Central dogma of biology
DNA RNA pre-mRNA
mRNA Protein
Central dogma
CGAACAAACCTCGAACCTGCTDNA:
mRNA: GCU UGU UUA CGA
Polypeptide: Ala Cys Leu Arg
Translation
Transcription
Basic molecular biology
Transcription
End modification
Splicing
Transport
Translation
Less basic molecular biology
Cy3 Cy5
ReferenceTest Sample
cDNA Clone(LIBRARY)
PCR Product
PE
Test Sample
OligonucleotideSynthesis
Biological Sample
RNA
ARRAY
ARRAY
Ramaswamy and Golub, JCO
Microarray technology
Lockhart and Winzler 2000
Oligonucleotide cDNA
Microarray technology
Yeast experiment
Microarray experiment
When the science is not well understood, resort to statistics:
Ultimate goal: discover the genetic pathways of cancers
Infer cancer genetics by analyzing microarray data from tumors
Curse of dimensionality: Far too few examples for so many dimensions to predict accurately
Immediate goal: models that discriminate tumor types or treatment outcomes and determine genes used in model
Basic difficulty: few examples 20-100, high-dimensionality 7,000-16,000 genes measured for each sample, ill-posed problem
Analytic challenge
Cancer Diagnosis
Acute Myeloblastic Leukemia v
Acute Lymphoblastic Leukemia
38 examples of Myeloid and Lymphoblastic leukemias Affymetrix human 6800, (7128 genes including control genes)
34 examples to test classifier
Results: 33/34 correct
d perpendicular distancefrom hyperplane
Test data
d
Cancer Classification
Coregulation: the expression of two genes must be correlated for a protein to be made, so we need to look at pairwise correlations as well as individual expression
Size of feature space: if there are 7,000 genes, feature space is about 24 million features, so the fact that feature space is never computed is important
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Two gene example: two genes measuring Sonic Hedgehog and TrkC
Coregulation and kernels
Nonlinear SVM helps when the most informative genes are removed,Informative as ranked using Signal to Noise (Golub et al).
Genes removed errors1st order 2nd order 3rd order
polynomials
0 1 1 110 2 1 120 3 2 130 3 3 240 3 3 250 3 2 2100 3 3 2200 3 3 3 1500 7 7 8
Gene coregulation
Golub et al classified 29 test points correctly, rejected 5 of which 2 were errors using 50 genes
Need to introduce concept of rejects to SVM
g1
g2
Normal
Cancer
Reject
Rejecting samples
Rejecting samples
Estimating a CDF
The regularized solution
1/d
P(c=1 | d)
.95
95% confidence or p = .05 d = .107
Rejections for SVMs
Results: 31 correct, 3 rejected of which 1 is an error
Test data
d
Results with rejections
SVMs as stated use all genes/features
Molecular biologists/oncologists seem to be convinced that only a small subset of genes are responsible for particular biological properties, so they want the genes most important in
discriminating
Practical reasons, a clinical device with thousands of genes is not financially practical
Possible performance improvement
Wrapper method for gene/feature selection
Gene selection
AML vs ALL: 40 genes 34/34 correct, 0 rejects. 5 genes 31/31 correct, 3 rejects of which 1 is an error.
B vs T cells for AML: 10 genes 33/33 correct, 0 rejects.
d
Test data
d
Test data
Results with gene selection
Dataset Total Samples
Class 0
Class 1
Leukemia Morphology (train)
38 27 ALL
11 AML
Leukemia Morpholgy (test)
34 20 ALL
14 AML
Leukemia Lineage (ALL)
23 15 B-Cell
8 T-Cell
Lymphoma Outcome (AML)
15 8 Low risk
7 High risk
Dataset Total Samples
Class 0
Class 1
Lymphoma Morphology
77 19 FSC
58 DLCL
Lymphoma Outcome
58 22 Low risk
36 High risk
Brain Morphology
41 14 Glioma
27 MD
Brain Outcome
50 38 Low risk
12 High risk
Hierarchy of difficulty:1. Histological differences: normal vs. malignant, skin vs. brain2. Morphologies: different leukemia types, ALL vs. AML3. Lineage B-Cell vs. T-Cell, folicular vs. large B-cell lymphoma4. Outcome: treatment outcome, elapse, or drug sensitivity.
Molecular classification of cancer
Dataset Algorithm Total Samples
Total errors
Class 1 errors
Class 0 errors
Number Genes
SVM 35 0/35 0/21 0/14 40
WV 35 2/35 1/21 1/14 50
Leukemia Morphology (trest) AML vs ALL
k-NN 35 3/35 1/21 2/14 10
SVM 23 0/23 0/15 0/8 10
WV 23 0/23 0/15 0/8 9
Leukemia Lineage (ALL) B vs T
k-NN 23 0/23 0/15 0/8 10
SVM 77 4/77 2/32 2/35 200
WV 77 6/77 1/32 5/35 30
Lymphoma FS vs DLCL
k-NN 77 3/77 1/32 2/35 250
SVM
41 1/41 1/27 0/14 100
WV
41 1/41 1/27 0/14 3
Brain MD vs Glioma
k-NN
41 0/41 0/27 0/14 5
Morphology classification
Dataset Algorithm Total Samples
Total errors
Class 1 errors
Class 0 errors
Number Genes
SVM 58 13/58 3/32 10/26 100
WV 58 15/58 5/32 10/26 12
Lymphoma LBC treatment outcome
k-NN 58 15/58 8/32 7/26 15
SVM 50 7/50 6/12 1/38 50
WV 50 13/50 6/12 7/38 6
Brain MD treatment outcome
k-NN 50 10/50 6/12 4/38 5
Outcome classification
Error rates ignore temporal information such as when a patient dies. Survivalanalysis takes temporal information into account. The Kaplan-Meier survivalplots and statistics for the above predictions show significance.
0 20 40 60 80 100 120
0.0
0.2
0.4
0.6
0.8
1.0
p-val = 0.0015
0 50 100 150
0.0
0.2
0.4
0.6
0.8
1.0
p-val = 0.00039
Lymphoma Medulloblastoma
Outcome classification
Breast Prostate Lung Colorectal
Lymphoma
Bladder
Melenoma Uterus Leuke
mia Renal Pancreas Ovary Mesothel
ioma Brain
Abrev B P L CR Ly Bl M U Le R PA Ov MS C
Total 11 10 11 13 22 11 10 10 30 11 11 11 11 20
Train 8 8 8 8 16 8 8 8 24 8 8 8 8 16
Test 3 2 3 5 6 3 2 3 6 3 3 3 3 4
Note that most of these tumors came from secondary sources and were notat the tissue of origin.
Multi tumor classification
CNS, Lymphoma, Leukemia tumors separate
Adenocarcinomas do not separate
Clustering is not accurate
+
+
+
+
R+1+1
Y-1-1
G+1-1
B-1+1
ClassG+RB+R
Combination approaches: All pairsOne versus all (OVA)
Multi tumor classification
GeneExpression
Dataset
FinalMulticlass
Call(Highest OVA
PredictionStrength)
Breast OVAClassifier
. . .
. . .
Prostate OVAClassifier
CNS OVAClassifier
TEST SAMPLE
BREAST TUMORS
ALL OTHER TUMORS
Hyperplane
Confidence
Breast (High Confidence)
-2
0
+2
Figure 2
Supervised methodology
0
0.2
0.4
0.6
0.8
1
-1 0 1 2 3 4
Accuracy Fraction of Calls
0
0.2
0.4
0.6
0.8
1
-1 0 1 2 3 4-1
0
1
2
3
4
5
Low HighLow High
Correct Errors Correct Errors
Lo
w
H
igh
Confidence Confidence
Co
nfi
den
ce
Train/ Test 1
cross -val.
Train/cross -val. Test 1
00.1
0.20.3
0.40.5
0.6
0.7
0.8
0.91
First Top 2 Top 3
Prediction Calls
Train/cross -val. Test 1
0
0.2
0.4
0.6
0.8
1
-1 0 1 2 3 4
Accuracy Fraction of Calls
0
0.2
0.4
0.6
0.8
1
-1 0 1 2 3 4-1
0
1
2
3
4
5
Low HighLow High
Correct Errors Correct Errors
Lo
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igh
Confidence Confidence
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Train/ Test 1
cross -val.
Train/cross -val. Test 1
0
0.1
0.20.3
0.40.5
0.6
0.7
0.8
0.91
First Top 2 Top 3
Prediction Calls
Train/cross -val. Test 1
Dataset Sample Type ValidationMethod
Sample Number
TotalAccuracy
Confidence High LowFraction Accuracy Fraction Accuracy
Train Well Differentiated Cross-val. 144 78% 80% 90% 20% 28%
Test 1 Well Differentiated Train/Test 54 78% 78% 83% 22% 58%
Well differentiated tumors
Feature selection hurts performance
0
0.2
0.4
0.6
0.8
1
-1 0 1 2 3 4
Accuracy Fraction of Calls
-1
0
1
2
3
4
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Low High
Confidence
Lo
w
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igh
Co
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Correct Errors
00.10.20.30.40.50.60.70.80.9
1
First Top 2 Top 3
Prediction Calls
Dataset Sample Type ValidationMethod
Sample Number
TotalAccuracy
Confidence High LowFraction Accuracy Fraction Accuracy
Test Poorly Differentiated Train/test 20 30% 50% 50% 50% 10%
Poorly differentiated tumors
Morphing
Morphing
Talking faces
Talking faces
Talking faces
Recursive feature elimination (RFE): based upon perturbationanalysis, eliminate genes that perturb the margin the least
Optimize leave-one out (LOO): based upon optimization of leave-one out error of a SVM, leave-one out error is
unbiased
Two feature selection algorithms
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Recursive feature elimination
Use leave-one-out (LOO) bounds for SVMs as a criterion to select features by searching over all possible subsets of n features for the ones that minimizes the bound.
When such a search is impossible because of combinatorial explosion, scale each feature by a real value variable and compute this scaling via gradient descent on the leave-one-out bound. One can then keep the features corresponding to the largest scaling variables.
The rescaling can be done in the input space or in a “Principal Components” space.
Optimizing the LOO
Rescale features to minimize the LOO bound R2/M2
x2
x1
R2/M2 >1
M
R
x2
R2/M2 =1
M = R
Pictorial demonstration
Radius margin bound: simple to compute, continuous very loose but often tracks LOO well
Jaakkola Haussler bound: somewhat tighter, simple to compute, discontinuous so need to smooth,
valid only for SVMs with no b term
Span bound: tight complicated to compute, discontinuous so need to smooth
Three LOO bounds
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Toy data