Dose Response and Concentration Response Analysis of Drug ... · 1/12/2016 24 Graded Dose-Effect Analysis •Identify the therapeutic dose/concentration •Define site of drug action

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Dose Response and Concentration

Response Analysis of Drug Effects

Juan J. L. Lertora. M.D., Ph.D.

NIH Clinical Center

January 14, 2016

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DOSE-EFFECT RELATIONSHIP

The intensity and duration of a drug’s

effect(s) are a function of the drug dose

and drug concentration at the effect site

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Monitoring Dose-Effect

• Level

– Molecular (e.g, enzyme inhibition)

– Cellular (in vitro tissue culture, blood cells)

– Tissue or organ (in vitro or in vivo)

– Organism

• Endpoint used to measure effect may be

different at each level

• Overall effect = sum of multiple drug effects

and physiological response to drug effects

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Endpoints to Monitor Drug Effect

LEVEL ENDPOINT

Molecular Farnesyltransferase inhibition

Cellular Proliferation rate, apoptosis

Tumor Response (change in tumor size)

Organism Survival, quality of life

Farnesyltransferase Inhibitors for Cancer

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Dose-Effect Endpoints

Graded

Quantal

• Continuous scale (dose effect)

• Measured in a single biologic unit

• Relates dose to intensity of effect

• All-or-none pharmacologic effect

• Population studies

• Relates dose to frequency of effect

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0

5

10

15

20

25

0 100 200 300 400 500

Erythropoietin and Anemia

Erythropoietin Dose [units/kg]

Peak

Hematocrit

Increment

[%]

Eschbach et al. NEJM 316:73-8, 1987

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Drug-Receptor Interactions

k1

k2

Drug

Receptor

Effect

Drug-Receptor

Complex

Effect = Maximal effect • [Drug]

KD + [Drug]

(KD = k2/k1)

Ligand-binding

domain

Effector domain

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Drug-Receptor Interactions

• Receptor-Effector system

(signal-transduction pathway)

G-protein coupled receptors

Receptor-enzymes

Ion channels

Nuclear receptors

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Effect = [Drug]

KD + [Drug] Maximal effect

[Drug]

KD + [Drug]

Dose-Effect Relationship

Effect = Maximal effect • [Drug]

KD + [Drug]

Effect = Maximal effect if [Drug] >> KD

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0

20

40

60

80

100

0 200 400 600 800

Graded Dose-Effect Curve

% of

Maximal

Effect

[Drug] EC50

Maximal effect

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0

20

40

60

80

100

1 10 100 1000

Log Dose-Effect Curve

% of

Maximal

Effect

[Drug]

EC50

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0

1

2

3

4

5

6

7

0 1 2 3

Lidocaine Graded Dose-Effect

Lidocaine Blood Level [µg/ml]

Analog

Pain Score

Ferrante et al. Anesth Analg 82:91-7, 1996

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0

20

40

60

80

100

1 10 100 1000

Theophylline Dose-Effect

PDE Inhibition

Relaxation

% Control

Theophylline [µM] Rabe et al. Eur Respir J 8:637-42, 1995

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Theophylline Pharmacodynamics

0

10

20

30

40

50

60

0 5 10 15 20 25 30

Theophylline [mg/L]

FEV1

(% normal)

Emax = 63%

EC50 = 10 mg/L

Mitenko & Ogilvie NEJM 289:600-3, 1973

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Metformin Dose-Response

0

20

40

60

80

100

0

0.5

1

1.5

2

2.5

3

500 1000 1500 2000 2500

Dec

rea

se i

n F

PG

fro

m P

lace

bo

[mg

/dl]

Decrea

se in H

bA

1c fro

m

Pla

cebo

[%]

Dose [mg/d] Garber et al. Am J Med 102:491-7, 1997

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Dose-Effect Parameters

POTENCY:

EFFICACY:

The sensitivity of an organ or

tissue to the drug

The maximum effect

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Comparing Dose-Effect Curves

0

20

40

60

80

100

1 10 100 1000

% of

Maximal

Effect

[Drug]

Drug A

Drug C

Drug B

Effect = Maximal effect • [Drug]

KD + [Drug]

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Thiopurine Cytotoxicity

0%

20%

40%

60%

80%

100%

10-9

10-8

10-7

10-6

10-5

Cytotoxic

Effect

Thiopurine [M]

Thioguanine

Mercaptopurine N

N N

N

H

H 2N

S

N

N N

N

H

S

Adamson et al. Leukemia Res 18:805-10, 1994

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Thiopurine Metabolic Activation

6

O

PO4CH 2

SH

N

NN

N

OHHO

O

(PO4)3CH 2

SH

N

NN

N

H 2N

HO R

O

PO4CH 2

SH

N

NN

N

OHHO

H2N

O

PO4CH 2

SH

N

NN

N

OHHO

HO

MP TG

TIMP TGMPTXMP(d)TGTP

6

PRPPPRPP

N

N N

N

SH

H 2N

H

N

N N

N

SH

H

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Oral Mercaptopurine

0

1

2

3

4

5

0 20 40 60 80 100

MP Dose (mg/m2)

MP AUC

[µM•hr]

AUC = Clearance

Dose • F

Balis et al. Blood 92:3569-77, 1998

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Receptor-Mediated Effects

%

Maximum

Effect

[Drug]

Agonist

Antagonist

Partial agonist

100

80

60

40

20

0

1 10010 1000

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Receptor-Mediated Effects

• Agonist

• Partial agonist

• Antagonist

• Inverse agonist

Receptors can exist in at least two

conformations: active and inactive.

An inverse agonist drives the equilibrium

toward the inactive conformation.

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Drug Interactions

0

20

40

60

80

100

1 10 100 1000

% of

Maximal

Effect

[Drug]

Agonist

Agonist + competitive

antagonist

Agonist + non-competitive

antagonist

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Graded Dose-Effect Analysis

• Identify the therapeutic dose/concentration

• Define site of drug action (receptor)

• Classify effect produced by drug-receptor interaction (agonist, antagonist)

• Compare the relative potency and efficacy of drugs that produce the same effect

• Assess mechanism of drug interactions

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Quantal Dose-Effect Distribution

Threshold Dose

# of

Subjects

0

10

20

30

40

50

1 3 5 7 9 11 13 15

ED50

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Cumulative Dose-Effect Curve

Dose

Cumulative

% of

Subjects

0

20

40

60

80

100

1 3 5 7 9 11 13 15

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Cumulative Dose-Effect Study

Dose Level

No. of

Subjects

No.

Responding

%

Response

1 10 0 0

2 10 1 10

3 10 3 30

4 10 5 50

5 10 7 70

6 10 8 80

7 10 9 90

8 10 10 100

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0

20

40

60

80

100

70 80 90100 200 300

Therapeutic and Toxic Effects

Dose

%

Responding

Therapeutic

Toxic

ED99

TD1 ED50 TD50

Indices

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Therapeutic Indices

Therapeutic Ratio = TD50

ED50

= 2.5

Certain Safety Factor = TD1

ED99

= 1.3

Standard Safety Margin = TD1 - ED99

ED99

X 100 = 31%

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95

90

80

40 30

20

10

5

60 50

70

Perc

ent of patients

5 40 10 20 80

Digoxin (single oral dose, µg/kg)

Ventricular

slowing

Vomiting

Digoxin Therapeutic Index

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Doxorubicin Cardiotoxicity

Total Doxorubicin Dose [mg/m2]

Probability

of CHF

0

0.20

0.40

0.60

0.80

1.0

0 200 400 600 800 1000

von Hoff et al. Ann Intern Med 91:710-7, 1979

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0

20

40

60

80

100

100 1000

Lidocaine Quantal Dose-Effect

%

Achieving

Complete

Analgesia

Total Lidocaine Dose (mg)

Ferrante et al. Anesth Analg 82:91-7, 1996

ED50 = 400 mg

ED90 = 490 mg

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Antihypertensive Dose-Effect

Johnston Pharmacol Ther 55:53-93, 1992

Dose Range [mg] Lowest Effective

Dose [mg] Drug Early Studies Present Dose

Propranolol 160-5000 160-320 80

Atenolol 100-2000 50-100 25

Hydrochlorothiazide 50-400 25-50 12.5

Captopril 75-1000 50-150 37.5

Methyldopa 500-6000 500-3000 750

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Antihypertensive Drugs

0

20

40

60

80

100

Log Dose

% with

Maximal

Effect Adverse

Effects

Desirable

Dose Range

Dose Range

most often used

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Relating Dose to Effect In Vivo

Dose Effect Effect site

Concentration

Pharmacokinetics Pharmacodynamics

Age

Absorption

Distribution

Elimination

Drug interactions

Tissue/organ sensitivity

(receptor status)

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Effect Compartment (PK/PD Model)

k0 k1e

k10 ke0

Central Effect

Peripheral

k12k21

dC

dtk0

Vc (k10 k12) C

k21 Xp

Vc

dX p

dt k12C Vc k21 X p

dCedt

k1e C VcVe

ke0 Ce

E(t) Emax Ce

H

EC50

H CeH

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Concentration and Effect vs. Time

0

2

4

6

8

10

0

20

40

60

80

100

0 5 10 15 20 25

Conc./

Amount

Effect

[% of Emax]

Time

Central

Compartment

Peripheral

Compartment

Effect Compartment

Effect

Non-Steady State

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Pharmacodynamic Models

• Fixed effect model

• Linear model

• Log-linear model

• Emax model

• Sigmoid Emax model

Effect = E0 + S•[Drug]

Effect = I + S•Log([Drug])

Effect = EC50 + [Drug]H

Emax•[Drug]H

H

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Sigmoid Emax PD Model

0

20

40

60

80

100

0 20 40 60 80 1000

20

40

60

80

100

1 10 100

[Drug]

Effect (%) Effect (%)

EC50 EC50

H = 0.1

H = 5

H = 2

H = 1

H = 0.5

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Hysteresis and Proteresis Loops

0

1

2

3

4

0 1 2 3 40

1

2

3

4

0 1 2 3 4

Plasma Drug Concentration

Intensity of

Drug Effect

Intensity of

Drug Effect Hysteresis Loop

(Counterclockwise)

Proteresis Loop

(Clockwise)

• Equilibration delay in

plasma and effect site conc.

• Formation of active

metabolite

• Receptor up-regulation

• Tolerance

• Receptor tachyphylaxis

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Role of Dose-Effect Studies

• Drug development

– Site of action

– Selection of dose and schedule

– Potency, efficacy and safety

– Drug interactions

• Patient management

– Therapeutic drug monitoring

– Risk-benefit (therapeutic indices)