Transcript Synergism - Telenet Service

The Search for Synergism
A Data Analytic Approach
L. Wouters, J. Van Dun, L. Bijnens
May 2003
Three Country Corner
Royal Statistical Society
Overview
 Combined action of drugs
 Screening for synergism
 Experimental Design
 Fitting concentration response curves, estimation of
IC50
 Graphical analysis of combined action
– isobolograms
– fraction plots
– combination index
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Drug Combinations
 Additive
 Sub-additive: antagonism
fight against one another
 Super-additive: synergism
work together
3
Drug Combinations:
Antagonism - Synergism
 Major therapeutic areas:
– Oncology
– Infectious disease
 Ideal combination:
– Synergistic for therapeutic activity
– Antagonistic for toxicity
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Non-additivity and Statistical
Interaction
 Drug A f(x), drug B g(x)
100
 Combination: a + b, h(a,b)
80
 f(a) = 50 %, g(b) = 60 %
additivity h(a,b) = 110 % ?
Drug can be antagonistic
with itself
% Effect
60
40
20
0
0.0
0.2
0.4
0.6
0.8
1.0
 f(a) = 0%, g(b)=0%
additivity h(a,b) = 0% ?
Drug can be synergistic
with itself
Concentration
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Problems with Synergism Antagonism
 Synergism is controversial issue
 Literature large but confusing
 Different definitions
 Different methods and experimental designs
 Pharmacological - biostatistical approaches
 Greco (1995) Pharmacol Rev 47: 331-385
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Sarriselkä agreement (1992)
Combined
effect
Both agents
active (Loewe
model)
Both agents
active (Bliss
model)
Only one agent Neither agent
active
active
> predicted
Loewe
synergism
Bliss
synergism
Synergism
Coalism
= predicted
Loewe
additivity
Bliss
independence
Inertism
Inertism
< predicted
Loewe
antagonism
Bliss
antagonism
Antagonism
-
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Loewe Additivity
 ICx,A, ICx,B concentrations required for each drug
A, B individually to obtain a certain effect x (x %
inhibition)
 Let Cx,A, Cx,B doses of drug A and drug B in the
combination that jointly yield same effect x
 Drug A has lower potency ICx,A > ICx,B
 Relative potency of A: ICx,A / ICx,B
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Loewe Additivity (cont.)
 Assume constant relative potency and additivity
 Combination can be expressed as equivalent
concentrations of either drug :
ICx , A
ICx , A
Cx , A 
C x ,B  ICx , A , C A
C x. B  ICx ,B
ICx ,B
ICx ,B
C x , A C x ,B

1
ICx , A ICx ,B
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Methods Based on Loewe Additivity
 Isobologram
 Interaction index of Berenbaum (1977)
 Bivariate spline fitting method of Sühnel (1990)
 Hypothesis testing approach of Laska (1994)
 Response surface methodology of Greco (1990),
Machado (1994)
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Isobologram
Cx , A
ICx, A

C x,B
ICx, B
 1  Cx, A  ICx, A 
ICx, A
ICx, B
C x, B
Cx, A
ICx, A
ICx, A
ICx, B
Antagonism
Synergy
ICx, B
Cx,B
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Bliss Independence
 i1, i2, i12 inhibition as a fraction [0; 1] by drug 1, drug 2,
and their combination
 from a probabilistic point of view, when fraction i1 is
inhibited by drug 1, only (1 - i1) is available to respond to
drug 2. Assuming independence:
i12  i1  (1  i1 )i2  i1  i2  i1i2
 can be reformulated in terms of u. = 1 - i., the fraction
remaining unaffected
u12  1  i12  1  1  u1   1  u2   1  u1 1  u2 
 u1u2
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Bliss Independence
Counter-argument
 A drug can be synergistic with
itself
 75 % of control at 0.9 mg/kg
 Assume a dose of 0.9 mg/kg of
the drug is combined with 0.9
mg/kg of the same drug
 Total dose = 1.8 mg/kg
 Under Bliss independence:
0.75 x 0.75 = 0.56 = 56 % for
combination
 1.8 mg/kg yields 15.7 % of
control
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Screening for Synergism in
Oncology
 Screening experiment
– as simple as possible with limited resources
– carried out on a routine basis
– analysis must be automated
 Screening experiments on tumor cells grown in
96-well microtiter plates
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Screening Experiment
Requirements
– Unbiased estimates of responses
– Avoidance of confounding of random error
and drug effects
– Elimination of plate effects and plate
location effects in 96-well plates
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Plate Location Effects in 96-well
Plates
 Microtiter plates
contain a substantial
amount of
unexplainable
systematic error along
their rows & columns
(Faessel, et al. 1999)
 Importance of
standardization
experiment (low,
middle, and high
response)
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Standardization Experiment (n = 3)
 Standardization
experiment at high level
of response, n=3
 Within assay presence of
systematic differences of
important magnitude (up
to 50 %) in untreated
microtiter plates after
edge removal
 Not repeatable between
different runs of assay
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How to Eliminate Bias &
Confounding ?
 Randomization assures:
– Equal probability to attain a
specific response for each
well
– Independence of results
– Absence of confounding
– Proper estimation of
random error
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Experimental Design
Ray Design
 Mixtures are composed based on preliminary
estimates of IC50 of constituents
 Assuming additivity: IC50,Mixture  fIC50, A  1  f IC50, B
f : mixturefactor
 Construct concentration response curve for different
mixture factors:
D
r
u
g
A
Drug B
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Ray Design
Composition of Mixtures
 Tested concentration Ci of
mixture is composed of:
Ci  kC  fIC50, A  1  f IC50, B
D
r
u
g
f : mixturefactor
k : dilution factor
A
 Proportion of constituents
in mixture:
Drug B
A 
fIC50 , A
C
B 
1 f IC50, B
C
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Advantages of strategy
 Simplified analysis:
– Consider mixture as new drug
– Fit concentration response curve to
different dilutions of mixture
 Easy to carry out in laboratory
 Limited number of samples
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Layout of Screening Experiments in
Oncology
 Ray design reference compound A, tested compound B
f = 0, 0.125, 0.25, 0.5, 0.75, 1
 Experiments carried out in 3 independent 96-well plates
 Dilutions (k): 10/1, 10/2, 10/3, 10/4, 1/1, 1/2, 1/4, 1/10
 All dilutions tested within single plate
 Wells for background and maximum effect
 Allocation of different treatment is randomized within
plate by robot
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Experimental Data
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Percentages
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Lessons from EDA
 Asymptotes of sigmoidal curve not reached
always
 Some part of sigmoidal curve is still present
 Computing percentages makes sense (common
system maximum)
 Proposed functional model:
100
yi 
1  exp log IC50  log Ci 
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Fit of 2 Parameter Logistic
Ignoring Plate
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Individual Fits of 2 Parameter
Logistic per Plate
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Studentized Residuals versus Fitted
Values after Individual Model Fitting
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Normal Quantile Plot of Pooled
Residuals after Individual Model Fits
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Individual Estimates per Plate-Factor
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Lessons from EDA for Functional
Model Fitting
 Sigmoidal shape as described by 2-parameter
logistic model
 Importance of plate effect even after correcting
for background, etc. by calculating
percentages
 How to obtain reliable estimate of IC50 and
standard errors ?
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Nonlinear Mixed Effects
 Nonlinear Mixed Effects Model (Pinheiro,
Bates) allows to model individual response
curves within plates and provides reliable
estimate of standard error
 Result = estimates and standard errors of
model parameters as fixed effects
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Isobologram
• Decompose IC50,M of mixture
into IC50 of constituents C50,A
and C50,B :
C50, A   A IC 50, M
Antagonism
C50, B   B IC 50, B
• Plot of drug B versus
drug A and line of additivity
C50, A
IC50, A

C 50, B
IC50, B
Synergism
1
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Fraction Plot
 Based upon refined
estimates of IC50 of Drug A
and B recalculate the correct
fraction f :
 A IC50, B
f
IC50, A   A IC50, A  IC50, B 
 Plot of IC50 of mixture
versus recalculated fraction
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Combination Index
Chou and Talalay (1984)
CI 
C 50 , A
IC50 , A

C 50 , B
IC50 , B
 1 : synergism

 1 : additivity
 1 : antagonism

 95% Confidence intervals by
parametric bootstrap (n = 10000)
based upon estimates and
standard errors from nlme fit
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Conclusions
 Present graphical approach appealing to
scientists
 Still a lot to be done
– T. O’Brien’s approach (TOB)
– Incorporating design issues in TOB
– Alternative distributions (e.g. gamma)
– Optimal design
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