Computational Diagnosis

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Computational Diagnostics A new research group
at the Max Planck Institute for molecular
Genetics, Berlin
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Will the patient respond to this drug?


?
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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
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computational diagnostics
Statistical Modeling
Experimental Design, Quality Control, Scaling,
Normalization, Dimension Reduction, Predictive
Classification, Quantifying the Evidence,
Identifying the Evidence
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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
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computational diagnostics
Clinical Practice
Large Patient Databases complemented by
expression profiles monitoring the Epidemiology
of the disease
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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
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Estrogen Receptor Status

• 7000 genes
• 49 breast tumors
• 25 ER
• 24 ER-

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Tumor Chip - 7000 Numbers
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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

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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
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Given
Wanted
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The probability that the tumor is ER
7000 Numbers
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7000 Numbers Are More Numbers Than We Need
Predict ER status based on the expression levels
of super-genes
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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-
• ???

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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

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Informative Priors
Likelihood
Prior
Posterior
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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

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The Prior Needs to Be Designed in 49 Dimensions

• Shape?
• Center?
• Orientation?
• Not to narrow ... not to wide

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Shape
multidimensional normal for simplicity
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Center
Assumptions on the model correspond to
assumptions on the diagnosis
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Orientation
orthogonal super-genes !
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Not to Narrow ... Not to Wide
Auto adjusting model Scales are hyper parameters
with their own priors
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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

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Which Genes Have Driven the Prediction ?
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Cysteine Rich Heart Protein
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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

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A Common Problem With Expression Profiles

• We do not have enough samples to answer a certain
  question
• A possible strategy
• Introduce additional model assumptions

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Differential Expression I
Setup Two conditions ( healthy vs sick ), some
repetitions, 10 000 genes Which genes are up or
down regulated ? The most basic question Good
because it is a hypothesis free approach
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Differential Expression II
10 000 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
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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

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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

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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