The document discusses dose-response modeling of gene expression data in microarray experiments, emphasizing the importance of identifying effective doses of compounds in drug discovery. It presents a structured approach involving feature selection, parametric modeling, and model averaging to analyze the relationship between drug doses and gene expression across multiple genes. The study highlights a case on antipsychotic compounds, demonstrating the significance of the estimated effective dose (ed50) in understanding drug efficacy and safety.

1. Dose-Response Modeling of Gene Expression Data
in Microarray Experiments
Setia Pramana
Interuniversity Institute for Biostatistics and Statistical Bioinformatics,
Universiteit Hasselt, Diepenbeek, Belgium
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 1 / 30

2. Research Team
I-Biostat
Setia Pramana
Dan Lin
Ziv Shkedy
Philippe Haldermans
J&J Pharmaceutical Research and Development
An De Bondt
¨
Hinrich Gohlmann
Willem Talloen
Luc Bijnens
Jose Pinheiro
Tobias Verbeke
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 2 / 30

3. Outline
Introduction to Dose-response Studies
Testing for Monotonic Trend
Model Based
Model Averaging
Application
Concluding Remarks
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 3 / 30

4. Dose-response (DR) studies: The fundamental study
in drug discovery
Good drugs: Strong effects on a specific biological pathways,
minimal effects on all other pathways.
Too high dose can be dangerous, too low dose decreases the
chance of it showing effectiveness.
DR studies:
Investigate the dependence of the response on doses: how the
drug works? Has it the desired properties?
What is the shape of the relationship?
Discover a dose or a range of dose that are both efficacious and
safe. Target dose: minimum effective dose (MED), maximally
tolerated dose (MTD) or half maximal effective dose (ED50 ).
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 4 / 30

5. Dose-response in Microarray Experiments
Monitoring of gene expression with respect to increasing dose of a
compound.
To identify a subset of genes with overall dose related trend.
To investigate the mechanism of action of potential drug in the
entire genome.
To compare between compounds using the gene expression
information.
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6. Dose-response in Microarray: The study
Compound
Dose 0/Control Dose 1 Dose 2 … Dose K
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7. Dose-response in Microarray: Data Structure
Gene 1
x011..x01n0 x111..x11n1 ..... xk11..xk1nk
Gene 2 x011..x02n0 x121..x12n1 ..... xk 21..xk 2nk
. . . ..... .
X
. . . ..... .
. . . ..... .
Gene m x0m1..x0mn0 x1m1..x1mn1 ..... xkm1..xkmnk
d0 d1 ….. dk
Dose levels
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8. Dose-response in Microarray: Modeling
No prior info about the dose-response shape, but it’s assumed to
be monotone.
Monotone assumption is based on in general, increasing the dose
of a harmful agent results a proportional increase in the incidence
of an adverse effect and the severity of the effect.
Genes have different shapes.
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 8 / 30

9. Modeling Framework
Step 1
Feature selection
Genes with monotone trend
Step 2
Parametric modeling
Estimation of = ED50
Step 3
Model Averaging
R
ˆ ˆ
MA r r
r 1
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10. Step 1: Feature Selection: Testing for Monotonic Trend
Gene specific test:
H0 : µ(d0 ) = µ(d1 ) = · · · = µ(dK )
Up
H1 : µ(d0 ) ≤ µ(d1 ) ≤ · · · ≤ µ(dK )
or
Down : µ(d ) ≥ µ(d ) ≥ · · · ≥ µ(d )
H1 0 1 K
with at least one inequality.
¯2
Test statistics: Likelihood Ratio Test (E01 ).
(Lin et al., 2007)
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11. Step 2: Dose-response Modeling
An increasing trend gene A gene with a flat profile
8.5
2.9
8.0
2.8
7.5
gene expression
gene expression
7.0
2.7
6.5
6.0
2.6
5.5
0 10 20 30 40 0 10 20 30 40
dose dose
For each differentially expressed gene:
Yij = f (di , θ) + εij , i = 1, 2, . . . , K , j = 1, 2, . . . , ni ,
where f (di , θ): the dose-response model (e.g., Emax , Logistic).
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 11 / 30

12. Dose-response Modeling: Target Dose (ED50 )
From the DR model the ED50 is estimated.
The ED50 : dose which induces a response halfway between the
baseline and maximum.
E0 E max
Slope (N)
Emax
E0
IC50
D ose
ED50 reflects the potency of the tested drug or compound.
The ED50 is restricted to lie within the interval (d1 , dk ] to avoid
problems arising from extrapolating beyond the dose range under
investigation.
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13. Dose-response Modeling: Pros and Cons
Assume a functional relationship between the response and the
dose 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 in
the actual study.
Its result validity depends on the correct choice of the DR model,
which is a priori unknown.
Multiple models describe the data equivalently, but the estimates
target dose are different.
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14. Step 3: 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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15. DR Model Candidates
Linear Linear Log Exponential
10
10
10
8
8
8
gene expression
gene expression
gene expression
6
6
6
4
4
4
2
2
2
0
0
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
dose dose dose
Logistic Hyp E−max Sigmoid E−max
10
10
10
8
8
8
gene expression
gene expression
gene expression
6
6
6
4
4
4
2
2
2
0
0
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
dose dose dose
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16. Model Averaging
Let θ be a quantity in which we are interested in and we can
estimate θ from R models, the model averaged (MA) θ is defined
as:
R
ˆ
θMA = ˆ
ωr × θr ,
r
ˆ
where θr is the estimate of θ from model r and ωr the weights that
sum to one assigned to model r .
Given the fits of R models, we can estimate the MA
dose-response curve as:
R
ˆMA (d ) =
f ωr × ˆ(θ, d )r .
f
r
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17. Model Averaging Weights
Information Criterion
exp(−∆Ir /2)
ωr =
exp(−∆Ir /2)
∆Ir = Ir − Imin , where Imin is the smallest Information Criterion
value, Ir = AIC, BIC.
Bootstrapping (Buckland et al. 1997).
We implemented AIC
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18. Model Averaged ED50
The model-averaged ED50 is defined as:
R
ED 50 = ωr ED 50,r , (1)
r =1
where ED50,r is the estimate of ED50 of model r , and ωr is the
akaike’s weight of model r .
Since the distribution of the ED 50 is unknown, the estimator for
variance of ED 50 is obtained using bootstrap method.
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19. Antipsychotic Study
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.
+
*
8.5
+
*
8.0
7.5
Gene Expression
+
7.0
*
+
*
6.5
+
* *
+
6.0
5.5
0 0.16 0.63 2.5 10 40
Doses
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20. Results: Feature Selection
72 genes have a significant monotonic trend (FDR=0.05).
Data and isotonic trend of four significant genes:
10.4
+
5.5 6.0 6.5 7.0 7.5 8.0 8.5
+
* *
+
*
10.2
Gene Expression
Gene Expression
+
*
+
*
10.0
+ +
*
*
+ +
*
+ **
+
9.8
+
*
0 10 20 30 40 0 10 20 30 40
Doses Doses
6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6
9.2
+
*
+
* +
*
Gene Expression
Gene Expression
9.0
+
*
+ + +
+
* * * *
* * +
8.8
+
+
*
+
*
8.6
0 10 20 30 40 0 10 20 30 40
Doses Doses
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21. Results: Model-based
Data and fitted value for the one of the genes
12
11
Gene Expression
10
9
linear
linlog
exponential
emax
sigEmax
logistic
Model Average
0 10 20 30 40
Dose
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22. Results: Model Averaging
ED50 , AIC, and AIC weight for one of the genes
Model ED50 AIC AIC weight
Linear 20.000 86.37 <0.0001
Linear log-dose 5.405 69.51 0.029
Exponential 22.502 89.78 <0.0001
4P Logistic 2.042 67.53 0.077
Hyperbolic Emax 1.241 63.30 0.640
Sigmoidal Emax 1.241 65.15 0.254
Model Average ED50 1.423
Setia Pramana () Dose-response in Microarray Experiments Groningen, March 16, 2011 22 / 30

23. Results: Model Averaging
ED50 and its confidence interval for each model
MA
Logis
SEmax
Model
HEmax
LinLog
Lin
0 5 10 15 20
ED50
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24. Results: Gene Ranking Based on MA ED50
Genes with a smaller ED50
react faster to the compound
(genes need less dose to be
expressed.).
30
Genes with high ED50 are less
interesting.
20
ED50
10
0
0 10 20 30 40
index
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25. Results: Gene Ranking
Genes profile with the smallest and highest ED50 .
Gene with lowest ED50 Gene with highest ED50
12
7.0
6.5
11
gene expression
gene expression
6.0
10
5.5
5.0
9
4.5
0 10 20 30 40 0 10 20 30 40
dose dose
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26. Results: Comparison with Other Compounds
Plot of MA ED50 compound JnJa
vs. Aripi
Genes express differently over
the two compounds.
20
Most of the genes react slower
to the compound JnJa than
15
Aripiprazole.
JnJa
10
5
5 10 15 20
Aripiprazole
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27. Results: Comparison with other compounds
Aripiprazole: ED50 = 1.143 Aripiprazole: ED50 =4.96
JnJa: ED50 = 4.25 JnJa: ED50 = 16.72
10.5
13
12
10.0
11
gene expression
gene expression
10
9.5
Aripiprazole
Aripiprazole JnJa
JnJa Aripiprazole
9
Aripiprazole JnJa
JnJa
9.0
8
0 10 20 30 40 0 10 20 30 40
doses doses
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28. Concluding Remarks
In the DR modeling in microarray settings, fitting directly the
proposed models to all genes (which can be tens thousands) can
create problems, such as complexity and time consumption.
There is no single model fits all genes.
We propose a three steps approach:
Select the genes with a monotone trend using the E 2 .
Fit the selected genes with the candidate models to get a target
dose.
Average the target dose from the candidate models.
These procedures combine the advantage of testing for monotone
trend, model-based and model averaging.
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29. Concluding Remarks
The MA(ED50 ) can be used to rank the genes and compare a
specific gene over the tested compounds.
Software:
IsoGene (CRAN) and IsoGeneGUI (bioconductor) R packages for
testing for monotonic trend,
http://www.ibiostat.be/software/IsoGeneGUI/index.html.
DoseFinding R package for non-linear DR modeling and model
averaging.
More details:
Dan Lin, Ziv Shkedy, Daniel Yekutieli, Dhammika Amaratunga,
and Luc Bijnens (Editors). (2011). Modeling Dose-response
Microarray Data in Early Drug Development Experiments Using R.
Springer.
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30. 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 Groningen, March 16, 2011 30 / 30