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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)