A Statistical Framework for Expression-Based Molecular Classification

1
A Statistical Framework for Expression-Based
Molecular Classification

• Elizabeth Garrett
• Sidney Kimmel Cancer Center
• Johns Hopkins University

2
Molecular Classification of Cancer

• Goals
• Short term
• To use gene expression array data to identify and
  hypothesize subtypes of cancer
• To discover new cancer classes that are
  interpretable and amenable to further biological
  analysis
• To translate classes into clinical tools
• Long term
• To eventually refine individualized prognosis and
  therapy

3
Outline of Talk

• Molecular Classifications
• the role of statistics in molecular
  classification
• defining a molecular profile
• Modeling latent classes POE (Probability of
  Expression)
• Bayesian mixture models
• visualization tools
• Mining using latent classes
• Using POE to combine across platforms

4
Botstein-Brown style of visualizing gene
expression data
(Garber et al. PNAS 2001)
5
The fine print
6
Motivating Datasets

• Unclassified cancer samples Are the gene
  expressions patterns informative about
  subclasses?
• Ductal breast cancers
• Adenocarcinomas of the lung
• Diffuse large B-cell lymphoma
• Related tissues Are subtypes associated with
  prognosis?
• Normal tissues and cancers tissues
• Outcome data (e.g. survival, recurrence,
  response)
• Genes Are hypothesized genes associated with
  cancer types?
• Functional information
• Custom array

7
General Approach of POE (Probability of
Expression)

• Define a reference expression value
• normal vs. over expressed vs. under expressed
• unsupervised in nature
• Use scale-independent measures of expression
• allows combination of data across platforms
• incorporates measurement errors
• Choose molecular profile that predicts cancer
  class based on a small number of genes
• yields clinical implications
• choose genes using combination of statistical and
  biological evidence
• Caveat NOT intended for gene clustering and not
  for manual clustering of genes

8
Molecular Profiles (based on 3 genes A, B, and C)
27 33 possible profiles
Gene A Gene B Gene C
Profile 1 -1 -1 -1
Profile 2 -1 -1 0
Profile 3 -1 -1 1
Profile 4 -1 0 -1
Profile 5 -1 0 0
Profile 6 -1 0 1
. . . .
Profile 24 1 0 1
Profile 25 1 1 -1
Profile 26 1 1 0
Profile 27 1 1 1
9
Mixture of Normal and Two Uniform Distributions
10
Empirical Density of Expression Levels in One
Gene Across 203 Lung Samples
Bhattacharjee, PNAS 2001
11
Latent Expression Classes

• Notation
• Modeling observed gene expression, agt
• For gene g, the proportions of differentially
  expressed tumors in the population of
  unclassified tumors are

12
Probability Scale for Expression Data
Interpretation The probability that gene g in
tumor t is over expressed given observed
expression and the model parameters
Interpretation The probability that gene g in
tumor t is under expressed given observed
expression and the model parameters
13
Distributional Assumptions
Samples Normal/Uniform mixture
Genes Second stage model
14
(No Transcript)
15
Original Scale
After Transformation
16
Harvard Lung Cancer Data (Bhattacharjee, PNAS,
2001)
17
MCMC Estimation Approach

• Relatively straightforward
• A couple comments
• Data augmentation using unknown expression
  variables egt. Sampling of ?s unconditional on
  es
• Starting conditions are critical. K-means
  clustering (k2 or 3) useful for picking starting
  centers and spread
• Constrain min(?g,?g- ) gt k?g

18
Denoising Expression Data
Provides cleaner version of the original
expression level data.
19
Mining for Genes

• Two quantities of interest in looking for and
  grouping genes.
• Probability that gene g follows a specified
  pattern
• Probability that all genes in set G0 have the
  same pattern across samples

20
Identifying Gene Groups

• Preselect proportions of over and under expressed
  genes (e.g. 20 under, 5 over)
• Select genes consistent with proportions via
  P(eg1,.,egT?)
• Chose genes which are similar in expression
  pattern to add to group via q(G0).
• Look at mining plot to identify genes which are
  sensible (biologically).

21
5 underexpressed, 15 overexpressed, 4 sets
22
Molecular Profiles
23
Combining Across Platforms

• Example Stanford, Harvard, Michigan lung cancer
  datasets
• Publicly available
• Different platforms Affymetrix, cDNA glass
  slides
• POE rescales to probability metric
• With some caveats, can combine data

24

• Statistics G. Parmigiani, E. Garrett
• Arrays, Biology E. Gabrielson, R. Anbazhagan
• http//astor.som.jhmi.edu/poe
• G. Parmigiani, E. Garrett, R. Anbazhagan, E.
  Gabrielson. A statistical framework for
  expression-based molecular classification in
  cancer. JRSS, in press.
• E. Garrett, G. Parmigiani. POE Statistical
  Methods for Qualitative Analysis of Gene
  Expression. In The Analysis of Gene Expression
  Data Methods and Software (eds. G Parmigiani,
  E. Garrett, R. Irrizarry, S. Zeger). To appear
  2003.