1. Computational Diagnostics
A new research group at the
Max Planck Institute for molecular Genetics,
Berlin

2. Will the patient
respond to this drug? ?

3. A simple solution for simple problems
computational diagnostics
A simple solution for simple problems
Find all genes that are induced at least x-fold and use them to predict clinical outcomes

4. computational diagnostics
Statistical Modeling
Experimental Design, Quality Control, Scaling, Normalization, Dimension Reduction, Predictive Classification, Quantifying the Evidence, Identifying the Evidence

5. Computational Infrastructure and more Data
computational diagnostics
Computational Infrastructure and more Data
Databases, Automatic Uploading, Standard Analysis Protocols, Analysis Software, Query Language, Understanding the disease, Designing a small Diagnostic Chip

6. computational diagnostics
Clinical Practice
Large Patient Databases complemented by expression profiles monitoring the Epidemiology of the disease

7. Duke Medical Center & Duke University
Breast Cancer, Expression Profiles and Binary Regression in 7000 Dimensions
Rainer Spang, Harry Zuzan, Carrie Blanchette, Erich Huang, Holly Dressman, Jeff Marks, Joe Nevins, Mike West
Duke Medical Center & Duke University

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

9. Tumor – Chip Numbers

10. We Assume That the Following Steps Are Done:
Choosing the patients
Doing the surgery
Handling the tissues
Preparing mRNA
Hybridizing the chips
Image analysis
Excluding low quality data
Normalization
Scaling

12. How Much Evidence Is There?
I am 80% sure The probability that
I know it the patient has xxx
It was a guess given the profile is
0.8, 1, 0.5

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

14. 7000 Numbers Are More Numbers Than We Need
Predict ER status based on the expression levels of super-genes

16. Overfitting: We Can Not Identify a Model
There are many different models that assign high probabilities for ER+ tumors and low probabilities for ER- tumors in the training set
For a new patient we find among these models some that support that she is ER+ and others that predict she is ER-
???

17. 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

18. Informative Priors
Likelihood
Prior
Posterior

19. 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

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

21. Shape
multidimensional normal
for simplicity

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

23. Orientation
orthogonal super-genes !

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

25. 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

27. 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 ...
...

28. Cysteine Rich Heart Protein

29. Summary ... so far
We have solved a relatively simple computational diagnostics problem (ER-status in human breast cancers)
Probit model
Overfitting is a problem
Additional model assumptions do the trick

30. A Common Problem With Expression Profiles
We do not have enough samples to answer a certain question
A possible strategy:
Introduce additional model assumptions

31. Differential Expression I
Setup: Two conditions ( healthy vs sick ), some repetitions, genes
Which genes are up or down regulated ?
The most basic question
Good because it is a hypothesis free approach

32. Differential Expression II
degrees of freedom
A very bad multiple testing problem
It is possible in principal, but might require many replications depending on signal to noise ratios
SAM: regularized t-statistic + permutation based false positive rates
Hard to improve the analysis because it is a hypothesis free approach

33. Clustering of Genes
Setup: many different conditions time series multiple knock-outs
100% explorative analysis
Essentially it is rearranging the data
Good for finding hypotheses but not for verifying them

34. Clustering of Profiles (Patients)
Maybe we can find new disease types or refine existing ones
Completely different results when different sets of genes are used
No predictive analysis

35. Think About Data Analysis Ahead of Time
Collect possible questions on the data
Which of them are easy ?
- Biologists and Bioinformaticians might have a different take on that -
Compare: number of samples vs. degrees of freedom
It is possible to compensate lack of data with model assumptions: Which assumptions make sense ?
More complex question can be the easier ones if they allow for an appropriate model