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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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High Dimensional Surrogacy: A JointModeling Approach
Rudradev Sengupta
October 4, 2018
Research Team
Affiliation Collaborators
Interuniversity Institute for Biostatistics and StatisticalBioinformatics (I-BioStat), Belgium
Ariel Alonso Abad, GeertMolenberghs, Ziv Shkedy.
Janssen Pharmaceutical Companies of Johnson &Johnson, Beerse, Belgium
Luc Bijnens, Nolen JoyPerualila-Tan, Wim Van derElst.
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
4 / 64
Overview
1 Introduction
2 Case Studies and Modeling Approaches
3 High Dimensional Surrogacy and Biomarker Detection
4 Conclusion
5 / 64
Clinical Trials
Very slow, costly and inefficient development process.The choice of endpoint(s), to assess the drug efficacy,plays an important role.Measuring the endpoint(s) can become difficult, timeconsuming and expensive.Surrogacy in clinical trials.
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“Surrogate” and “True” Endpoint in Clinical Trials
A “true” endpoint can be a response or a clinical outcomeor time to event etc.A “surrogate” endpoint serves as a substitute for the “true”endpoint as it can usually be measured more cheaply andconveniently.Before using a surrogate as a substitute for the trueendpoint it should be validated.Statistical methods for the identification and evaluation ofsurrogate endpoints in randomized clinical trials have beendeveloped over last three decades.
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Biomarkers in Clinical Trials
A biomarker is objectively measured and evaluatedindicator of normal biological or pathogenic processes orpharmacologic responses to a therapeutic intervention.A surrogate marker is a biomarker intended to substitute aclinical endpoint.All surrogate markers are biomarkers, but not allbiomarkers can qualify as surrogate markers.
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Biomarkers in Drug Discovery Experiments
Understanding the mechanism of action of a newcompound.Integrating multiple data sources.High dimensional data.
I High dimensional surrogacy.
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The Surrogacy Framework: Graphical Illustration
X
Y
Z
The surrogacy framework for two endpoints, X and Y .The variable Z represents a binary grouping variable.The association between the biomarker (X ) and the clinicalendpoint (Y ) after adjusting for the grouping variable (Z ).
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Three Decades of Surrogacy
1989: Prentice
Surrogate endpoints in clinical trials
1998: Buyse and Molenberghs
Individual Level Surrogacy
2000: Buyse et al.
Trial Level Surrogacy
2005: Burzykowski et al. Evaluation of Surrogate Endpoints
2007: Alonso and Molenberghs
Information Theory Approach
2016: Alonso et al.
Applied Surrogate Endpint Evaluation with SAS and R
2016: Perualila et al.
Joint Model
2010: Lin et al.
Biomarkers in pre-clinical and clinical microarray experiments
2012: Van Sanden et al.
Genomic biomarkers in microarray experiments
2015: Verbist et al.
Lessons learned from the qstar project.
Clinical Trials
High Dimensional DataNon-clinical Trials
2018: Sengupta et al.
1992: Freedman et al.
Statistical Validation of Intermediate Endpoints
Main focus: different approaches to evaluate individual level surrogacy.
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker Detection
4 Conclusion
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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QSTAR Framework
Data integration in drug discovery.Why is QSTAR important?
Compound
target
Biological processes
Known: the chemical structure of the new compound. Unknown: targets & biological process. The main idea: Information about gene expression will help to understand the biological processes related to the new compound (i.e. understanding the mechanism of action).
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QSTAR Data Structure
An indicator variable for the k th fingerprint feature (FF) and i thcompound,
Zki =
{1, if the k th FF is present in the i th compound,0, otherwise.
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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transPAT Data
PAT - Pulsed Antibiotic Treatment model of pediatric exposures.
Hypothesis: A series of short, therapeutic-dose pulses ofantibiotic administered early in life will perturb the intestinalmicrobiota and lead to long-lasting alterations in metabolic andimmune profiles.
Exactly same data structure.
“Donor” Mouse “Donor” Mouse
Germ-free mice (n=7) Germ-free mice (n=8)
Microbiota Transfer
Pulsed Antibiotic (Tylosin) Treatment
Normal Microbiota Development
PAT-altered Microbiota (loss of some early-life protective bacteria)
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transPAT Data Structure
intervention variable
Similar setting as beforewith three different datasources.Main goal:
The associationbetween microbiomeand immunity taking theintervention intoaccount).Development of modelsto identify microbiomebiomarkers.
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CERTIFI Case Study
A phase II study.Explores association between the fecal microbiota and itsrole in therapeutic response of Chron’s disease.Patients are treated with ustekinumab (UST; Stelara).Brings back to the biomarker framework.Talk by Dea Putri - Session 6a, 16:35 - 16:55).
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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Model Formulation
1989: Prentice
Surrogate endpoints in clinical trials
1998: Buyse and Molenberghs
Individual Level Surrogacy
2000: Buyse et al.
Trial Level Surrogacy
2005: Burzykowski et al. Evaluation of Surrogate Endpoints
2007: Alonso and Molenberghs
Information Theory Approach
2016: Alonso et al.
Applied Surrogate Endpint Evaluation with SAS and R
2016: Perualila et al.
Joint Model
2010: Lin et al.
Biomarkers in pre-clinical and clinical microarray experiments
2012: Van Sanden et al.
Genomic biomarkers in microarray experiments
2015: Verbist et al.
Lessons learned from the qstar project.
Clinical Trials
High Dimensional DataNon-clinical Trials
2018: Sengupta et al.
1992: Freedman et al.
Statistical Validation of Intermediate Endpoints
Xj
Y
Z ρj
α j
β
αj : fingerprint effect on the j th gene.
ρj : fingerprint-adjusted associationbetween the gene expression andbioactivity data.
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Joint Model: Estimation and Inference
Estimation:(XjiYi
)∼ N
[(µj + αjZiµY + βZi
),Σj
],
Σj =
(σjj σjYσjY σYY
)and ρjk =
σjY√σjjσYY
.
Inference:H0j : αjk = 0,H1j : αjk 6= 0.
H0j : ρjk = 0,H1j : ρjk 6= 0.
Gene-specific analysis, per fingerprint feature.BH-FDR multiplicity adjustment is done.
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Overview
1 Introduction
2 Case Studies and Modeling Approaches
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy MeasuresComputational Aspects
4 Conclusion
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High Dimensional Surrogacy
Computational solutions for an upscaled analysis.Surrogacy setting with multiple candidates that can serveas biomarkers.
Application of the Joint Model within a High Dimensional Setting
- Single Surrogacy - Multiple Surrogacy - Partial Surrogacy - Orthogonal Surrogacy
Modeling Aspects
Computational Aspects
- Optimized Implementation with R
- Parallel computing using computer cluster
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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Example - EGFR Project
Biomarkers (X): A 3595 × 35 transcriptomics matrix.
Primary endpoint (Y): The bioassay measurements (i.e. the pIC50
values) is a vector of length 35.
Z: A 138 × 35 binary grouping variable.
Per fingerprint feature, there are 3595 models to be fitted.
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Example of One Gene (FOSL1)
X
X
X
ρ=−0.76
Computation time toanalyze onefingerprint and all3595 genes ∼ 377seconds (in laptop).Fingerprint effect ongene experession.Negativeassociation.
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Top 5 Differentially Expressed Genes with HighAdjusted Correlation
Verbist et al. (2015) linked cell growth activity with downregulation ofgenes FOSL1 and FGFBP1 for a particular chemical feature.
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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Single Surrogacy
Xj
Y
Z ρj
Models to identify one biomarkerat a time.
Reduction in computation time tofind one biomarker.
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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Multiple Surrogacy: Introduction
Once a primary biomarker is known,can we add something more in thecontext of surrogacy?
A subset of k genes is used as abiomarker - multiple adjustedassociation replaces single surrogacy.
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Multiple Surrogacy: Model Formulation (I)
Considers a subset of k genes that can be used as a jointsurrogate for pIC50.Example: genes in the same biological pathway that wasfound by the joint model.Van der Elst et al. (2018) extended the joint model,
Xi1Xi2...
XikYi
∼ N
µ1 + α1Ziµ2 + α2Zi
...µk + αkZiµY + βZi
,Σ
.
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Multiple Surrogacy: Model Formulation (II)
Σk =
σ11 σ12 . . . σ1k σ1yσ21 σ22 . . . σ2k σ2y
......
. . ....
...σk1 σk2 . . . σkk σkyσy1 σy2 . . . σyk σyy
Adjusted correlation between two biomarkers:
ρij =σij√σiiσjj
.
Adjusted correlation between the j th biomarker and theresponse, pIC50
ρyj =σyj√σyyσjj
.
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Multiple Surrogacy: Model Formulation (III)
The covariance matrix:
Σk =
(ΣX ,X Σ
′
X ,YΣX ,Y σY ,Y
).
Multivariate adjusted association:
γ2 = ρ2Y ,X1,X2,...,Xk
=ΣX ,Y Σ−1
X ,X Σ′
X ,Y
σY ,Y.
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Gene FOSL1
FOSL1 is used as a known primary biomarker.
X
X
X
ρ=−0.76
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EGFR Project: Illustration when K=2
Joint model: FOSL1i1Xi2Yi
∼ N
µFOSL1 + αFOSL1Ziµ2 + α2ZiµY + βZi
,Σ
.γ2 = ρ2
Y ,FOSL1,X2= joint surrogacy value of X2 and FOSL1.
ρY ,FOSL1 and ρY ,X2 are the marginal surrogacy values forFOSL1 and X2, respectively.Gain in surrogacy = ρ2
Y ,FOSL1,X2- ρ2
Y ,FOSL1.
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EGFR Project: Multiple Surrogacy
Top 5 genes, sorted according to their multiple adjustedassociation, when used together with FOSL1:
Genes ρY ,X2 ρ2Y ,FOSL1,X2
Gain in Surrogacy ValueMPHOSPH9 -0.26 0.69 0.11TOP2A -0.35 0.69 0.11MYO6 0.73 0.68 0.10PNISR 0.76 0.68 0.10EREG -0.60 0.67 0.09
ρ2Y ,FOSL1 = 0.58.
Gain in surrogacy = ρ2Y ,FOSL1,X2
- 0.58.
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Top Genes
Density of multipleadjusted association forthe remaining genes,given FOSL1:Multiple Adjusted Association for the remaining genes|FOSL1
ρY,FOSL1,X2
2
Density
0.58 0.60 0.62 0.64 0.66 0.68 0.70
020
40
60
80
MPHOSPH9
TOP2A
MYO6
PNISR
EREG
KRT10
Example of the top gene,MPHOSPH9:
ρY ,MPHOSPH9 = -0.26.ρ2
Y ,MPHOSPH9,FOSL1 = 0.69.
pIC50
−1.5 −0.5 0.5 1.0 1.5
−1
.0−
0.5
0.0
0.5
1.0
−1
.5−
0.5
0.5
1.0
1.5
−0.76 FOSL1
−1.0 −0.5 0.0 0.5 1.0
−0.26 0.66
−0.15 −0.05 0.05 0.15
−0
.15
−0
.05
0.0
50
.15
MPHOSPH9
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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Partial Surrogacy (I)
X1
Y
Z X2
ρY,X
1 ρX1,X2
ρY ,X2
Adjusted association between Y and X1: ρY ,X1|Z .Adjusted association between Y and X2: ρY ,X2|Z .Adjusted association between X1 and X2: ρX1,X2|Z .
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Partial Surrogacy (II)
partial surrogacy effect : surrogacy value of X2, given X1and Z .For k = 2, the covariance matrix:
Σ =
σ11 σ12 σ1yσ21 σ22 σ2yσy1 σy2 σyy
.Partial adjusted association:
ρY ,X2|X1,Z = ρY ,X2|X1 =ρy2 − ρy1ρ12√
(1− ρ2y1)(1− ρ2
12).
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Graphical Illustration: Partial Surrogacy (I)
Low correlation between all three variables.Low partial adjusted correlation between Y and X2, givenX1.
Y
−1 0 1 2
−1
01
2
−1
01
2
0.19 X1
−1 0 1 2
0.0023 0.19
−2 −1 0 1 2
−2
−1
01
2
X2
ρY,X2|X1= − 0.0396
−1
0
1
2
−2 −1 0 1 2
Residuals: X2*
Resid
uals
: Y
*
FP: 0 − absent 1 − present
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Graphical Illustration: Partial Surrogacy (II)
Three correlated variables.Low partial adjusted correlation between Y and X2, givenX1.
Y
−1.5 −0.5 0.5 1.0 1.5
−2.
0−
1.0
0.0
0.5
1.0
−1.
5−
0.5
0.5
1.0
1.5
0.87 X1
−2.0 −1.0 0.0 0.5 1.0
0.85 0.98
−1 0 1 2
−1
01
2
X2
ρY,X2|X1= − 0.0028
−0.5
0.0
0.5
1.0
−0.2 0.0 0.2
Residuals: X2*
Resid
uals
: Y
*
FP: 0 − absent 1 − present
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Graphical Illustration: Partial Surrogacy (III)
Three correlated variables.Relatively high partial adjusted correlation between Y andX2, given X1.
Y
−2 −1 0 1 2
−1
01
2
−2
−1
01
2
0.82 X1
−1 0 1 2
0.67 0.54
−2 −1 0 1 2
−2
−1
01
2
X2
ρY,X2|X1= 0.4587
−0.5
0.0
0.5
1.0
1.5
−1 0 1
Residuals: X2*
Resid
uals
: Y
*
FP: 0 − absent 1 − present
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EGFR Project: Partial Surrogacy (I)
Density of partial correlationfor all the genes, excludingFOSL1:
Partial Correlation for the remaining genes|FOSL1
ρY,X2 | FOSL1
Density
−0.4 −0.2 0.0 0.2 0.4 0.6
0.0
0.5
1.0
1.5
2.0
2.5
MPHOSPH9
TOP2A
MYO6
PNISR
EREG
TCIRG1
MYC
Top 5 genes:
Genes ρY ,X2 ρY ,X2|FOSL1
MPHOSPH9 -0.26 0.51TOP2A -0.35 0.51MYO6 0.73 0.49PNISR 0.76 0.48EREG -0.60 0.47
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Gene TCIRG1
●●●●
●
●
●●●● ●●●●●● ●● ●
●
●
●●
●●
●
●
●
●
●
●
●●
●●
TCIRG1,Observed:−442307337
9.5 9.6 9.74.5
5.0
5.5
6.0
6.5
7.0
Gene Expression
pIC
50Unadj. Asso. −0.3569
●
●
●
●●
●
●●●● ●●●●●● ●● ●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
TCIRG1,Residuals:−442307337
−0.1 0.0 0.1
−1.0
−0.5
0.0
0.5
1.0
Gene Expression
pIC
50
FP: ● ●Absent Present
Adj. Asso. −0.3476
Negatively associatedwith pIC50.ρY ,TCIRG1 = −0.35.
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EGFR Project: Partial Surrogacy (II)
Three correlated variables.Zero partial adjusted correlation between pIC50 andTCIRG1, given FOSL1.
pIC50
−1.5 −0.5 0.5 1.0 1.5
−1.0
−0.5
0.0
0.5
1.0
−1.5
−0.5
0.5
1.0
1.5
−0.76 FOSL1
−1.0 −0.5 0.0 0.5 1.0
−0.35 0.46
−0.15 −0.05 0.05
−0.1
5−
0.0
50.0
5
TCIRG1
ρpIC50,TCIRG1|FOSL1 = 0
−0.5
0.0
0.5
1.0
−0.10 −0.05 0.00 0.05
Residuals: TCIRG1*
Resid
uals
: pIC
50
*
FP: 0 − absent 1 − present
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
49 / 64
Orthogonal Surrogacy: Introduction
X1
Y
Z X2
ρY,X
1
ρY ,X2
Adjusted association between Y and X1: ρYX1|Z .Adjusted association Y and X2: ρYX2|Z .X1 and X2 are conditionally independent: ρX1X2|Z = 0.High partial surrogacy: ρYX2|X1,Z .
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Orthogonal Surrogacy
Σ =
σ11 0 σ1y0 σ22 σ2yσy1 σy2 σyy
and P =
ρ11 0 ρ1y0 ρ22 ρ2yρy1 ρy2 ρyy
It is a special case of partial surrogacy.X1 and X2 are uncorrelated but both are correlated with Y .High partial adjusted association between X2 and Y sinceX1 does not explain the variation of X2.
ρY ,X2|X1,Z = ρY ,X2|X1 =ρy2√
(1− ρ2y1)
Inference:H0 : σ12 = 0,H1 : σ12 6= 0.
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Graphical Illustration: Orthogonal Surrogacy
X1 and X2 are independent.High adjusted partial correlation between Y and X2, givenX1.
Y
−3 −2 −1 0 1 2
−2
−1
01
2
−3
−2
−1
01
2
0.71 X1
−2 −1 0 1 2
0.58 −0.14
−3 −2 −1 0 1 2
−3
−2
−1
01
2
X2
ρY,X2|X1= 0.9677
−2
−1
0
1
2
−3 −2 −1 0 1 2
Residuals: X2*
Resid
uals
: Y
*
FP: 0 − absent 1 − present
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Overview
1 Introduction
2 Case Studies and Modeling ApproachesQSTAR ProjectMicrobiome ProjectJoint Modeling Approach
3 High Dimensional Surrogacy and Biomarker DetectionSingle Surrogacy for High Dimensional DataDifferent Surrogacy Measures
Multiple SurrogacyPartial SurrogacyOrthogonal Surrogacy
Computational Aspects
4 Conclusion
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Computational Issues
Computation time for one fingerprint feature ∼ 377seconds.R code with loop over all genes.For all fingerprint features and all genes: a loop over allgenes, nested within a loop over all fingerprint features -takes around 14.45 hours.
Main Question: How to have faster implementation when wehave more data and do further analysis to utilize all the data ?
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Code Structure
Loop over genes.For each gene:
gls() - joint model.Summarize and combine results from the model.
Summarize and combine results for all the genes.Computation time for all genes and all fingerprint features∼ 14.45 hours.
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Distribution of Computational Time for Joint Model
All the functions used for the analysis fall into three groups:
gls(),anova() & summary() functions andall other functions e.g., data.frame() and cor().
gls anova + summary others
Functions
% o
f Tota
l C
om
puta
tional T
ime
020
40
60
80
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Parallelization for the Joint Model
Using R packages:foreach package - foreach().parallel package - clusterApply(),clusterApplyLB().
Using worker framework:It is a “master-slave” framework.Master: divides the bigger and more complex main probleminto smaller subproblems and supplies them to the slaves.Slaves: finish the computations and return the results backto the master and check for the next jobs assigned to them,if any.A user-specific parallelization framework in a cluster.Requires small tweaks, e.g., additional files, restructuringthe code etc., to run the code.
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Upscaling the Analysis for EGFR Project
Computational time for complete analysis with for loopover genes and fingerprint features ∼ 14.45 hours.With the worker framework:
With one master and 138 workers and each worker with afor loop over 3595 genes for one of the 138 fingerprintfeatures = 259.35 seconds.With 880 cores and 190 genes per core = 97.64 seconds,
67 seconds to fit the models and 30.64 to gather the resultsfrom different cores and combine them.880139 = 6.33 times more cores.259.3597.64 = 2.66 times speedup.
Sengupta et al. (2018) - accepted in Journal ofBiopharmaceutical Statistics.
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Density of Adjusted Correlation
All fingerprint features for one gene (FGFBP1):
−0.85 −0.80 −0.75
010
20
30
40
Gene FGFBP1
Estimated adjusted correlation (ρ̂)
Density
−442307337
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Gene FGFBP1 for a Particular Fingerprint Feature(-1592278635)
α̂ = 1.24239.
−2 −1 0 1 2
0.0
0.2
0.4
0.6
0.8
Gene FGFBP1
Estimated fingerprint effect on gene expression (α̂)
Density
−1592278635
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Overview
1 Introduction
2 Case Studies and Modeling Approaches
3 High Dimensional Surrogacy and Biomarker Detection
4 Conclusion
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Summary (I)
Biomarker
Clinical Endpoint
Treatment
For drug discovery often some biomarkers are known.Partial and orthogonal surrogacy allow us to evaluate thesurrogacy value of adding possible biomarker(s), fromdifferent sources, to the primary biomarker.
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Summary (II)
Similar approach can be implemented in other experimentsas well,
Joint model to identify microbiome biomarkers (talk by DeaPutri - Session 6a, 16:35 - 16:55).Multiple surrogacy in the context of microbiome data hasbeen studied by Van der Elst et al., 2018.
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