Exhaustive Search ES:

1

• If the reported SNP is found among 100 SNPs then
  the probability that the SNP is associated with a
  disease by
• mere chance becomes 100 times larger
  (Bonferroni).
• Bonferroni is too crude (e.g., 3-SNP
  combinations among 100 SNPs, p lt 0.0510-6)
• We adjust resulted p-values via randomization
• Unadjusted p-value Probability of case/control
  distribution in a set defined by MSC, computed by
  binomial distribution
• Multiple-testing adjusted p-value
  randomization
• Randomly permute the disease status of the
  population to generate 1000 instances.
• Apply searching methods on each instance to get
  MSCs.
• Compute the probability of MSCs that have a
  higher unadjusted p-value than the observed
• p-value.
• In our search we report only MSC with adjusted
  p-value lt 0.05

Human Genome and SNP
Disease association analysis

• Length of Human Genome ? 3 ? 109 base pairs
• Difference between any two people ? 0.1 of
  genome
• Total number of single nucleotide polymorphisms
  (SNP) ? 3 ? 106
• SNP - single nucleotide site where two or more
  different
• nucleotides occur in a large percentage of
  population
• 0 willde type/major (frequency) allele
• 1 mutation/minor (frequency) allele
• International HapMap project
• SNP maps are constructed across the human
• genome with density of about one SNP per
• thousand nucleotides.
• HapMap tries to identify 1 million tag SNPs
• providing almost as much mapping informa-
• tion as entire 10 million SNPs
• Unfortunately, not as much known about SNP
• combinations
• HapMap initial budget was 100Million dollars
• Due today around 1.5Million SNPs are typed

• Analysis of variation in suspected genes in
  disease and nondisease individuals is aimed at
  identifying SNPs with considerably higher
  frequencies among the disease individuals than
  among the nondisease individuals
• Most searches are done on a SNP-by-SNP basis
• Recently two-SNP analysis shows promising results
  (Marchini et al, 2005)
• Multi-SNP analyses are expected to find even
  stronger disease associations
• Common diseases can be caused by combinations of
  several unlinked gene (SNPs) variations
• We address the computational challenge of
  searching for such multi-gene causal combinations
  
• The number of multi-SNP combinations is
  infeasible high (3100 for 100 SNPs).
• How to find associated multi-SNP combinations
  without total checking?
• Disease association analysis searches for a SNPs
  or multi-SNP combinations with frequency among
  disease individuals considerably higher than
  among nondisease individuals.

Our contributions

• A novel combinatorial method for finding disease-
  associated multi-SNP combinations was
  developed.
• Multi-SNP combinations significantly associating
  with diseases were found.
• For Crohn's disease data (Daly, et al., 2001), a
  few associated multi-SNP combinations with
  multiple-testing-adjusted to p lt 0.05 were found,
  while no single SNP or pair of SNPs showed
  significant association.
• For a dataset for an autoimmune disorder (Ueda,
  et al., 2003), a few previously unknown
  associated multi-SNP combinations were found.
• For tick-borne encephalitis virus-induced
  disease, a multi-SNP combination within a group
  of genes showing a high degree of linkage
  disequilibrium significantly associated with the
  severity of the disease was found.

MSC
x x 1 x x 2 x x x
0 1 1 0 1 2 1 0 2 sick
Genetic epidemiology
0 1 1 1 0 2 0 0 1 sick
4 sick 1 healthy
0 0 1 0 0 0 0 2 1 sick
0 1 1 1 1 2 0 0 1 sick
check significance
0 0 1 0 1 2 1 0 2 sick

• Searching for genetic risk factors for diseases
• Monogenic diseases
• A mutated gene is entirely responsible for the
  disease
• Typically rare in population lt 0.1
• Practically all cases are already reported
• Complex diseases
• Affected by the interaction of multiple genes
• Significance of risk factor is usually measured
  by Risk Rate or _ _ _Odds Ratio
• We measure significance by the p-value of the
  set of genotypes _defined by risk factor

0 1 0 0 1 1 0 0 2 healthy
0 1 1 0 1 2 0 0 2 healthy
Statistical significance
Disease-Associated Multi-SNP Combinations Search

• Multi-SNP combination (MSC) define a set of
  disease and nondisese individuals
• MSC is considered statistically significant if
  the frequency of disease and nondisese
  distribution has p-value lt 0.05
• A lot of reported findings are frequently not
  reproducible on different populations. It is
  believed that this happens because the p-values
  are unadjusted to multiple testing

• Given a population of n genotypes (or
  haplotypes) each containing values of m SNPs from
  0,1,2 and disease status (diseased or
  nondisease)
• Find all multi-SNP combinations with multiple
  testing adjusted p-value of the frequency
  distribution below 0.05

• Disease-closure allow finding of the
  statistically significant MSC on the earlier
  stage of searching.
• Trivial MSCs and MSCs which coincide after
  disease-closure are avoided. That significantly
  speedups the searching.
• Faster than ES
• Finds more significant association on the early
  stage of searching
• Still slow for wide-genome studies
• Searching level number of SNPs which define MSC
  before disease-closure
• Indexed Combinatorial Search (ICS)
• Combinatorial search on the indexed datasets
  obtained by extracting k indexed SNPs with MLR
  based tagging method.
• Can perform complete searching for the larger
  datasets

Proposed searching methods
Results/comparison of searching methods

• Exhaustive Search (ES)
• In order to find a multi-SNP combination with
  the p-value of the frequency distribution below
  0.05, it checks all one-SNP, two-SNP, ..., m-SNP
  combinations.
• Runtime is O(n3m) making complete searching
  unfeasible even for small numbers of SNPs m
• We restrict searching to 1,2,3,4,5 SNPs
• Searching level number of SNPs which
  participate in MSC
• Indexed Exhaustive Search (IES)
• Exhaustive search on the indexed datasets
  obtained by extracting k indexed SNPs with MLR
  based tagging method.
• MLR - multiple linear regression based tagging
  method (He and Zelikovsky, 2006).
• The tradeoff between the number of chosen
  indexing SNPs and quality of reconstruction
  requires choosing the maximum number of index
  SNPs that can be handled by ES in a reasonable
  computational time.
• Can perform complete searching for the larger
  datasets
• For wide-genome study number of tags cant be
  reduced to 5-10 tags. Therefore, IES will not be
  able to perform complete search

• The relative qualities of the searching methods
  are compared using the number of statistically
  significant multi-SNP combinations found.
• The statistical significance was adjusted to
  multiple testing and the adjusted 0.05 threshold
  is shown (third column).
• In the 4th, 5th and 6th columns, we give the
  frequencies of the best multi-SNP combination
  among disease and nondisease populations and the
  unadjusted p-value, respectively.

Data Sets

• Crohn's disease 387 genotypes with 103 SNPs
  derived from the 616 KB region of human
  Chromosome 5q31, 144 disease genotypes and 243
  nondisease genotypes. (Daly et al., 2001).
• Autoimmune disorder 1024 genotypes with 108
  SNPs containing gene CD28, CTLA4 and ICONS, 378
  disease genotypes and 646 nondisease genotypes.
  (Ueda et al., 2003).
• Tick-borne encephalitis 75 genotypes with 41
  SNPs containing gene TLR3, PKR, OAS1, OAS2, and
  OAS3, 21 disease genotypes and 54 nondisease
  genotypes. (Barkash et al., 2006).

Discussion

• Comparing indexed counterparts with ES and CS
  shows that indexing is quite successful. Indeed,
  the indexed searches found the same multi-SNP
  combinations as the non-indexed searches but were
  much faster and the multiple-testing adjusted
  0.05-threshold was higher and easier to meet.
• Comparing the CS with the ES counterparts is
  advantageous to the former. Indeed, for the
  Crohn's disease data (Daly.et al., 2001), the ES
  on the first and second search levels is
  unsuccessful while the CS finds several
  statistically significant multi-SNP combinations.
  Similarly, for the tick-borne encephalitis
  virus-induced disease data, the CS and ICS(20)
  found a significant association on the first
  level while no association was found by the ES or
  IES(20). For the autoimmune disorder data
  (Ueda.et al., 2003), the CS found many more
  statistically significant multi-SNP combinations
  then the ES.
• We conclude that the proposed indexing approach
  and the combinatorial search method are very
  promising techniques for searching for
  statistically significant diseases-associated
  multi-SNP combinations and disease susceptibility
  prediction.