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, 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”

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 -11 Profile 4 . . . . . . . . . . . . . . . Profile 26 1 1 0 Profile 27 1 1 1 where -1 = underexpressed 0 = “normally” expressed 1 = overexpressed

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)

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

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 κparameters: • 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)

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, 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

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! 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

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 > 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 • 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: • Applications in breast cancer, lung cancer, AML….

33. 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. ACKNOWLEDGEMENTS AND REFERENCES