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Title: Evaluation of Surrogate Markers in Early Drug Development Microarray Experiments


1
Evaluation of Surrogate Markers in Early Drug
Development Microarray Experiments
ISCB 28 Greece, 28 July- 2 August, 2007
  • Magdalena Murawska, Ziv Shkedy
  • Maria Sklodowska Curie Memorial Cancer Center
    and Institute of Oncology
  • Hasselt University

2
OVERVIEW
  • Introduction
  • Definition of surrogate endpoint in clinical
    trials
  • The setting
  • Data description, objective of the study
  • Methods
  • Two types of genes
  • Measures for surrogacy
  • Joint surrogacy
  • Gene Selection
  • Data Reduction
  • Evaluation
  • Results
  • Discussion

3
Definition of Surrogate Endpoint in clinical
trials
Let T and S be the true and the surrogate
endpoint, respectively. We will call S a good
surrogate for T at individual level, if a large
amount of uncertainty about T, measured by
entropy based parameters, is reduced when S is
known, or equivalently, if the lack of knowledge
about the true endpoint is significantly REDUCED
when the surrogate endpoint is known. Alonso
Molenberghs (2006) surrogate marker validation
from an information theory perspective
4
Introduction the setting
response
Gene expression data
  • Microarray data (n samples and m genes) X
  • A response variable Y
  • Treatment Z
  • We wish to select a subset of k genes which can
    be used as a biomarkers for the response

Two treatment groups
5
Data description, objective of the study
  • 24 rats were randomized into 2 treatment groups
    (active drug and control).
  • The response of primary interest is the distance
    traveled during the behavioral experiment
  • Sample taken from each rat and a microarray with
    5644 genes from the thalamus part of the brain
  • The active drug was expected to increase the
    distance traveled
  • Objective find a gene profile
  • (group of genes) for the subject,
  • which allows to predict
  • the response for this subject

6
Relationship Between Gene Expression and the
Response (Type I gene)
(a)
(b)
  • Linear association between the gene expression
    and the response (a)
  • The association remains linear after adjusting
    for treatment effect (b)
  • The gene is NOT differentially expressed

response
gene expression
7
Relationship Between Gene Expression and the
Response (Type I/II gene)
(a)
(b)
  • Linear association between the gene expression
    and the response (a)
  • The association remains linear after adjusting
    for treatment effect (b)
  • The gene expression and the response are
    differentially expressed

response
gene expression
8
Relationship Between Gene Expression and the
Response (Type II gene)
  • Two clouds of points, one for each treatment
    group
  • No linear association between the gene expression
    and the response (a)
  • Nonlinearity remains after adjsustment for
    treatment effect (b)

(a)
(b)
response
gene expression
Relative Effect the slope of the line which
connects the means of the response in two clouds
of points
9
Measure of surrogacy for Type I genes
  • Adjusted association the correlation between the
    gene expression and the response after adjustment
    for treatment effects

GENE SPECIFIC SURROGACY We fit the joint model
for each gene twice and the LR test is used to
test
  • Estimated from the joint model

10
Measure of surrogacy for Type II genes relative
reduction in deviance
Variability of the response
Variability of the response using information
about the gene expression

Relative reduction in deviance
11
How to Choose the Cutoff Point?
Regression tree model with two terminal nodes is
used. The cutoff point is chosen in order
to maximize RD
X
X lt
X gt
If RD R2 RD reaches maximum
12
GENE SPECIFIC SURROGACY
Type II We test treatment effect in a joint
model. We calculate RD for each gene
TYPE I We test correlation in a joint model.
We calculate R2 for each gene
13
Joint Surrogacy 3 steps
n subjects
Combine the information from all genes to 1 score
and use this score as a biomarker
n subjects
m genes
Microarray data
The gene profile of the subject
Gene specific surrogacy
Joint surrogacy
  • Selection of K genes (among the m genes in the
    micrroarray).
  • Data reduction combine the information from the
    K
  • selected genes into one score (the gene
    profile of the
  • subject).
  • Evaluation
  • Each step takes into account the type of the
    genes

14
Step 1 Gene selection
Type I genes (correlation)
Type II genes (treatment effects)
For each gene Xi the regression model fitted
genes with the highest absolute values of
selected
SAM (Significance Analysis of Microarrays) False
discovery rate estimation
genes selected
genes selected
We select K1/2 genes which maximize
adjusted association
RD
15
Step 2 Supervised Principle Components
Type I gene (correlation)
Type II gene (treatment effects)
K1 genes
n subjects
n subjects
3. Compute the first principle component (data
reduction).
3b. Compute PLS component
16
Step 3 Evaluation
Type II gene (treatment effects)
Type I gene (correlation)
Calculate R2 for the regression model of the
form
Calculate RD for the regression tree model with
U(X)
Adjusted association estimated from the joint
variance-covariance matrix
RE to measure the direction of the surrogacy
17
ResultsType I
  • Models with PC fit better than models
  • with PLS components
  • The best fit (based on univariate
  • models) for the PC component
  • built of 10 genes
  • From the joint model
  • 0.86 (-0.9)
  • Separate covariance matrices
  • for the two treatment groups

18
ResultsType II
  • SAM method applied with 100 permutations
  • FDR estimates for 3 subsets range from 0 to about
    0.2.
  • -Preserving 0.05 not an issue since a single gene
    not evaluated as a surrogate endpoint.

RD76,5 (PC built of 10 top genes)
None of the type I gene selected as type II and
vice versa. The type I/II genes not expected
19
Discussion
  • Alternative approaches
  • ridge regression
  • mixed variance-covariance criterion
  • gene shaving
  • Bair at al.(2004) the behavior of gene shaving
    similar to SPCA , the ridge regression
  • and the mixed criterion suffer from the very
    high dimensions
  • Possible extensions
  • class prediction based on the chosen gene
    components for the 2
  • treatment groups (Fisher analysis, quadratic
    discriminant analysis,
  • nearest-neighbor rules, classification trees
    and many others)
  • other types of response binary, ordinal etc.

20
  • THANK YOU!

21
REFERNCES 1 Bair, E., Hastie, T., Paul, D. and
Tibshirani, R. (2004). Prediction by supervised
principal components. Technical report.
Departament of Statistics, Stanford
University. 2 Burzykowski, T., Molenberghs, G.
and Buyse, M. (2005). The Evaluation of Surrogate
Endpoint. New York 3 Buyse, M., Molenberghs,
G., Burzykowski, T., Didier, R. and Geys, H.
(2000). Statistical validation of surrogate
endpoints Problems and proposals. Drug Inf.
Assoc.,34, 447-454. 4 Dudoit, S., Fridlyand, J.
and Speed, T.P. (2002). Comparison of
discrimination methods for the classification of
tumors using gene expression data. J. Amer.
Statist. Assoc.,vol.97, 457, 77-87. 5
McLachlan, G.J, Do, K., Ambroise, C. (2004).
Analyzing Microarray Gene Expression Data. New
Jersey John Wiley Sons. 6 Nguyen. D.V. and
Rocke, D.M. (2002). Multi-class cancer
classification via partial least squares with
gene expression profiles. Oxford University
Press, vol. 18, 9 2002, 1216-1226. 7 Nguyen.
D.V. and Rocke, D.M. (2002). Partial least
squares proportional hazard regression for
application to DNA microarray survival data.
Oxford University Press, vol. 18, 12 2002,
1625-1632. 8 Shkedy, Z. (2006). Testing and
evaluation of gene expression data as surrogate
biomarkers in pre-clinical experiments. Technical
report. Center for Statistics, Universiteit
Hasselt. 9 Simon, R.M., McShane, L.M., Wright,
G.W., Korn, E.L., Radmacher, M.D. and Zhao, Y.
(2004). Design and Analysis of DNA Microarray
Investigations. New York Springer-Verlag. 10
Speed, T.P. (2003). Statistical Analysis of Gene
Expression Microarray Data, New York Chapman
Hall/CRC. 11 Tusher, V.G., Tibshirani, R. and
Chu, G. (2001). Significance analysis of
microarrays applied to the ionizing radiation
response. PNAS, vol. 98, 9, 5116-5121.
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