Download a nested unsupervised approach to identifying novel molecular

A NESTED UNSUPERVISED
APPROACH TO
IDENTIFYING NOVEL MOLECULAR
SUBTYPES
ELIZABETH GARRETT-MAYER
ONCOLOGY BIOSTATISTICS
JOHNS HOPKINS UNIVERSITY
"MCMSki": The Past, Present, and Future of Gibbs Sampling
Bormio, Italy
January 12-14, 2005
INTRODUCTION:
MOLECULAR SUBTYPING IN LUNG CANCER
• Lung cancer remains the leading cause of
cancer deaths for men and women
• Lung cancer diagnosis includes evaluation of
–
–
–
–
type of cancer (e.g. non-small cell, adenocarcinoma)
location and size
lymph node involvement
evidence of metastases outside the lungs.
• But, tumors with identical diagnosis often
– progress differently,
– respond to therapy differently
– result in different long-term outcomes.
MOLECULAR SUBTYPING IN LUNG CANCER
• Genome-wide analyses of gene expression profiles show promise:
different subclasses of tumors correspond to distinct gene
expression patterns
• Multiple studies in lung cancer have found gene expression profiles
for lung cancer subtypes.
–
–
–
–
Bhattacharjee et al. (PNAS 2001)
Beer et al. (Nature Medicine 2002)
Garber et al. (PNAS 2001)
and more…..
• Some overlap and some disagreement between profiles.
– Different technologies used (e.g. Affymetrix versus cDNA chips)
– Different genes on the arrays.
– Different statistical methods for developing profiles
• Validation: Some are, but most are not validated.
MOLECULAR CLASSIFICATION
• Goal: To use expression data to identify or hypothesize subtypes of
cancer that are as yet undefined.
• Eventually, we’d like to be able to have individualized prognoses
and therapy based on molecular profiles
• Success story: Gefitinib (Iressa)
– Non-small cell lung cancers
– Those with EGFR protein mutation have high probability of
response
– Clinical test developed for screening lung cancer patients
• We need additional new classes that are
– Interpretable (biologically)
– Amenable to further analyses
– Translatable into “clinical tools”
STAGES OF MOLECULAR CLASSIFICATION
• Dimension reduction
– We start with too many genes: we need to pare it
down
• Subtype identification
– Identify homogenenous clusters of samples
– Ideally, based on outcome data
• Expert elicitation
– We do not want all genes related to subtypes
– Ideally: small, non-redundant set of genes that is
highly predictive of subtype/outcome
DESIGN OF MICROARRAY STUDIES
• Samples included:
– All cancers
– Cancers plus some “normals” or other types (e.g. non-malignant
disease)
– Often few samples
• Sometimes we have outcome data
– Time to progression
– Time to death
– Response rate
• Our data example: 156 lung samples (Bhattacharjee et al., 2001)
–
–
–
–
Affymetrix chips used for measuring expression
139 adenocarcinomas and 17 normal samples
5665 genes available for analysis
no outcome data available
COMMON WAY OF SEEING MICROARRAY DATA PRESENTED
Garber et
al. 2001,
PNAS
MOLECULAR PROFILE OF THREE GENES
Profile 1
Profile 2
Profile 3
Profile 4
.
.
.
Profile 26
Profile 27
Gene A
-1
-1
-1
.
.
.
.
1
1
Gene B
-1
-1
-1
.
.
.
.
1
1
where -1 = underexpressed
0 = “normally” expressed
1 = overexpressed
Gene C
-1
0
1
.
.
.
.
0
1
LATENT EXPRESSION CLASSES
g  1,..., G indexes genes; t  1,..., T samples
egt   1 gene g has abnormally low expression in sample t
egt  0
gene g has normal expression in sample t
egt  1
gene g has abnormally high expression in sample t
agt |(egt  e) ~ f e, g (),
e  { 1,0,1}
The proportion of underexpressed and overexpressed samples
for each gene g are defined by:
 g  P(egt   1)
 g  P(egt  1)
POE: PROBABILITY OF EXPRESSION
Variation across samples (population variation)
f 1, g ()  U (   g   t   g ,  t   g )
f 0, g ()  N ( t   g ,  g )
f 1, g ()  U ( t   g ,  t   g   )

g
g
g   g
g
g   g
POE: PROBABILITY OF EXPRESSION
• Sometimes we have relatively few samples
• Borrow strength across genes
• Bayesian hierarchical model for gene-specific parameters
 g |  ,   ~ N (  ,   )
 g2 | ,  ~ G( ,  )
 g | k ~ E ( k )
 | ~ E ( )

g

k

k
• Constrain parameters such that
 g  r g ;  g  r g where r  3
Special Case:
Normal samples included
• If tumor sample t is normal, then
egt  0 for g  1,..., G
• If tumor sample t is not normal, then
egt is unknown for g  1,..., G
• Allows us to define the normal component of
the mixture distribution
ESTIMATION PROCEDURE
• MCMC with Metropolis-Hastings algorithm in R.
• Takes too long (overnight with 200 samples,
10000 genes)
• Currently being reprogrammed in C++
• Tried WinBUGS, but could not program a mixture
of 1 normal and two uniforms.
• Data are augmented with trichotomous indicator
egt for each agt (Diebolt and Robert, 1994)
• egt is not “fully” missing: egt = 0 if normal sample
ESTIMATION PROCEDURE
• Sampling of κ parameters:
[ | *], [e| ,  *], [ *| e, ]
• where ω represents the full set of parameters, and ω* is ω
with κ removed.
• [κ| ω*] [e|κ,ω*] combine so that we are sampling them
from [κ, e|ω*]
• Facilitates mixing of the κ parameters (can be a
problem if there are few or no samples in the uniform
components)
ESTIMATION PROCEDURE
• Why a mixture of uniforms and normals?
– Mathematically
• Identifiability is an issue due to small sample size
• Fewer parameters than a mixture of three normals
– Three component normal mixture has 6 parameters (μ1,
σ1, μ2, σ2, μ3, σ3)
– Our parameterization has 4 parameters (κ+, κ-, μ, σ)
• No points are assigned very low densities
• Estimates are more stable
– Practically
• Gaussian errors are reasonable for measuring gene
expression
• Cancer is often thought to be caused by “failure” of some
biological mechanism -> expressions in cancer can take
broad range of values
POE TRANSFORMATION
Each data point, agt, is transformed to the POE
scale
pgt  P(egt  1| agt ,  ) 
pgt  P(egt   1| agt ,  ) 
 g f1, g (agt )
 g f1, g (agt )   g f 1, g (agt )  (1   g   g ) f 0, g (agt )
 g f 1, g (agt )
 g f1, g (agt )   g f 1, g (agt )  (1   g   g ) f 0, g (agt )

gt

gt
pgt  p  p
POE TRANSFORMATION
• Does not depend on original units of
measure (e.g. absolute expression versus
log-ratios)
• Probability scale (loosely)
• Long term goal: studies using different
technologies can be represented in the
same “unit free” scale
• Denoises!
SIMULATED DATA EXAMPLE
Original scale
POE scale
LUNG CANCER DATA EXAMPLE
EVALUATING DIAGNOSTIC
CHARACTERISTICS OF GENES
• For each gene, determine egt based on a fixed
threshold p0 (e.g. p0 = 0.50):
  1 if pgt   p0

egt   1 if pgt  p0
 0 otherwise

• Calculate sensitivities and specificities for each gene
• Knowing which samples are normal allows us to
compute these quantities
• We can screen genes at this stage, discarding genes
with poor predictive power
EVALUATING DIAGNOSTIC
CHARACTERISTICS OF GENES
 1 sample t is cancer
Assume ct  
 0 sample t is normal
spg  P(sample t is classified as normal by gene g| sample t is normal)
 P(egt  0| ct  0)
seg  P(sample t is classified as differential by gene g| sample t is cancer)
 P(egt  0| ct  1)
seg  P(sample t is classified as overexpressed by gene g| sample t is cancer)
 P(egt  1| ct  1)
seg  P(sample t is classified as underexpressed by gene g| sample t is cancer)
 P(egt   1| ct  1)
EVALUATING DIAGNOSTIC
CHARACTERISTICS OF GENES
• Better approach exploits MCMC estimation
• We spent all this (computational) time sampling egt at
each iteration of chain! Let’s make better use of them.
• Calculate sensitivities and specificities as part of the
chain, using sampled trichotomous indicators.
• Better estimates of sensitivities and specificities
– Posterior distributions
– Does not rely on (arbitrary) cutoff p0
SPECIFICITY
SENSITIVITY
CLASSIFICATION: GENE MINING
1. Choose an expression pattern of interest. The idea is to state a target for
how many samples are expected to show low expression and how many
to show high expression for a gene. For example, the pattern
{0.05,0.20} indicates that 5% of samples should be low, and 20% should
be high for a gene. The remaining 75% would then be in the ``typical''
component of the mixture.
2. Sort genes according to consistency with ``low-high'' distribution defined
in step 1. Using the estimates of pgt we can calculate, for each gene g,
the probability that the distribution of over and under expression among
the samples is the same as in the specified low-high distribution. We sort
genes by this probability.
3. Choose the gene with the largest probability from step 2 and which is
sufficiently coherent as the ``seed'' gene (i.e., rgg > rc
where rc is the cutoff for gene coherence).
4. Choose genes that show substantial agreement with the seed gene,
either as a fixed agreement cutoff, or as a proportion of coherence of the
seed variable. Add these genes to the ``group'' which is seeded by gene
chosen in step 3.
5. Remove the genes in the group defined in step 4 from further
consideration. Repeat steps 3 and 4 to identify remaining groups.
GENE PROFILES
• Three genes selected for profiling
BRCA1 (breast cancer 1): tumor suppressor
gene related to familial breast/ovarian cancer
and other cancers
MEIS1 (myeloid ecotropic viral integration):
transcription factor related to oncogenesis
FGF7 (fibroblast growth factor 7): related to
lung development
FGF7
MEIS1
BRCA1
GENE PROFILES
OTHER POINTS
• CAVEAT: Weak Identifiability
• κ’s only meaningful when “enough” samples in over- and
under-expression components
• If sample size is small.
• Future/Other work
• “Normal” does not have to be “normal
• Gefitinib analogy:
 1 sample t has good prognosis
ct  
 0 sample t has poor prognosis
• Applications in breast cancer, lung cancer, AML….
ACKNOWLEDGEMENTS AND
REFERENCES
Giovanni Parmigiani
Ed Gabrielson
Jiang Huang
Xiaogang Zhong
Garrett, E.S., Parmigiani, G. A nested unsupervised approach to identifying novel
molecular subtypes. Bernoulli, 10(6), 2004.
Garrett, E.S., Parmigiani, G. POE: Statistical Methods for Qualitative Analysis of Gene
Expression. In The Analysis of Gene Expression Data: Methods and Software
(eds. G. Parmigiani, E.S. Garrett, R.A. Irizarry, S.L. Zeger) Chapter 16, Springer:
New York, 2003.
Parmigiani, G., Garrett, E., Anbazhagan, R., Gabrielson, E. A Statistical Framework
forExpression-Based Molecular Classification in Cancer. Journal of Royal
Statistical Society, Series B, with discussion, 64: 717-736, 2002.
Scharpf, R., Garrett, E.S., Hu, J., Parmigiani, G. Statistical Modeling and Visualization
of Molecular Profiles in Cancer. Biotechniques, 34: S22-S29, 2003.