Combinatorial Methods for Disease Association Search and Susceptibility Prediction Alexander Zelikovsky joint work with Dumitru Brinza Department of Computer Science

2 Outline SNPs, Haplotypes and Genotypes Disease Association Search Genome-wide association search challenges Problem formulation Exhaustive & Combinatorial Search Optimization formulation & complimentary greedy search Predicting susceptibility to complex diseases Problem formulation/cross-validation Previous methods: SVM, RF, LP Optimum clustering and prediction via model-fitting Conclusions

3 Length of Human Genome  3  10 9 #Single nucleotide polymorphism (SNPs)  1  10 7 SNPs are mostly biallelic, e.g., A  C Minor allele frequency should be considerable e.g. >.1% Difference b/w ALL people  0.25% (b/w any 2  0.1%) Diploid = two different copies of each chromosome Haplotype = description of a single copy (expensive) example: (0 is for major, 1 is for minor allele) Genotype = description of the mixed two copies example (0=00, 1=11, 2=01) International Hapmap project: SNP, Haplotypes, Genotypes

4 Challenges of Disease Association Monogenic disease A mutated gene is entirely responsible for the disease. Typically rare in population: < 0.1%. Complex disease Interaction of multiple genes 2-SNP interaction analysis for a genome-wide scan with 1 million SNPs (3 kb coverage) has pairwise tests Multiple independent causes Each cause explains < 10-20% of cases Common: > 0.1%. In NY city, 12% of the population has Type 2 Diabetes Multiple testing adjustment Reason for non-reproducible findings

5 Disease Association Search Problem Disease Status Non-diseased genotypes: H Sample population S of individual genotypes Risk/resistance factor = multi-SNP combination (MSC) a subset of SNP-columns of S the values of these SNPs, 0, 1, or 2 Cluster C= subset of S with an MSC, d(C) = diseased, h(C) = non-diseased PROBLEM: Find all MSCs significantly associated with the disease Diseased genotypes: D SNPs

6 Significance of Risk/Resistance Factors Measured by Relative risk (RR) Odds ratio (OR) Their p-values Unadjusted p-value: Probability of case/control distribution among exposed to risk factor, computed by binomial distribution Multiple-testing adjustement: Bonferroni easy to compute overly conservative Randomization computationally expensive more accurate

7 Exhaustive & Combinatorial Search Exhaustive search is infeasible sample with n genotypes/m SNPs requires O(n 3m ) Combinatorial search Definition: Disease-closure of a multi-SNP combination C is a multi-SNP combination C’, with maximum number of SNPs, which consists of the same set of disease individuals and minimum number of nondisease individuals. Searches only closed clusters Closure of cluster C = C’ d(C’)=d(C) and h(C’) is minimized Avoids checking of trivial MSCs Small d(C) implies not looking in subclusters Finds faster associated MSCs but still too slow Tagging: compress S by extracting most informative SNPs restore other SNPs from tag SNPs multiple regression method

8 MLR Tagging Stepwise Index SNP Algorithm: Choose as a tag the SNP which best predicts all other SNPs Choose the next one which together with a first best predicts all other SNPs and so on. Prediction method is based on Multiple Linear Regression (MLR) So far beats in quality other methods (STAMPA)

9 Data Sets Crohn's disease (Daly et al ): inflammatory bowel disease (IBD). Location: 5q31 Number of SNPs: 103 Population Size: 387 case: 144 control: 243 Autoimmune disorders (Ueda et al) : Location: containing gene CD28, CTLA4 and ICONS Number of SNPs: 108 Population Size: 1024 case: 378 control: 646 Tick-borne encephalitis dataset of (Barkash et al) : Location: containing gene TLR3, PKR, OAS1, OAS2, and OAS3. Number of SNPs: 41 Population Size: 75 case: 21 control: 54

10 Disease association search results IES(30): exhaustive search 30 indexed SNPs with MLR based tagging method ICS(30): combinatorial search 30 indexed SNPs with MLR based tagging method.

11 Disease Association Search Optimum Association Search Problem: Find MSC that is the most associated with the disease Measure: positive predictive value = find (non-)diseased-free cluster of maximum size Bad news: Generalization of max independent set NP complete and cannot be well approximated Hope: sample S is not arbitrary

12 Complimentary Greedy Algorithm Algorithm Start with C=S (resp. MCS is empty) Repeat until h(C)=0 (non-diseased-free) Find 1-SC s maximizing (h(C)-h(C  {s})) / (d(C) – d(C  {s})) = minimize payment with diseased for removal of non-diseased Add s to SNPs of C’s MSC Analogy: finding independent set by greedy removing highest degree vertecies Extremely fast but inaccurate Can be used in susceptibility prediction

13 Most disease-associated & disease-resistant MSC Comparison of three methods for searching the disease-associated and disease- resistant multi-SNPs combinations with the largest PPV. The starred values refer to results of the runtime-constrained exhaustive search

14 Genetic Susceptibility Prediction Given: Genotypes of diseased and non-diseased individuals, Genotype of a testing person. Find: The disease status of the testing person GenotypeDisease Status healthy sick testing - g t s(g t )

15 Cross-validation 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 Leave-many-out test: Repeat randomly picking 2/3 of the population as training set and predict the other 1/3. 1 Genotype Real Disease Status 1 Predicted Disease Status Accuracy = 80%

16 Quality Measures of Prediction (confusion table) Sensitivity: The ability to correctly detect disease. sensitivity = TP/(TP+FN) Specificity: The ability to avoid calling normal as disease. specificity = TN/(FP+TN) Accuracy = (TP +TN)/(TP+FP+FN+TN) Risk Rate: Measurements for risk factors. Prediction Disease +- Test + True PositiveFalse Positive (TP)(FP) - False NegativeTrue Negative (FN)(TN)

17 Prediction Methods Support vector machine Random forest LP-based prediction

18 Prediction via Clustering Drawback of the prediction problem formulation = need of cross-validation  no optimization Clustering P = partition into clusters defined by MSC’s Minimizing number of errors S.t. bounded information entropy –∑(S i /S) log(S i /S) Model-fitting prediction Set status of testing genotype to diseased Find number of errors Set status of testing genotype to diseased Find number of errors Predict status that implies lesser number of errors

19 Leave-1-out cross-validation results Leave-one-out cross-validation for 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.

20 ROC curve Comparison of 5 prediction methods on (Barkash et. al,2006 ) data on all SNPs. Area under the CSP ’ s curve is 0.81 vs 0.52 under the SVM ’ s curve.

21 Conclusions Combinatorial search is able to find statistically significant multi-gene interactions, for data where no significant association was detected before Complimentary greedy search can be used in susceptibility prediction Optimization approach to prediction New susceptibility prediction is by 8% higher than the best previously known MLR-tagging efficiently reduces the datasets allowing to find associated multi-SNP combinations and predict susceptibility

22 International Symposium on Bioinformatics Research and Applications May 6-9, 2007, Georgia State University, Atlanta, Georgia Submissions must and must not exceed 12 pages in Springer LNCS style The proceedings of ISBRA 2007 will be published in LNBI Important Dates Submission DeadlineNotification of AcceptanceFinal Version Submission December 20, 2006January 31, 2007February 21, 2007 Symposium Organizers General Chairs: Dan Gusfield (University of California, Davis) and Yi Pan (Georgia State University) Program Chairs: Ion Mandoiu (University of Connecticut) and Alexander Zelikovsky (Georgia State University) ISBRA provides a forum for the exchange of ideas and results among researchers, developers, and practitioners working on all aspects of bioinformatics and computational biology and their applications

23 History of ISBRA ISBRA is the successor of the International Workshop on Bioinformatics Research and Applications (IWBRA), held on - May 22-25, 2005 in Atlanta, GA and - May 28-31, 2006 in Reading, UK in conjunction with the International Conference on Computational Science The two editions of IWBRA have enjoyed a great success, with special issues devoted to full versions of selected papers in Springer LNCS Transactions on Computational Systems Biology and IEEE/ACM Transactions on Computational Biology and Bioinformatics

24 Support Vector Machine (SVM) Algorithm Learning Task Given: Genotypes of patients and healthy persons. Compute: A model distinguishing if a person has the disease. Classification Task Given: Genotype of a new patient + a learned model Determine: If a patient has the disease or not. Linear SVMNon-Linear SVM

25 Random Forest Algorithm Random Forests grows many classification trees. To classify a new object from an input vector, put the input vector down to each tree in the forest. Each tree gives a classification, and we say the tree “votes” for that class. The forest chooses the classification having the most votes (over all the trees in the forest). Growing Tree, Split selection and Prediction. Random sub-sample of training data, Random splitter selection.

26 LP-based Prediction Algorithm Model: Certain haplotypes are susceptible to the disease while others are resistant to the disease. The genotype susceptibility is assumed to be a sum of susceptibilities of its two haplotypes. Assign a positive weight to susceptible haplotypes and a negative weight to resistant haplotypes such that for any control genotype the sum of weights of its haplotypes is negative and for any case genotype it is positive. For each vertex-haplotype h i assign the weight p i, such that for any genotype-edge e i,j =(h i,,h j ) where s(e i,j )  {-1,1} is the disease status of genotype e i,j. The sum of absolute values of genotype weights is maximized.