Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray...
Transcript of Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray...
![Page 1: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/1.jpg)
Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods:
Modeling and multiplicity adjustments
Adetayo Kasim
Durham University UK
![Page 2: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/2.jpg)
Outline
• Introduction to dose-response modeling in microarray experiments.
• Bayesian estimation in the presence of equality constraints
• Inference for monotone genes
• Multiplicity adjustment
• Discussion
• Current work: Bayesian isotonic regression
![Page 3: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/3.jpg)
Dose-response Microarray Experiments
![Page 4: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/4.jpg)
Dose-response Microarray studies
Biological information from gene expression data create
new opportunities for developing effective therapies:
To understand mechanism of action of a new treatment.
To explore the desired properties (efficacy/toxicity…).
Explore functions of genes/pathways in a dose-dependency
manner .
![Page 5: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/5.jpg)
Case Study: Human epidermal squamous carcinoma celllines
– 4 dose levels.
– 12 arrays.
– 16,998 genes measured on each
array.
EGF (ng/ml)
Dose 0 1 10 100
# of arrays
3 3 3 3
![Page 6: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/6.jpg)
Examples: Dose-response relationships with gene expression
![Page 7: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/7.jpg)
Bayesian Estimation in the Presence of equality constraint between parameters
![Page 8: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/8.jpg)
Objective
Primary interest:
• Discovery of genes with monotone relationship with respect to dose.
Order restricted inference.
• Simple order (monotone) alternatives.
![Page 9: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/9.jpg)
Model Formulation
2,~ iij NY
Estimation under strict inequality constraints
• Order constraints of priors (Gelfand et al., 1992).
Kg ,...,: 10
![Page 10: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/10.jpg)
2,~ iij NY
),(,~ 11
2
iii IN
otherwise
NP iii
0
,,| 11
2
Specification of the prior :
unconstrained prior.
Likelihood:
2, N
Model Formulation
![Page 11: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/11.jpg)
1
1
0
)|()|(K
K
S
SPyP
The posterior distribution, given the order constraints, is the
same as the unconstrained distribution defined on the
constraints set.
The constraints set
Model Formulation
![Page 12: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/12.jpg)
K
K
H
H
,...,:
,...,:
101
100
? What happen if there is equality constraints between parameters.
Model Formulation
![Page 13: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/13.jpg)
•The null model
32107
32106
32105
32104
32103
32102
32101
32100
:
:
:
:
:
:
:
:
g
g
g
g
g
g
g
g
32101 : H
• We decompose the simple order alternative to all sub alternatives.
• All possible monotone models
Model Formulation
![Page 14: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/14.jpg)
• Monotone models
32107
32106
32105
32104
32103
32102
32101
32100
:
:
:
:
:
:
:
:
g
g
g
g
g
g
g
g
μμμμg
μμμg
μμμg
μμμg
μμg
μμg
μμg
μg
3210
'
7
2310
'
6
3201
'
5
3120
1
4
1230
'
3
2301
'
2
3012
'
1
0123
'
0
:
:
:
:
:
:
:
:
Model Formulation
![Page 15: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/15.jpg)
32105 : g
32107 : g
1.0 1.5 2.0 2.5 3.0 3.5 4.0
8.2
8.4
8.6
8.8
9.0
dose
ge
ne
exp
ressio
n
32107 : g
32105 : g
•We fitted two monotone models:
Equality constraints are replaced with a single parameter.
Model Formulation
![Page 16: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/16.jpg)
Bayesian Variable Selection Method
ijKjKjjjij xxxxY 1322110
Alternative approach,
Where X is a design matrix with ordered columns, reflecting the direction of the monotone constraints
0l
2,0~ Nij
![Page 17: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/17.jpg)
2,~ iij NY
01
0
i
i
),0(,~ 2 IN
32103
2102
101
0
d
d
d
c
dose mean
2
0 ,~ N
•Alternative approach •For a dose-response experiment with 4 dose levels (control + 3 doses):
Ki ,...,0 10
Bayesian Variable Selection Method
![Page 18: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/18.jpg)
•Simple order alternative.
32107
32106
32105
32104
32103
32102
32101
32100
:
:
:
:
:
:
:
:
g
g
g
g
g
g
g
g
0 ;0 ;0:
0 ;0 ;0:
0 ;0 ;0:
0 ;0 ;0:
0 ;0 ;0:
0 ;0 ;0:
0 ;0 ;0:
0 ;0 ;0:
3217
3216
3215
3214
3213
3212
3211
3210
g
g
g
g
g
g
g
g
Bayesian Variable Selection Method
![Page 19: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/19.jpg)
i
i
iz
0
1
•The mean structure:
included in the model
not Included in the model
i
i
1
0
•Bayesian Variable Selection: a procedure of deciding which of the model parameters is equal to zero. •Define an indicator variable:
Bayesian Variable Selection Method
![Page 20: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/20.jpg)
K
i
iii z1
0
K
K
r Sg ,...,,: 10
1
),0(,~ 2 INi
)(~ ii Bz
)1,0(~ Ui
2
0 ,~ N
•The mean structure for a candidate model:
Order restrictions Variable selection
Bayesian Variable Selection Method
![Page 21: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/21.jpg)
1.0 1.5 2.0 2.5 3.0 3.5 4.0
8.2
8.4
8.6
8.8
9.0
dose
ge
ne
exp
ressio
n
g_7
g_5
BVS
g7
g5
BVS
Bayesian Variable Selection Method
![Page 22: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/22.jpg)
Inference for Monotone Genes
![Page 23: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/23.jpg)
101
100
:
:
H
H
• suppose we want to identify genes with differential
expression between the control dose and the first dose.
Comparisons Between Two Doses/Groups
![Page 24: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/24.jpg)
);( );( );( 22
00
2
- NNNm
• Inference is based on the posterior probabilities for each to belong to the non-differential components
• Down regulated component
• Non differential component
• Up regulated component
0
00
0
Comparisons Between Two Doses/Groups
![Page 25: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/25.jpg)
• Inference is based on the posterior probabilities for each gene to belong to the non-differential component
• The posterior probabilities could be treated like p-values
• The differentially expressed would be expected to have very
low probability if belonging the null component
),|( 10 HHpp mm
Comparisons Between Two Doses/Groups
![Page 26: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/26.jpg)
• Inference is based on the posterior probabilities for each gene to belong to the non-differential component
• The posterior probabilities could be treated like p-values
• The differentially expressed would be expected to have very
low probability if belonging the null component
),|( 10 HHpp mm
Inference for Monotone Genes
![Page 27: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/27.jpg)
• We assumed a gene specific model for the present
approach
Inference for Monotone Genes
K
K
H
H
,...,:
,...,:
101
100
![Page 28: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/28.jpg)
R
r
rgij gNy0
2 );(
• Inference is based on the posterior probabilities for each to belong to the non-differential components
• Where R=7 and
32107
32101
32100
g
g
g
Inference for Monotone Genes
![Page 29: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/29.jpg)
• We need the posterior probabilities for each gene to belong to the null model
),,|( 2
0 rij gygpp
Inference for Monotone Genes
![Page 30: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/30.jpg)
• Which is equivalent to the posterior probabilities of flat
profile in the Bayesian variable selection approach.
),,|( 2
0 rij gygpp
Inference for Monotone Genes
),,|0,,( 2
0321 ijyδδδp
![Page 31: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/31.jpg)
K
i
iii z1
0
K
K
r Sg ,...,,: 10
1
),0(,~ 2 INi
)(~ ii Bz
)1,0(~ Ui
2
0 ,~ N
•The mean structure for a candidate model:
Order restrictions Variable selection
Inference for Monotone Genes
![Page 32: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/32.jpg)
32107
32106
32105
32104
32103
32102
32101
32100
:
:
:
:
:
:
:
:
g
g
g
g
g
g
g
g
)1,1,1(
)0,1,1(
)1,1,0(
)1,0,1(
)0,1,0(
)0,0,1(
)1,0,0(
)0,0,0(
z
z
z
z
z
z
z
z
•4 dose levels. •The triplet defines uniquely all candidate models: ),,( 321 zzzz
The set of off possible monotone models for an experiment with 4 dose levels
Inference for Monotone Genes
![Page 33: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/33.jpg)
),|(),|)0,0,0(( 0 RdatagpRdatazp
3210
1
0
K
i
iii z
),,|)0,0,0(( 2
0321 ijyzzzzp
•The posterior probability that the triplet equal to zero: )0,0,0(z
Inference for Monotone Genes
![Page 34: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/34.jpg)
514.0),|( 0 Rdatagp
g0 g3 g2 g6 g1 g4 g5 g7
0.0
0.1
0.2
0.3
0.4
0.5
•The highest posterior probability is obtained for the null model
(0.514).
Inference for Monotone Genes
![Page 35: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/35.jpg)
4186.0),|( 5 Rdatagp
001.0),|( 0 Rdatagp
g0 g3 g2 g6 g1 g4 g5 g7
0.0
0.1
0.2
0.3
0.4
4059.0),|( 1 Rdatagp
•The highest posterior probability is obtained for model g5.
•Data do not support the null model.
Inference for Monotone Genes
![Page 36: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/36.jpg)
Multiplicity Adjustment
![Page 37: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/37.jpg)
)(
)()(
N
cFDcFDR
•Choose τ such that
Multiplicity Adjustment
![Page 38: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/38.jpg)
),|( 0 Rdatagpmgene m is included in the discovery list
),|( 0 Rdatagpmthe posterior probability of the null model = the probability that we make a mistake when we include the gene in the discovery list.
)(
)()(
N
cFDcFDR
the false discovery rate for a discovery list in which the g’th gene and all other genes with smallest posterior probabilities of the null model are included (Newton 2004,2007).
Multiplicity Adjustment
![Page 39: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/39.jpg)
),|(0
),|(1
0
0
Rdatagp
RdatagpI
m
m
m
)(N
gene m is included in the discovery list
gene m is not included in the discovery list
The number of genes in the discovery list.
M
m
mIN1
)(
•Primary interest: discovery of subset of genes with monotone relationship with respect to dose.
Multiplicity Adjustment
![Page 40: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/40.jpg)
)(),|()(1
0 cFDIRdatagpFDEM
m
mm
)(
)()(
N
cFDcFDR
•The conditional (on the data) expected number of false discoveries (in the discovery list):
•The conditional false discovery rate:
•Choose τ such that .)( cFDR
Multiplicity Adjustment
![Page 41: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/41.jpg)
%5
3295
,,|
)102.0(
0
Rdatazgp
cFDR
g
The expected error rate for the list with all genes for which the posterior probability of the null model < 0.102 are included.
τ
Multiplicity Adjustment
![Page 42: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/42.jpg)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
Cut-off
FD
R
TRUE FDR
Estmated FDR
Multiplicity Adjustment
• From Simulation Study
![Page 43: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/43.jpg)
• BVS methods: estimation and inference.
• Multiplicity adjustment is based on the posterior probability of the null model.
• Connection between BVS and MCT.
• Connection between BVS and Bayesian model averaging.
• BVS for order restricted but non-monotone alternatives (umbrella alternatives/partial order alternatives).
• Posterior probabilities for the number of levels and the level probabilities for isotonic regressions.
Discussion
![Page 44: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/44.jpg)
Current Work: Bayesian Isotonic Transformation
• Motivated by Dunson and Neelon (2003)
• Generate posterior samples from unconstrained full conditional distributions
for the model parameters
• Obtain constrained samples through isotonic transformation of the
unconstrained samples.
![Page 45: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/45.jpg)
Current Work: Bayesian Isotonic Regression
• Examples
![Page 46: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/46.jpg)
Current Work: Bayesian Isotonic Regression
• Bayes factor for model selection
• The Bayes factor account for the fact that the model not equally like under the
null model
![Page 47: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/47.jpg)
Current Work: Bayesian Isotonic Regression
• Probability under the null model
• The probability under the null model is equivalent to to level probability in
ORIC (Anraku, 1999)
![Page 48: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/48.jpg)
Current Work: Bayesian Isotonic Regression
• The Bayesian isotonic transformation approach provide good estimates of dose-
specific means under simple ordered constraints
• However, adjusting for multiplicity is less straight forward for this approach.
![Page 49: Analysis of dose-response microarray data using Bayesian ...Analysis of dose-response microarray data using Bayesian Variable Selection (BVS) methods: Modeling and multiplicity adjustments](https://reader034.fdocuments.us/reader034/viewer/2022050417/5f8d19e56147744b543d2a0c/html5/thumbnails/49.jpg)
Research Team
• Ziv Shkedy.
• Luc Bijnens.
• Willem Talloen.
• Hinrich Gohlmann.
• Dhammika Amaratunga
Hasselt University, Belgium Johnson & Johnson Pharmaceutical
Durham University, UK
• Adetayo Kasim.
Imperial College, UK
• Bernet Kato.
pfizer, Belgium
• Dan Lin