A NESTED UNSUPERVISED APPROACH TO IDENTIFYING NOVEL MOLECULAR SUBTYPES

1
A NESTED UNSUPERVISED APPROACH TOIDENTIFYING
NOVEL MOLECULARSUBTYPES

• ELIZABETH GARRETT-MAYER
• ONCOLOGY BIOSTATISTICS
• JOHNS HOPKINS UNIVERSITY
• "MCMSki" The Past, Present, and Future of Gibbs
  Sampling
• Bormio, Italy
• January 12-14, 2005

2
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.

3
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.

4
MOLECULAR CLASSIFICATION

• Goal To use expression data to identify or
  hypothesize subtypes of cancer that are as yet
  undefined.
• Eventually, wed 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

5
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

6
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

7
COMMON WAY OF SEEING MICROARRAY DATA PRESENTED
Garber et al. 2001, PNAS
8
MOLECULAR PROFILE OF THREE GENES
Gene A Gene B Gene
C Profile 1 -1 -1 -1 Profile
2 -1 -1 0 Profile 3 -1 -1 1 Profile
4 . . . . . . . . . . . . . . . Pro
file 26 1 1 0 Profile 27 1 1 1
where -1 underexpressed 0 normally
expressed 1 overexpressed
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
LATENT EXPRESSION CLASSES
The proportion of underexpressed and
overexpressed samples for each gene g are
defined by
13
POE PROBABILITY OF EXPRESSION
Variation across samples (population variation)
14
(No Transcript)
15
POE PROBABILITY OF EXPRESSION

• Sometimes we have relatively few samples
• Borrow strength across genes
• Bayesian hierarchical model for gene-specific
  parameters
• Constrain parameters such that

16
Special Case Normal samples included

• If tumor sample t is normal, then
• If tumor sample t is not normal, then
• Allows us to define the normal component of the
  mixture distribution

17
(No Transcript)
18
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

19
ESTIMATION PROCEDURE

• Sampling of ? parameters
• where ? represents the full set of parameters,
  and ? is ? with ? removed.
• ? ? e?,? combine so that we are sampling
  them from ?, e?
• Facilitates mixing of the ? parameters (can be a
  problem if there are few or no samples in the
  uniform components)

20
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, s1, µ2, s2, µ3, s3)
• Our parameterization has 4 parameters (?, ?-, µ,
  s)
• 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 -gt expressions in
  cancer can take broad range of values

21
POE TRANSFORMATION

• Each data point, agt, is transformed to the POE
  scale

22
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!

23
SIMULATED DATA EXAMPLE
Original scale
POE scale
24
LUNG CANCER DATA EXAMPLE
25
EVALUATING DIAGNOSTIC CHARACTERISTICS OF GENES

• For each gene, determine based on a fixed
  threshold p0 (e.g. p0 0.50)
• 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

26
EVALUATING DIAGNOSTIC CHARACTERISTICS OF GENES
Assume
27
EVALUATING DIAGNOSTIC CHARACTERISTICS OF GENES

• Better approach exploits MCMC estimation
• We spent all this (computational) time sampling
  egt at each iteration of chain! Lets 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

28
SPECIFICITY
SENSITIVITY
29
CLASSIFICATION GENE MINING

• 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 gt 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.

30
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

31
GENE PROFILES
MEIS1
FGF7
BRCA1
32
OTHER POINTS

• CAVEAT Weak Identifiability
• ?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
• Applications in breast cancer, lung cancer, AML.

33
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.