Slide 9


Model Parts

tV

CL

eV

doseC


Pharmacokinetics

Drug Elimination

Bolus Input

Infusion Input

tV

CL

eV

doseC

)1(t

V

CL

eCL

rateC

ConcCLRateOut *

Slide 11


Receptors/Enzymes

Ligand Binding

Enzyme Velocity

CbB Cu

Cu KdNS Cu

max

VV S

S Km

max

Slide 12


Pharmacodynamics

Emax

Sigmoid Emax

050

maxS

CC

CEE

050

maxS

CC

CEE

HillHill

Hill


PK Model Building

One compartment model

» First order elimination

» Mixed order elimination

» Combined First order and Mixed order

Two compartment model

» First order elimination

» etc

Slide 14


PD Model Building

Single Drug

» Linear

» Emax

» Sigmoid Emax

Combinations

» Competitive

» Non-competitive

Slide 15


PKPD Model Building

PK Model

» One compartment, etc

Link Model

» Immediate

» Slow receptor dissociation

» Distribution delay

» Turnover of mediator

PD Model

» Linear, etc


Pharmacometric Tools

Simulation

» Excel

» Berkeley Madonna

» Certara Trial Simulator

Individual Non-Linear Regression

» WinNonLin

Population Non-Linear Regression

» NONMEM / Monolix

Slide 17


Slide 18


Berkeley Madonna


CertaraTrial Simulator

Slide 20


Certara Trial Simulator

Slide 21



Monolix Model

INPUT:

parameter={htmax,wt50}

regressor={wt}

EQUATION:

ht=htmax*wt/(wt+wt50)

OUTPUT:

output = {ht}

Slide 23


VPC Emax WT vs HT

Slide 24


Phoenix allows models to be run using WinNonLin, nlme (Phoenix population model) and NONMEM


Slide 26


NONMEM$PROB Demographics from GFR data

$INPUT ID WT HT=DV PMA SEX

$DATA demographics.csv

$EST METHOD=COND LAPLACIAN

NSIG=3 SIGL=9 MAX=9990

$COV

$THETA

200. ; POP_WMAX kg

10 ; POP_WT50 cm

$OMEGA 0 FIX ; PPV_WMAX

$SIGMA 20 ; RUV_SD cm

$PRED

WMAX=POP_WMAX*EXP(PPV_WMAX)

WT50=POP_WT50

Y=WMAX*WT/(WT+WT50) + RUV_SD

$TABLE ID WT DV PMA SEX

ONEHEADER NOPRINT FILE=emax_ruvsd.fit

Slide 27


NONMEMTHETA: POP_WMAX POP_WT50

ETA: PPV_WMAX

ERR: RUV_SD

wmax_ruvsd.lst 1935.526 FOCE eval=86 sig=3.8 sub=391 obs=391 NM7.3.0

THETA = 209 16.3

ETASD = 0.000

ETAPval = 1.000

ETAshr% = 100.0

EBVshr% = 0.0

EPSshr% = 0.0

EPSSD = 7.211

MINIMIZATION SUCCESSFUL


Ernest Rutherford

“Science is either

stamp collecting or physics”

Stamp

CollectingPhysicsModels

pharmacology model uses slide 1 university of auckland...

Documents