Classification, Dose-response Modelling, and the Evaluation of - - PowerPoint PPT Presentation

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research

Classification, Dose-response Modelling, and the Evaluation of Biomarker in a Microarray Setting

Dan Lin Promoter: Prof. dr. T. Burzykowski Co-promoter: Prof. dr. Z. Shkedy

Diepenbeek March 28, 2008

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research

Outline

1

Introduction to microarrays

2

Contents of the dissertation

3

Focus: dose-response modelling + applications

Test for trend Classification of dose-response curve shapes Ratio test

4

Conclusion & future research

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research

• 1. Introduction

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research What are microarrays all about Microarray technology Analysis of microarray data

Study of Functional Genomics

Genome research

Study of genetic sequences Tools of gene-expression analysis

cDNA microarrays

• ligonucleotide

microarrays SAGE

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research What are microarrays all about Microarray technology Analysis of microarray data

Central Dogma of Molecular Biology

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research What are microarrays all about Microarray technology Analysis of microarray data

Microarray Basics

mRNA quantitation mRNA labeled scan sample apply to Chip process

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research What are microarrays all about Microarray technology Analysis of microarray data

Process of Microarray Data Analysis

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research What are microarrays all about Microarray technology Analysis of microarray data

• 2. Contents of the Dissertation

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part I: Gene selection and class prediction Part II: Significance tests Part III: Dose-response modelling Part IV: Evaluation of biomarkers

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part I: Gene selection and class prediction

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part I: Gene selection and class prediction

Control group Treatment group

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part II: Significance test Case study: human epidermal squamous carcinoma cell lines

Table: Number of arrays in the case study.

EGF (ng/ml) Setting 1 10 100 Control 3 3 3 3 Treatment A 3 3 3 3 Treatment B 3 3 3 3 Treatment C 3 3 3 3

16,998 genes on each array used for analysis

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part II: Significance test (inference and multiplicity)

Multiplicity: comparisons of several treatments with one control

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part II: Significance test (inference and multiplicity)

Multiplicity: comparisons of several treatments with one control

Case Study

EGF (ng/ml) Setting 1 10 100 Control 3 Treatment A 3 Treatment B 3 Treatment C 3

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part II: Significance test (inference and multiplicity)

Multiplicity: comparisons of several treatments with one control Inference: Dunnett t-test and resampling-based procedure Several methods used for adjusting for multiple testing

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part III: Dose-response modelling

Dose-response relationship Minimum-effective-dose (MED)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part III: Dose-response modelling

Dose-response relationship Minimum-effective-dose (MED)

Case Study

EGF (ng/ml) Setting 1 10 100 Control 3 3 3 3 Treatment A Treatment B Treatment C

1 2 3 4 dose gene expression + + + + * * * * 1 10 100

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Contents of the Dissertation

Part IV: Evaluation of biomarkers

Clinical Outcome Biomarkers: Gene Expressions Treatment Z Y Xi

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Too Few or Too Many

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Issues in Analyzing Microarray Data

Multiplicity

Testing thousands of genes simultaneously Control of the Type I error

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Issues in Analyzing Microarray Data

Test Results Hypotheses Accept H0 Reject H0 Total H0 True U V m0 H0 False T S m1 Total W R m

Control of the Type I error

Family-Wise Error Rate: FWER = p(V> 0) False Discovery Rate: FDR = E(Q) (Benjamini and Hochberg 1995) Q = V/R R > 0 R = 0

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Mixed Directional FDR

For one-sided test statistics MD-FDR = E(Q′) (Yekutieli and Benjamini 2005)

Q′ = 0, for R = 0 Q′ = V ′/R, for R > 0, where V ′ is the sum of

results that are false positives results that are true positives but declared with a wrong direction

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Adjusting for Multiplicity

Control of the FWER

Bonferroni procedure Holm’s procedure (1979) maxT (Westfall and Young 1993)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Adjusting for Multiplicity

Control of the FWER

Bonferroni procedure Holm’s procedure (1979) maxT (Westfall and Young 1993)

Control of the FDR

Benjamini and Hochberg procedure (BH-FDR 1999) Benjamini and Yekutieli procedure (BY-FDR 2001) Significance analysis of microarrays (SAM 2001)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Issues in Analyzing Microarray Data

Multiplicity

Testing thousands of genes simultaneously Control the Type I error

Small sample size

Distribution of test statistics can be unknown or asymptotics can not be assumed Resampling-based inference

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Resampling-based Inference

Observed test statistics

tobs =      t1 t2 . . . tm     

Permutation matrix

T perm =      t11 t12 . . . t1B t21 t22 . . . t2B . . . . . . . . . . . . tm1 tm2 . . . tmB     

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Contents Issues in Analysis of Microarray Data

Resampling-based Inference

Based on the joint or marginal null distribution of test statistics approximated from permutations, For gene i, the two-sided p-value:

−2 2 4 6 0.0 0.1 0.2 0.3 0.4

two−side p−value

null distribution Density + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Contents of the Dissertation

Part I: Gene selection and class prediction Part II: Significance tests Part III: Dose-response modelling Part IV: Evaluation of biomarkers

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

• 3. Dose-response Modelling

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Part III: Dose-response Modelling

Find genes with monotone trend Classify dose- response shapes Ratio test u4/u1 Multiple CIs for Ratios

1 2 3 4

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Dose-response relationship

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Dose-response relationship

1 2 3 4 5 dose gene expression

+ + + + * * * *

Gene a: increasing monotonic trend

1 10 100 −1 1 2 3 4 dose gene expression

+ + + + * * * *

Gene b: decreasing monotonic trend

1 10 100 1 2 3 dose gene expression

+ + + +

Gene c: non−monotonic trend

1 10 100 −0.5 0.5 1.5 dose gene expression

+ + + +

Gene d: no dose−response relationship

1 10 100

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

For gene i (i = 1, · · · , m) with K doses (j = 1, · · · , K) H0 : µ1 = µ2 = · · · = µK HUp

1

: µ1 ≤ µ2 ≤ · · · ≤ µK

• r

HDown

1

: µ1 ≥ µ2 ≥ · · · ≥ µK with at least one inequality. Pooled-adjacent-violator-algorithm (PAVA) to obtain estimates of the isotonic means ˆ µ⋆

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an increasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * *

+ + + +

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * * * * * * Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for an decreasing trend

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * *

+ + + + + + + +

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining estimates of the isotonic means ˆ µ⋆ for both directions

0.5 1.0 1.5 2.0 2.5 3.0 3.5 doses gene expression 1 2 3 4

PAVA

* * * *

+ + + + + + + + + + + +

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Test Statistics

LRT: λ =

• ˆ

σ2

H1

ˆ σ2

H0

n/2 (Bartholomew 1959) Direction of trend is unknown in advance In practice, we calculate LRT statistics twice for each direction

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Test Statistics

LRT: λ =

• ˆ

σ2

H1

ˆ σ2

H0

n/2 (Bartholomew 1959) W =

ˆ µ⋆

j −¯

y0 st

(Williams 1971, 1972)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Test Statistics

LRT: λ =

• ˆ

σ2

H1

ˆ σ2

H0

n/2 (Bartholomew 1959) W =

ˆ µ⋆

j −¯

y0 st

(Williams 1971, 1972) W ′ =

ˆ µ⋆

j −ˆ

µ⋆ st

(Marcus 1976)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Test Statistics

M =

ˆ µ⋆

K −ˆ

µ⋆

• jl(yjl−ˆ

µ⋆

j )2/(n−K)

(Hu et al. 2005) M′ =

ˆ µ⋆

K −ˆ

µ⋆

• jl(yjl−ˆ

µ⋆

j )2/(n−J)

where J = unique(ˆ µ⋆) (Lin et al. 2007)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend

Obtaining pUp and pDown using permutations

−2 2 4 6 0.0 0.2 0.4

p^{Up}−value=0.0163

null distribution Density + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + −6 −4 −2 2 4 0.0 0.2 0.4

p^{Down}−value=0.9667

null distribution Density + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Directional Inference

Two-sided p-values p = min(2 × min(pUp, pDown), 1)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Directional Inference

Two-sided p-values p = min(2 × min(pUp, pDown), 1) Determination of the direction

If pUp ≤ α/2, reject H0 and declare HUp

1 ;

If pDown ≤ α/2, reject H0 and declare HDown

1

; If pUp and pDown ≤ α/2, reject H0 and declare a non-monotonic trend.

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend: Application

Case study: data for EGF doses for the control compound Test # sign LRT 3499 W 3209 W’ 3533 M 3562 M’ 3567

5000 10000 15000 0.0 0.2 0.4 0.6 0.8 1.0 index Adjusted p−values E2 Williams Marcus M Modified M maxT Bonf/Holm/FDR−BY FDR−BH

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Testing for Trend: Conclusions

Results:

Five test statistics show a similar number of significant findings maxT gives the smallest number of discoveries

Simulations:

Similar power: LRT, M and modified M Williams’ and Marcus’ tests yield slightly lower power after multiple testing adjustment Williams’ and Marcus’ tests are robust to the presence of genes with non-monotonic trends

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Part III: Dose-response Modelling

Find genes with monotone trend Classify dose- response shapes Ratio test u4/u1 Multiple CIs for Ratios

1 2 3 4

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends

1.0 1.2 1.4 1.6 1.8 2.0 2.2 dose gene expression + + + +

g1

1 10 100 1.0 1.2 1.4 1.6 1.8 2.0 dose gene expression + + + +

g2

1 10 100 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 dose gene expression + + + +

g3

1 10 100 1.0 1.5 2.0 dose gene expression + + + +

g4

1 10 100 0.5 1.0 1.5 2.0 dose gene expression + + + +

g5

1 10 100 0.6 0.8 1.0 1.2 1.4 1.6 1.8 dose gene expression + + + +

g6

1 10 100 0.4 0.6 0.8 1.0 1.2 1.4 1.6 dose gene expression + + + +

g7

1 10 100

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends

Alternatives # parameters MED µ1 = µ2 = µ3 < µ4 2 4 µ1 = µ2 < µ3 = µ4 2 3 µ1 < µ2 = µ3 = µ4 2 2 µ1 < µ2 = µ3 < µ4 3 2 µ1 = µ2 < µ3 < µ4 3 3 µ1 < µ2 < µ3 = µ4 3 2 µ1 < µ2 < µ3 < µ4 4 2 Shapes

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends Using Information Criteria

Akaike information criterion (Akaike 1973, 1974)

AIC = −2logℓ(θ|D) + 2M

Bayesian information criterion (Schwarz 1978)

BIC = −2logℓ(θ|D) + Mlog(n)

Order restricted information criterion (Anraku 1999)

ORIC = −2logℓ(θ|D) +

K

• j=1

jP(j, K, wj)

where P(j, K, wj) denotes the level probability that for given K doses under H0 the isotonic regression will result in j unique isotonic means.

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends Using Information Criteria

Penalty values for the AIC, BIC, and ORIC under seven models:

2 4 6 8 10 models penalty values g1,g2,g3 g4,g5,g6 g7

BIC AIC ORIC Likelihood

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends: Application

Case study: data for EGF doses for the control compound Classification of 3499 genes found significant by LRT

Model Likelihood AIC BIC ORIC g1 344 1528 1648 1348 g2 25 307 369 221 g3 14 106 126 86 g4 343 370 337 253 g5 885 823 715 655 g6 178 170 149 120 g7 1710 195 155 816

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends: Application

Example gene 3467:

4.6 4.8 5.0 5.2 5.4 5.6 Doses Gene expression 1 2 3 4 + + + + + + + + + + + +

Likelihood/ORIC AIC BIC

Gene 3467

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Classification of Trends: Conclusions

Results:

Likelihood always favors more complex models AIC and BIC tend to classify genes with simpler models ORIC penalizes less on complex models

Simulations:

Under simple models, AIC and BIC show low misclassification error Under more complex models, AIC and BIC over-penalize but are still robust

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Part III: Dose-response Modelling

Find genes with monotone trend Classify dose- response shapes Ratio test u4/u1 Multiple CIs for Ratios

1 2 3 4

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

Given µ1 ≤ µ2 ≤ . . . , ≤ µK

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

Given µ1 ≤ µ2 ≤ . . . , ≤ µK

Difference: ˆ ∆a = 1 and ˆ ∆b = 1.8 Ratio: ˆ γa = 1.3 and ˆ γb = 1.3

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

For γ0 = 1 + δ, we test H∗U : µ4/µ1 ≤ γ0 vs. H∗U

1

: µ4/µ1 > γ0 Equivalent to test H

′U

: γ0µ4 − µ1 ≤ 0 vs. H

′U

: γ0µ4 − µ1 > 0 Test statistics for ratio tγ = γ0ˆ µ∗

4 − ˆ

µ∗

1

sγ Obtain ˆ µ∗ from sample means ¯ y

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

Representation of isotonic means (ˆ µ⋆)

ˆ µ⋆

i = max1≤u≤imini≤v≤K

v

i=u ni ¯

yi v

i=u ni

, i = 1, . . . , K

Isotonic mean difference

ˆ µ⋆

K − ˆ

µ⋆

1

= max

• 1, max0≤i,j≤K
• nj¯

yj + ... + nk ¯ yK nj + ... + nK − n1¯ y1 + ... + ni ¯ yi n1 + ... + ni

• =

max(C¯ y)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

Contrast matrix C for the test of difference µ4 − µ1

• 4

3 2 1 17 4 3 2 1 16 4 3 2 1 15 4 3 2 1 14 4 3 2 1 13 4 3 2 1 12 4 3 2 1 11

: : : : : : : 1 1 1 1 1 3 / 1 3 / 1 3 / 1 1 2 / 1 2 / 1 3 / 1 3 / 1 3 / 1 1 2 / 1 2 / 1 1 1 1 es Alternativ matrix Contrast

• H

H H H H H H C

Test statistic for µ4 − µ1 is equal to max (C¯ y)

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

Contrast matrix C for the test of difference µ4 − µ1

C =        −1 1 −1 1/2 1/2 −1 1/3 1/3 1/3 −1/2 −1/2 1 −1/3 −1/3 −1/3 1 −1 −1 1 1       

Contrast matrix for the test of ratio µ4/µ1

C =        1 1/2 1/2 1/3 1/3 1/3 1 1 1 1        −        1 1 1 1/2 1/2 1/3 1/3 1/3 1 1        = CNum − CDen

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test

Ratio test statistics:

tγ = γ0 ˆ µ∗

4 − ˆ

µ∗

1

sγ = max

• γ0CNum − CDen

¯ y

• Sγ

= max (t1, . . . , tℓ, . . . , tr ) where tℓ =

• γ0cNum

ℓ

−cDen

ℓ

• ¯

y

sℓ

, ℓ = 1, . . . , r.

Multiple ratio test statistics t = (t1, t2, . . . , tr)′ ∼ MVT with correlation matrix R

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test: Application

Case study: data for EGF doses for the control compound Genes found significant by the ratio test

Declare δ H∗U

1

H∗D

1

2879 3387 0.05 934 968 0.1 429 330 0.15 247 133 0.2 142 66

2 4 6 8 10 12 dose gene expression

+ + + + * * * *

1 2 3 4

gene a: +0.2

2 4 6 8 10 12 dose gene expression

+ + + + * * * *

1 2 3 4

gene b: +0.2

2 4 6 8 10 12 dose gene expression

+ + + + * * * *

1 2 3 4

gene c: +0.1

2 4 6 8 10 12 dose gene expression

+ + + + * * * *

1 2 3 4

gene d: +0.1

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Testing for Trend Classification of Trends Ratio Test

Ratio Test: Conclusion

Equivalent to Marcus’ test Genes tested significant with a larger margin are more interesting MCT can be used to classify dose-response curve shapes

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

• 4. Concluding Remarks

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Part III: Dose-response Modelling

Find genes with monotone trend Classify dose- response shapes Ratio test u4/u1 Multiple CIs for Ratios

1 2 3 4

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Discussion

Test for trend:

Order restricted directional inference Future research: distribution of M and modified M

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Discussion

Test for trend:

Order restricted directional inference Future research: distribution of M and modified M

Classification of trends

Information criteria Future research: classification of trends without the initial testing step

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Discussion

Ratio test:

Efficient use of MCT and parametric inference Future research:

MCT for M and modified M tests Comparison of classification of trends vs. MCT

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Part III: Dose-response Modelling

Find genes with monotone trend Classify dose- response shapes Ratio test u4/u1 Multiple CIs for Ratios

1 2 3 4

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Future Research

Target sensitivity: how dose-response relationship differs across treatments Table

EGF (ng/ml) Setting 1 10 100 Control 3 3 3 3 Treatment A 3 3 3 3 Treatment B 3 3 3 3 Treatment C 3 3 3 3

Two-way ANOVA model under order restriction Inference: test statistics

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Concluding Remarks

Small sample issue needs the use of resampling-based procedures Multiplicity adjustment in the form of the control of the FDR and FCR

Between-gene and within-gene comparisons Multiple CIs after selection

... Biological confirmation

Dan Lin Analysis of Microarray Data

Introduction to Microarrays Contents of the Dissertation Dose-response Modelling Concluding Remarks and Future Research Discussion and Future Research Final Remarks

Thank you for your attention!

Dan Lin Analysis of Microarray Data