Disease Association Search and Susceptibility Prediction Algorithms

1
Disease Association Search and Susceptibility
Prediction Algorithms

• Irina Astrovskaya

2
Outline

• Introduction
• SNPs, Haplotypes, Genotypes
• Genetic Epidemiology
• Case/Control Study
• Risk/Resistance factors
• Significance of Risk/Resistance Factors
• Multiple-Testing Adjustment
• Disease Association Search
• Disease Susceptibility Prediction

3
SNPs, Haplotypes, Genotypes

• Human Genome all genetic material in the
  chromosomes(3109 base pairs).
• Difference between any two people
  occur in 0.1 of genome.
• SNP single nucleotide polymorphism, site where
  two or more different nucleotides occur in a
  large percentage of population (? 3 ? 106)
• mostly biallelic.
• Diploid two different copies of each chromosome
• Haplotype description of a single copy
  (expensive)
• (notation 0 is for major, and 1 is for minor
  allele)
• Genotype entire genetic identity of an
  individual
• mixture of two haplotypes
• (notation 0,1 is for
  homozygote, 2 is for heterozygote)

4
Genetic Epidemiology

• Genetic epidemiology searches for genetic risk
  factors of diseases.
• Monogenic disease
• A mutated gene is entirely responsible for the
  disease .
• Typically rare in population lt 0.1.
• Practically all cases are already reported
• Complex disease
• interaction of multiple non-linked genes
• 2SNP analysis vs one-by-one SNP analysis
• Multiple independent causes
• Each cause can be result of interaction of
  several genes
• Each cause explains lt 10-20 of cases
• Common diseases are mostly complex diseases gt
  0.1.

5
Case/Control study
Given a population of n genotypes each containing
values of m SNPs and disease status.
Disease Status
SNPs
0101201020102210 0220110210120021 0200120012221110
0020011002212101 1101202020100110 012012001010001
1 0210220002021112 0021011000212120
0 0 0 0 1 1 1 1
Case genotypes
Control genotypes
Disease association analysis searches for
risk (resistance) factor of a disease.
6
Risk/Resistance factors

• one SNP with fixed allele value

0 1 1 0 1 2 1 0 2 case
present in 4 cases 2 control
0 1 1 1 0 2 0 0 1 case
0 0 1 0 0 0 0 2 1 case
0 1 1 1 1 2 0 0 1 case
0 0 1 0 1 1 1 0 2 control
Third SNP with fixed allele value 1 is a risk
factor
0 1 0 0 1 1 0 0 2 control
0 1 1 0 1 2 0 0 2 control

• multi-SNP combination (MSC) subset of SNPs with
  fixed values

0 1 1 0 1 2 1 0 2 case
0 1 1 1 0 2 0 0 1 case
0 0 1 0 0 0 0 2 1 case
0 1 1 1 1 2 0 0 1 case
present in 3 cases 1 control
0 0 1 0 1 1 1 0 2 control
0 1 0 0 1 1 0 0 2 control
0 1 1 0 1 2 0 0 2 control
x x 1 x x 2 x x x
MSC
Cluster (C) - subset of genotypes which share the
same MSC C d(C) cases in
cluster(C) , h(C) controls in cluster(C)
7
Significance of Risk/Resistance Factors

• Measured by
• Relative risk (RR) a ratio of event probability
  occurring in the cases versus controls
• Odds ratio (OR) compares whether the probability
  of a certain event is the same for two groups
• P-value probability of obtaining at least the
  same case/control distribution among exposed to
  risk factor, assuming null hypothesis (happened
  by chance)
• Unadjusted p-value (computed by binomial
  distribution)

where
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Multiple-testing adjustment

• Bonferroni
• easy to compute
• overly conservative
• reported SNP is among 100 tests gt p-value100
• Randomization
• Randomly permute the disease status gt 10000
  samples
• Apply searching methods to each sample and get
  MSCs
• Count of MSCs unadjusted p-value lt the
  observed p-value
• If this lt 500 gt MSC is significant
• computationally expensive
• more accurate
• statistically significant adjusted p-value lt
  0.05

9
Outline

• Introduction
• Disease Association Search
• Disease Association Problem
• Exhaustive and Combinatorial Searches
• Maximum Control-Free Cluster
• Complimentary Greedy Algorithm
• Complimentary Greedy Search
• CGS Results
• Future
• Disease Susceptibility Prediction

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Disease Association Search
Problem Given a case/control study data
consisting of n genotypes
(haplotypes), each containing values of m SNPs
and disease status (case or control) Find
(all) Risk/Resistance factors (MSCs) with
multiple testing adjusted p-value
below 0.05
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Exhaustive Combinatorial Searches

• Exhaustive search (ES)
• complete (infeasible)
• sample with n genotypes and m SNPs requires
  O(n3m)
• Combinatorial search (CS)
• Case-closure of MSC C is a MSC C (with
  maximum number of SNPs with fixed values),which
  consists of the same set of case as C and
  minimum number of controls individuals from C.
• Efficient way for finding case-closure
  Extend MSC with those SNPs that have common
  values in all cases.
• Searches only among closed clusters
• Closure of cluster (C) cluster (C)
• d(C)d(C) and h(C) is minimized
• Avoids checking of trivial MSCs
• faster than ES, but still too slow for large data
• Tagging(indexing) multiple regression method
• ES and CS find more statistically significant
  MSCs on indexed data.

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Maximum Control-Free Cluster

• Maximum Control-Free Cluster Problem
• Given case/control study
• Find cluster (C) that is does not contain
  controls and has the maximum number of cases.
• It is maximum control-free cluster.
• Maximal Control-Free Cluster Risk Factor
• Maximal Disease-Free Cluster Resistance Factor
• Complexity
• Includes max independent set problem
• NP complete
• However,
• Sample S is not arbitrary

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Complimentary Greedy Algorithm

• Algorithm
• Start with Clt-S
• Repeat until h(C)gt0 (control-free)
• For each SNP s with value i find
• hh(C)-h(C ? s)
• dd(C) d(C ? s)
• Find SNP (s, i) minimizing d/h
• Add s to MSC
• Min vertex cover picking and removing vertices
  of maximum degree until no edges left

14
Complimentary Greedy Search (CGS)

• Algorithm (covering)
• Start with empty MSC that is present in all
  genotypes
• Find SNP with allele value, that define a set of
  genotypes with highest ratio of controls over
  cases (Max(controls/cases))
• Remove it
• Add the SNP to resulted MSC
• Repeat 2-3 until all controls are removed
• Output resulted MSC
• Adjust to multiple testing the p-value of the
  resulted MSC

Cases
Controls
15
CGS Results

• CGS finds MSCs with non-trivially high
  association on real data
• CGS finds more significant MSCs on full dataset
  than CS on indexed in reasonable amount of time

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Future

• Clustering algorithm
• Instead of removing found cluster for
  maximum control-free cluster problem, redefine
  controls in the cluster as cases (redefinition is
  visible only for controls in sample).

Cases
Controls
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Outline

• Introduction
• Disease Association Search
• Disease Susceptibility Prediction
• Disease Susceptibility Prediction Problem
• Cross-Validation Tests
• Quality Measures of Prediction
• Prediction Methods
• Optimum Disease Clustering Problem
• From Clustering to Prediction
• Leave-One-Out Results
• CDC Algorithm
• Experiments
• Plans

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Disease Susceptibility Prediction
Problem

• Given Case/Control study
• Genotype of a testing individual
  t
• Find The disease status of the testing
  individual

Disease Status
SNPs
0101201020102210 0220110210120021 0200120012221110
0020011002212101 1101202020100110 012012001010001
1 0210220002021112 0021011000212120
0 0 0 0 1 1 1 1
Case genotypes
Control genotypes
testing - gt
0110211101211201
?
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Cross-validation tests

• Leave-one-out test
• The disease status of each genotype in the data
  set is predicted while the rest of the data is
  regarded as the training set

Real Disease Status
Predicted Disease Status
Genotype
0
0
0101201020102210
0
0
0220110210120021
Accuracy 80
0
1
0200120012221110
1
1
0020011002212101
1
1
0020011002212101

• Leave-many-out test
• Repeat randomly picking 2/3 of the population as
  training set and predict the other 1/3

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Quality Measures of Prediction

• Sensitivity The ability to correctly detect
  cases.
• Sensitivity
  TP/(TPFN)
• Specificity The ability to avoid calling control
  as case.
• Specificity
  TN/(FPTN)
• Accuracy (TP TN)/(TPFPFNTN)
• Risk Rate Measurements for risk factors

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Prediction Methods

• Support Vector Machine
• Random Forest
• LP-based prediction

• Drawback of the prediction problem formulation
• need of cross-validation ? no optimization

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Optimum Disease Clustering Problem

• Given Case/Control study S
• Find partition P of S into clusters S
  S1?..?Sk , with disease status 0 or 1 assigned to
  each cluster Si , minimizing entropy(P) for a
  given bound on the number of individuals who are
  assigned incorrect status in clusters in
  partition P

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From Clustering to Prediction

• Intuition
• If tested genotype is predicted correctly then
  optimum clustering will have smaller entropy
• Model-Fitting Prediction Algorithm
• Set status of testing genotype t to case
• Find optimum clustering P0 of the dataset S U
  t
• Set status of testing genotype to control
• Find optimum clustering P1 of the dataset S U t
• Find the clustering, which is better fits to
  model (has smaller enthropy), and accordingly
  predict status

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Leave-One-Out Results

• Leave-one-out cross validation results of four
  prediction methods for three real data sets.
  Results of combinatorial search-based prediction
  (CSP) and complimentary greedy search-based
  prediction (CGSP) are given when 20, 30, or all
  SNPs are chosen as informative SNPs.

25
CDC Algorithm (B.N. Goertzel Combinations of
SNPs in neuroendocrine effector and receptor
genes predict chronic fatique syndrome,
Pharmacogenomics(2006),7(3))

• Find the best pattern strength classifier for
  training sample S
• - all subsets of SNPs with cardinality less
  than k potential rules.
• - For each potential rule
• - evaluate each genotype g from S
• for each SNP in the potential
  rule
• if this SNP has value 0 or
  1 in g gt add 2 for a sum
• if the value is
  2gt add 1.
• - set threshold
• sum_casesltthresholdsum_controlsgtt
  hreshold -gt min
• - compute accuracy
• - pattern strength classifier potential
  rule with the maximum accuracy.
• Predict status of tested individual
• - compute the sum for a tested individuals
• for each SNP in the pattern strength
  classifier
• if this SNP has value 0 or
  1 gt add 2 for a sum
• if the value is 2gt add 1.
• - if the sum is less than threshold gt
  control,
• otherwise
  gt case.

26
Experiments

• Different mask for sum in evaluation.
• Experiments with swap SNPs if SNP is more
  associated with controls.

27
Plans

• Finish Leave-one-out for all sum masks.
• CDC method is slow
• CDC method exhaustively search the best pattern
  strength classifier
• If there is any way to take it in greedy way?