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Statistical Methods for Microarray Experiments:Analysis of Dose-response Studies and
Software Development in R
Setia Pramana
Promotors:Prof. dr. Ziv Shkedy
Prof. dr. Dan Lin
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 1 / 50
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Outline
Introduction to dose-response microarray analysis
Content of the dissertation.
Focus: dose-response modeling and model averaging of targetdoses in microarray experiments
Discussion, conclusion, and future research
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 2 / 50
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1. Introduction
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 3 / 50
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Dose-response Study
The fundamental study in drug development.
Main goal: obtain safe and efficacious dose.
Investigate the dependence of the phenotypic response on doses.
Interest to discover monotone dose-response relationship
Monotonicity − > order restricted profile.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 4 / 50
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Dose-response Study
The fundamental study in drug development.
Main goal: obtain safe and efficacious dose.
Investigate the dependence of the phenotypic response on doses.
Interest to discover monotone dose-response relationship
Monotonicity − > order restricted profile.
Dose-response Microarray Studies:
Monitoring of gene expression with respect to increasing doses.
To identify a subset of genes with a monotonic trend.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 4 / 50
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Dose-response Microarray studies
The StudyCompound
Dose 0/Control Dose 1 Dose 2 … Dose K
Data Structure
mKnmKmnmmnm
KnKnn
KnKnn
K
K
K
YYYYYY
YYYYYY
YYYYYY
Y
...........
.
.
.
.....
.....
.....
.
.
.
.
.
.
...........
...........
1111001
2122111220012
1111111110011
10
10
10Gene 1
Gene 2
.
.
.
Gene m
d0 d1 ….. dK
Dose levels
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 5 / 50
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Dose-response Microarray Studies
Case study: a study focuses on antipsychotic compounds.
6 dose levels with 4-5 samples at each dose level.
Each array consists of 11,565 genes.
One gene profile:
Doses
Gen
e E
xpre
ssio
n
0 0.16 0.63 2.5 10 40
67
89
+
+
+
+
+
+
* *
*
*
*
*
Gene:
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2. Contents of the Dissertation
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Contents of the Dissertation
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Contents of the Dissertation
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Contents of the Dissertation
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 9 / 50
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Contents of the Dissertation
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 10 / 50
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3. Dose-response Modeling and ModelAveraging in Microarray Experiments
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The Framework
Dose-response relationship for each gene:
Yij = f (di , θ) + εij , i = 0, 2, . . . , K , j = 1, 2, . . . , ni ,
A secondary analysis to investigate dose-response relationship.
f (di , θ): linear or non-linear models (e.g., Emax , logistic).
More than one model fit the data.
Focus only on monotone relationship.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 12 / 50
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The Framework
Feature Selection Significant test: Genes with a
monotonic trend
Parametric Modeling Target dose estimation
Model Uncertainty
with Model Averaging
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 13 / 50
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Feature Selection: Case Study
11,565 genes.
Test for monotone trend : Likelihood Ratio Test (Bartholomew,1959).
BH-FDR for multiplicity adjustment (Benjamini and Hochberg,1995.
Number of significant genes (FDR=0.05)
JNJa JNJb JNJc CompB CompA CompC211 251 164 332 72 242
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Next Step
Focus on the CompA: We have 72 significant genes.
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Next Step
Focus on the CompA: We have 72 significant genes.
Rank the genes.
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Next Step
Focus on the CompA: We have 72 significant genes.
Rank the genes.
Compare the compounds.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 15 / 50
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Next Step
Focus on the CompA: We have 72 significant genes.
Rank the genes.
Compare the compounds.
Based on what criterion?
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 15 / 50
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Rank Genes Based on the Fold-change? or t-typeStatistics?
Fold-changes: after log2 transformed, µ̂∗
K − µ̂∗
0
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Rank Genes Based on the Fold-change? or t-typeStatistics?
Fold-changes: after log2 transformed, µ̂∗
K − µ̂∗
0
Modified t-type statistics:µ̂∗
K −µ̂∗
0se − > Marcus (1976)
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 16 / 50
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Rank Genes Based on the Fold-change? or t-typeStatistics?
Fold-changes: after log2 transformed, µ̂∗
K − µ̂∗
0
Modified t-type statistics:µ̂∗
K −µ̂∗
0se − > Marcus (1976)
Two genes with similar fold-changes and t-type tests:
0 1 2 3 4
01
23
45
Dose
Gen
e ex
pres
sion
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 16 / 50
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Rank Genes Based on the Fold-change? or t-typeStatistics?
More suitable parameter: the ED50
0 1 2 3 4
01
23
45
Dose
Gen
e ex
pres
sion
genes 1, ED50=1mg/mlgenes 2, ED50=3mg/ml
Two genes with similar fold-changes, t-type tests, and differentED50 estimates.
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The Target Dose: ED50
The ED50: dose which induces a response halfway between thebaseline and maximum.
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The Target Dose: ED50
The ED50: dose which induces a response halfway between thebaseline and maximum.
0 1 2 3 4
01
23
45
Dose
Gen
e ex
pres
sion
compound 1, ED50=1mg/mlcompound 2, ED50=2mg/ml
ED50 reflects the potency of the tested drug or compound.
Rank genes or compare compounds based on the ED50.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 18 / 50
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ED50 Within Dose Range
To avoid problems, the ED50 is restricted to lie within the interval(d0, dK ].
ED50, 1 ED50, 2
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ED50 Within Dose Range
To avoid problems, the ED50 is restricted to lie within the interval(d0, dK ].
ED50, 1 ED50, 2
For gene expression data, the ED50 within dose-range = dose ofhalf way to the fold-change.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 19 / 50
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Dose-response Model
Dose
Res
pons
e
8
9
10
11
12
13
emax
0 10 20 30 40
exponential linear
0 10 20 30 40
linlog logistic
0 10 20 30 40
8
9
10
11
12
13
sigEmax
Responses Model Predictions 0.95 Pointwise CI Estim. Dose
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Dose-response Modeling: Pros and Cons
Assume a functional relationship between the response and thedose according to a pre-specified parametric model.
The dose is taken as a quantitative factor.
Provides flexibility in investigating the effect of doses not used inthe actual study.
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Dose-response Modeling: Pros and Cons
Assume a functional relationship between the response and thedose according to a pre-specified parametric model.
The dose is taken as a quantitative factor.
Provides flexibility in investigating the effect of doses not used inthe actual study.
Its result validity depends on the correct choice of thedose-response model, which is a priori unknown.
Multiple models describe the data equivalently, but the target doseestimates are different.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 21 / 50
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The Framework: Model Averaging
Feature Selection Significant test: Genes with a
monotonic trend
Parametric Modeling Target dose estimation
Model Uncertainty
with Model Averaging
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Model Averaging
Account for model uncertainty.
All fits are taken into consideration.
Combines results from different models.
Poor fits receive small weights.
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Model Averaging
Fit R candidate models:
f1, f2, f3, . . . , fR
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Model Averaging
Fit R candidate models:
f1, f2, f3, . . . , fR
Calculate the Information Criterion (IC) of each model.
IC1, IC2, IC3, . . . , ICR
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Model Averaging
Fit R candidate models:
f1, f2, f3, . . . , fR
Calculate the Information Criterion (IC) of each model.
IC1, IC2, IC3, . . . , ICR
IC: measure relative goodness of fit and account for modelcomplexity e.g, AIC, BIC.AIC = −2logL(θ|data) + 2M.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 24 / 50
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Model Averaging
Fit R candidate models:
f1, f2, f3, . . . , fR
Calculate the Information Criterion (IC) of each model.
IC1, IC2, IC3, . . . , ICR
IC: measure relative goodness of fit and account for modelcomplexity e.g, AIC, BIC.AIC = −2logL(θ|data) + 2M.
Model selection: Choose the model with minimum AIC, ignoringthe other results.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 24 / 50
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Model Averaging
Model Averaging: Each model is given a weight:
ω1, ω2, ω3, . . . , ωR
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Model Averaging
Model Averaging: Each model is given a weight:
ω1, ω2, ω3, . . . , ωR
ωr =exp(−∆ICr/2)∑
exp(−∆ICr/2)
∆ICr = ICr − ICmin
0 ≤ ωr ≤ 1,
R∑
r
ωr = 1
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 25 / 50
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Model Averaging
θ is the parameter of interest: ED50
θ̂MA =
R∑
r
ωr × θ̂r ,
θ̂r is the estimate of θ from model r
v̂ar(θ̂MA) is obtained using bootstrap.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 26 / 50
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Model Averaging
θ is the parameter of interest: ED50
θ̂MA =
R∑
r
ωr × θ̂r ,
θ̂r is the estimate of θ from model r
v̂ar(θ̂MA) is obtained using bootstrap.
Given the fits of R models, we can estimate the MAdose-response curve as:
f̂MA(d) =
R∑
r
ωr × f̂ (θ, d)r .
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 26 / 50
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Dose-response Models for One Gene (FOS)
Data and fitted value for Gene FOS
0 10 20 30 40
910
1112
Dose
Gen
e E
xpre
ssio
n
LinearLinlogExponentialEmaxsigEmaxLogisticModel Average
0 10 20 30 409
1011
12Dose
Gen
e E
xpre
ssio
n
EmaxModel Average
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 27 / 50
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Model Averaging for One Gene (FOS)
ED50, AIC, and AIC weightsfor the gene FOS
Model ED50 AIC WeightsLinear 20.000 86.37 <0.001Linear log-dose 5.405 69.51 0.029Exponential 22.502 89.78 <0.0014P Logistic 2.042 67.53 0.077Hyperbolic Emax 1.241 63.30 0.640Sigmoidal Emax 1.241 65.15 0.254Model Average ED50 1.423
MA ED50 and its confidenceinterval for each model
ED50M
odel
s
Lin
LinL
ogE
xpon
entia
lH
Em
axS
Em
axLo
gis
MA
0 5 10 15 20
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 28 / 50
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What Is Next?
Feature Selection Significant test: Genes with a
monotonic trend
Parametric Modeling Target dose estimation (ED50)
Model Averaging
MA ED50
What is the next
step?
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 29 / 50
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What Is Next?
Model Averaging
MA ED50
Gene Ranking in a
Single Compound
Comparison between
Compounds
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 30 / 50
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Gene Ranking in a Single Compound
0 10 20 30 40
010
2030
index
ED
50
42 genes have a significantupward trend (FDR=0.05).
Genes with a smaller ED50
react faster to the compound(genes need smaller dose tobe expressed).
Genes with high ED50 are lessinteresting.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 31 / 50
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Gene Ranking in a Single Compound
Genes profile with the smallest and highest MA ED50.
0 10 20 30 40
7.5
8.0
8.5
9.0
9.5
MA ED50 = 0.04
doses
gene
exp
ress
ion
0 10 20 30 40
2.6
2.8
3.0
3.2
MA ED50 = 30.78520
doses
gene
exp
ress
ion
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 32 / 50
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Gene Ranking in a Single Compound
3D scatter plot: Fold Change, ED50, µ̂∗
0
0 5 10 15 20 25 30 35
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2
4
6
8
10
12
14
ED50
Mu0
Fol
d ch
ange
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Gene Ranking in a Single Compound
3D scatter plot:Fold Change, ED50, µ̂∗
0
0 5 10 15 20 25 30 35
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2
4
6
8
10
12
14
ED50
Mu0
Fol
d ch
ange
0 10 20 30 40
910
1112
MA ED50=1.42, FC =2.56, Mu0= 9.20
doses
gene
exp
ress
ion
0 10 20 30 40
45
67
8
MA ED50=4.82, FC =2.90, Mu0= 4.32
doses
gene
exp
ress
ion
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Gene Ranking in a Single Compound
Genes with similar MA ED50
different E0
0 10 20 30 40
45
67
8
doses
gene
exp
ress
ion
Genes with similar Fold change,different E0 and MA ED50
0 10 20 30 40
46
810
12
doses
gene
exp
ress
ion
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 35 / 50
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Compounds Comparison
Model Averaging
MA ED50
Gene Ranking in a
Single Compound
Comparison between
Compounds
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Compounds Comparison Based on the MA ED50
Plot of MA ED50
compound JnJa vs. CompA
5 10 15 20
510
1520
CompA
JnJa
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Compounds Comparison Based on the MA ED50
Plot of MA ED50
compound JnJa vs. CompA
5 10 15 20
510
1520
CompA
JnJa
0 10 20 30 40
3.5
4.0
4.5
5.0
CompA, MA ED50 = 16.89
doses
gene
exp
ress
ion
0 10 20 30 40
3.4
3.6
3.8
4.0
4.2
JnJa, MA ED50 = 3.41
doses
gene
exp
ress
ion
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 38 / 50
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Compounds Comparison Based on the MA ED50
Plot of MA ED50
compound JnJa vs. CompA
5 10 15 20
510
1520
CompA
JnJa
0 10 20 30 40
7.0
7.5
8.0
8.5
9.0
CompA, MA ED50 = 2.47
doses
gene
exp
ress
ion
0 10 20 30 40
8.0
8.5
9.0
JnJa, MA ED50 = 12.46
doses
gene
exp
ress
ion
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 39 / 50
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Testing for Compound Effect
Investigate the activity of different compounds on the expressionlevel of a single gene.
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Testing for Compound Effect
Investigate the activity of different compounds on the expressionlevel of a single gene.
Based on a specific dose-response model (the Emax model).
Emax model: f (d) = E0 + d×(EMax )d+ED50
E0 + Emax
E0
Emax
ED50
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 40 / 50
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Testing for Compound Effect
The parameters are formulated as a linear function of thecompounds:
E0k
ED50k
Emaxk
=
θ1 + γk
θ2 + δk
θ3 + ηk
, k = 2, ..., K ,
For the ED50 parameter, we test the null hypothesis of nocompound effect:
H0 : δk = 0,H1 : δk 6= 0.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 41 / 50
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Testing for Compound Effect
Model with common E0 for allcompounds.
doses
Gen
e ex
pres
sion
0 0.16 0.63 2.5 10 40
89
1011
1213
CompAJnJaCompBCompCJnJbJnJc
doses
Gen
e ex
pres
sion
0 0.16 0.63 2.5 10 40
89
1011
1213
CompAJnJaCompBCompCJnJbJnJc
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 42 / 50
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Testing for Compound Effect
Model with common E0 for allcompounds.
doses
Gen
e ex
pres
sion
0 0.16 0.63 2.5 10 40
89
1011
1213
CompAJnJaCompBCompCJnJbJnJc
doses
Gen
e ex
pres
sion
0 0.16 0.63 2.5 10 40
89
1011
1213
CompAJnJaCompBCompCJnJbJnJc
Model with common Emax and E0
for all compounds.
doses
Gen
e ex
pres
sion
0 0.16 0.63 2.5 10 40
89
1011
1213
CompAJnJaCompBCompCJnJbJnJc
doses
Gen
e ex
pres
sion
0 0.16 0.63 2.5 10 40
89
1011
1213
CompAJnJaCompBCompCJnJbJnJc
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 42 / 50
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Application to Another Target Dose: MED
The previous approach can also be implemented to other targetdoses such as: Minimum Effective Dose (MED).
MED is defined as ”the lowest dose producing a clinicallyimportant response that can be declared statistically, significantlydifferent from the placebo response”
(Pinheiro, Bretz, and Branson, 2006)
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 43 / 50
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The Minimum Effective Dose
MED is formulated as:
MED = argmind∈(d0,dk ](f (d , θ) > f (d0, θ) + ∆). (1)
The clinically relevant difference (∆): is the smallest relevantdifference, by which we expect a dose to be better than theplacebo.
∆ = τ × µ̂∗
0, where τ is the percentage change from the isotonicmean response in the placebo (µ̂∗
0)
(Bretz et.al, 2010)
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The Minimum Effective Dose
MED graphical representation
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4. Discussion, Conclusion, and FutureResearch
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 46 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
There is no single model which fits all genes.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
There is no single model which fits all genes.
Three steps approach:
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
There is no single model which fits all genes.
Three steps approach:Select the genes with a monotone trend.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
There is no single model which fits all genes.
Three steps approach:Select the genes with a monotone trend.
Fit the selected genes with the candidate models to get a targetdose.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
There is no single model which fits all genes.
Three steps approach:Select the genes with a monotone trend.
Fit the selected genes with the candidate models to get a targetdose.
Average the target dose from the candidate models.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Discussion
Parametric modeling is aimed to investigate in more details theresponse of genes to the dose.
There is no single model which fits all genes.
Three steps approach:Select the genes with a monotone trend.
Fit the selected genes with the candidate models to get a targetdose.
Average the target dose from the candidate models.
These procedures combine the advantage of testing for amonotone trend, model-based, and model averaging.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 47 / 50
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Conclusion
The three steps dose-response modeling approach:Overcome the weakness of model selection approach.
Provide a realistic target dose.
Can be implemented in other target doses.
The model-average ED50 can be used to rank the genes andcompare the tested compounds.
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 48 / 50
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Future Research
Investigate two possible approaches: Average the ED50 orAverage Model?
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 49 / 50
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Future Research
Investigate two possible approaches: Average the ED50 orAverage Model?
Probe level dose-response modeling.
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Thank you for your attention...
” All things are poison and nothing is without poison;only the dose makes that a thing is no poison.”
(Paracelsus)
Setia Pramana () Dose-response in Microarray Experiments Diepenbeek, 09/09/2011 50 / 50