1. Computational Diagnostics based on Large Scale Gene Expression Profiles using MCMC
Rainer Spang,
Max Planck Institute for Molecular Genetics, Berlin
Harry Zuzan, Carrie Blanchette, Erich Huang, Holly Dressman, Jeff Marks, Joe Nevins, Mike West
Duke Medical Center & Duke University

2. Estrogen Receptor Status
7000 genes
49 breast tumors
25 ER+
24 ER-

3. Tumor – Chip Numbers

4. Given
Wanted
89%
The probability that the tumor is ER+
7000 Numbers

5. 7000 Numbers Are More Numbers Than We Need
Predict ER status based on the expression levels of super-genes

6. Singular Value Decomposition
Singular values
Loadings
Data
Expression levels of super genes, orthogonal matrix

7. Probit Model Class of tumor i
Distribution Function of a Standard Normal
Regression weight for super gene i
Expression Level of super gene i

8. Overfitting
Using only a small number of super genes is not robust at all
When using many (all) supergenes, the linear model can be easily saturated, i.e. we have several models that fit perfectly well
Consequence: For a new patient we find among these models some that support that she is ER+ and others that predict she is ER-

9. Given the Few Profiles With Known Diagnosis:
The uncertainty on the right model is high
The variance of the model-weights is large
The likelihood landscape is flat
We need additional model assumptions to solve the problem

10. Informative Priors
Likelihood
Prior
Posterior

11. If the Prior Is Chosen Badly:
We can not reproduce the diagnosis of the training profiles any more
We still can not identify the model
The diagnosis is driven mostly by the additional assumptions and not by the data

12. The Prior Needs to Be designed in 49 Dimensions
Shape?
Center?
Orientation?
Not to narrow ... not to wide

13. Shape
multidimensional normal
for simplicity

14. Assumptions on the model correspond to assumptions on the diagnosis
Center
Assumptions on the model correspond to assumptions on the diagnosis

15. Orientation
orthogonal super-genes !

16. Not to Narrow ... Not to Wide
Auto adjusting model
Scales are hyper parameters with their own priors

17. Prior given the hyper parameter
Rescaling by singular values
Hyper parameter
Independent super genes
Unbiased prior

18. A prior for the hyper parameters
Conjugate prior
Flexibility for
Symmetric U-Shaped prior for
k=2 or k=3

19. Latent Variable
Albert & Chip 1993

20. MCMC - Gibbs Sampler - Sequential updates of conditional distributions
All conditional posteriors can be calculated analytically
West 2001, Albert & Chip 1993

21. What are the additional assumptions that came in by the prior?
The model can not be dominated by only a few super-genes ( genes! )
The diagnosis is done based on global changes in the expression profiles influenced by many genes
The assumptions are neutral with respect to the individual diagnosis

23. Which Genes Have Driven the Prediction ?
Weight
nuclear factor 3 alpha
0.853
cysteine rich heart protein
0.842
estrogen receptor
0.840
intestinal trefoil factor
x box binding protein 1
0.835
gata 3
0.818
ps 2
liv1
0.812
... many many more ...
...

24. Thank you!