model averaging in dose-response study in microarray expression

Dose-Response Modeling of Gene Expression Datain 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

Research Team

I-BiostatSetia PramanaDan LinZiv ShkedyPhilippe Haldermans

J&J Pharmaceutical Research and DevelopmentAn De BondtHinrich GohlmannWillem TalloenLuc BijnensJose PinheiroTobias Verbeke


Outline

Introduction to Dose-response Studies

Testing for Monotonic Trend

Model Based

Model Averaging

Application

Concluding Remarks


Dose-response (DR) studies: The fundamental studyin 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 thechance of it showing effectiveness.

DR studies:Investigate the dependence of the response on doses: how thedrug 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 andsafe. Target dose: minimum effective dose (MED), maximallytolerated dose (MTD) or half maximal effective dose (ED50).


Dose-response in Microarray Experiments

Monitoring of gene expression with respect to increasing dose of acompound.

To identify a subset of genes with overall dose related trend.

To investigate the mechanism of action of potential drug in theentire genome.

To compare between compounds using the gene expressioninformation.


Dose-response in Microarray: The study

Compound

Dose 0/Control Dose 1 Dose 2 … Dose K


Dose-response in Microarray: Data Structure

k

k

k

kmnkmmnmmnm

nkknn

nkknn

xxxxxx

xxxxxx

xxxxxx

X

...........

.

.

.

.....

.....

.....

.

.

.

.

.

.

...........

...........

1111010

2211212102011

1111111101011

10

10

10Gene 1

Gene 2

.

.

.

Gene m

d0 d1 ….. dk

Dose levels


Dose-response in Microarray: Modeling

No prior info about the dose-response shape, but it’s assumed tobe monotone.

Monotone assumption is based on in general, increasing the doseof a harmful agent results a proportional increase in the incidenceof an adverse effect and the severity of the effect.

Genes have different shapes.


Modeling Framework

Step 1

Feature selectionGenes with monotone trend

Step 2

Parametric modelingEstimation of = ED50

Step 3

Model Averaging

r

R

r

rMA

ˆˆ

1


Step 1: Feature Selection: Testing for Monotonic Trend

Gene specific test:

H0 : µ(d0) = µ(d1) = · · · = µ(dK )

HUp1 : µ(d0) ≤ µ(d1) ≤ · · · ≤ µ(dK )

or

HDown1 : µ(d0) ≥ µ(d1) ≥ · · · ≥ µ(dK )

with at least one inequality.

Test statistics: Likelihood Ratio Test (E201).

(Lin et al., 2007)


Step 2: Dose-response Modeling

0 10 20 30 40

5.5

6.0

6.5

7.0

7.5

8.0

8.5

An increasing trend gene

dose

gene

exp

ress

ion

0 10 20 30 40

2.6

2.7

2.8

2.9

A gene with a flat profile

dose

gene

exp

ress

ion

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).


Dose-response Modeling: Target Dose (ED50)

From the DR model the ED50 is estimated.

The ED50: dose which induces a response halfway between thebaseline and maximum.

max0EE

0E

Slope (N)

maxE

Dose

50IC

ED50 reflects the potency of the tested drug or compound.

The ED50 is restricted to lie within the interval (d1, dk ] to avoidproblems arising from extrapolating beyond the dose range underinvestigation.


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 the DR model,which is a priori unknown.

Multiple models describe the data equivalently, but the estimatestarget dose are different.


Step 3: Model Averaging

Account for model uncertainty.

All fits are taken into consideration.

Combines results from different models.

Poor fits receive small weights.


DR Model Candidates

0.0 0.5 1.0 1.5 2.0 2.5 3.0

02

46

810

Linear

dose

gene

exp

ress

ion

0.0 0.5 1.0 1.5 2.0 2.5 3.0

02

46

810

Linear Log

dosege

ne e

xpre

ssio

n

0.0 0.5 1.0 1.5 2.0 2.5 3.0

02

46

810

Exponential

dose

gene

exp

ress

ion

0.0 0.5 1.0 1.5 2.0 2.5 3.0

02

46

810

Logistic

dose

gene

exp

ress

ion

0.0 0.5 1.0 1.5 2.0 2.5 3.0

02

46

810

Hyp E−max

dose

gene

exp

ress

ion

0.0 0.5 1.0 1.5 2.0 2.5 3.0

02

46

810

Sigmoid E−max

dose

gene

exp

ress

ion


Model Averaging

Let θ be a quantity in which we are interested in and we canestimate θ from R models, the model averaged (MA) θ is definedas:

θMA =R∑

r

ωr × θr ,

where θr is the estimate of θ from model r and ωr the weights thatsum to one assigned to model r .

Given the fits of R models, we can estimate the MAdose-response curve as:

fMA(d) =

R∑

r

ωr × f (θ, d)r .


Model Averaging Weights

Information Criterion

ωr =exp(−∆Ir/2)∑

exp(−∆Ir/2)

∆Ir = Ir − Imin, where Imin is the smallest Information Criterionvalue, Ir = AIC, BIC.

Bootstrapping (Buckland et al. 1997).

We implemented AIC


Model Averaged ED50

The model-averaged ED50 is defined as:

ED50 =R∑

r=1

ωr ED50,r , (1)

where ED50,r is the estimate of ED50 of model r , and ωr is theakaike’s weight of model r .

Since the distribution of the ED50 is unknown, the estimator for

variance of ED50 is obtained using bootstrap method.


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.

Doses

Gen

e E

xpre

ssio

n

0 0.16 0.63 2.5 10 40

5.5

6.0

6.5

7.0

7.5

8.0

8.5

+

+

+

+

++

* *

*

*

**


Results: Feature Selection72 genes have a significant monotonic trend (FDR=0.05).

Data and isotonic trend of four significant genes:

0 10 20 30 40

5.5

6.0

6.5

7.0

7.5

8.0

8.5

Doses

Gen

e E

xpre

ssio

n

++

++

+ +

**

**

* *

0 10 20 30 40

9.8

10.0

10.2

10.4

Doses

Gen

e E

xpre

ssio

n

+

++

+

+

+

*

**

*

*

*

0 10 20 30 40

8.6

8.8

9.0

9.2

Doses

Gen

e E

xpre

ssio

n +

+

+

+

+

+

*

*

** *

*

0 10 20 30 40

6.2

6.4

6.6

6.8

7.0

7.2

7.4

7.6

Doses

Gen

e E

xpre

ssio

n

+

+

+

+ +

+

*

*

* * *

*


Results: Model-based

Data and fitted value for the one of the genes

0 10 20 30 40

910

1112

Dose

Gen

e E

xpre

ssio

n

linearlinlogexponentialemaxsigEmaxlogisticModel Average


Results: Model Averaging

ED50, AIC, and AIC weight for one of the genes

Model ED50 AIC AIC weightLinear 20.000 86.37 <0.0001Linear log-dose 5.405 69.51 0.029Exponential 22.502 89.78 <0.00014P 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


Results: Model Averaging

ED50 and its confidence interval for each model

ED50

Mod

el

Lin

LinL

ogH

Em

axS

Em

axLo

gis

MA

0 5 10 15 20


Results: Gene Ranking Based on MA ED50

0 10 20 30 40

010

2030

index

ED

50

Genes with a smaller ED50

react faster to the compound(genes need less dose to beexpressed.).

Genes with high ED50 are lessinteresting.


Results: Gene Ranking

Genes profile with the smallest and highest ED50.

0 10 20 30 40

910

1112

Gene with lowest ED50

dose

gene

exp

ress

ion

0 10 20 30 40

4.5

5.0

5.5

6.0

6.5

7.0

Gene with highest ED50

dose

gene

exp

ress

ion


Results: Comparison with Other Compounds

Plot of MA ED50 compound JnJavs. Aripi

5 10 15 20

510

1520

Aripiprazole

JnJa

Genes express differently overthe two compounds.

Most of the genes react slowerto the compound JnJa thanAripiprazole.


Results: Comparison with other compounds

Aripiprazole: ED50= 1.143JnJa: ED50= 4.25

0 10 20 30 40

89

1011

1213

doses

gene

exp

ress

ion

AripiprazoleJnJaAripiprazoleJnJa

Aripiprazole: ED50=4.96JnJa: ED50= 16.72

0 10 20 30 40

9.0

9.5

10.0

10.5

doses

gene

exp

ress

ion

AripiprazoleJnJaAripiprazoleJnJa


Concluding Remarks

In the DR modeling in microarray settings, fitting directly theproposed models to all genes (which can be tens thousands) cancreate 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 E2.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 monotonetrend, model-based and model averaging.


Concluding Remarks

The MA(ED50) can be used to rank the genes and compare aspecific gene over the tested compounds.Software:

IsoGene (CRAN) and IsoGeneGUI (bioconductor) R packages fortesting for monotonic trend,http://www.ibiostat.be/software/IsoGeneGUI/index.html.DoseFinding R package for non-linear DR modeling and modelaveraging.

More details:Dan Lin, Ziv Shkedy, Daniel Yekutieli, Dhammika Amaratunga,and Luc Bijnens (Editors). (2011). Modeling Dose-responseMicroarray Data in Early Drug Development Experiments Using R.Springer.


http://www.ibiostat.be/software/IsoGeneGUI/index.html

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)


model averaging in dose-response study in microarray expression

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