Merlin - M ultipoint E ngine for R apid L ikelihood In ference

1. Merlin - Multipoint Engine for Rapid Likelihood Inference Ido Feldman Merlin - Multipoint Engine for Rapid Likelihood Inference

2. Agenda • What’s wrong with Genehunter • What’s Merlin • Merlin from the user’s viewpoint • Merlin: Pro’s and Con’s • Algorithms and Ideas Merlin - Multipoint Engine for Rapid Likelihood Inference

3. What’s wrong with Genehunter? • The running time / memory is exponential in the size of the pedigree. • Intractable for pedigrees larger than 22-23. • Ideal Solution: Finding an algorithm which is polynomial in pedigree size and markers. • No such luck so far… We’ll try to improve the constants. Merlin - Multipoint Engine for Rapid Likelihood Inference

4. Merlin is an improved Genehunter • Pedigree error detection • Pedigree simplification • Smart inheritance vectors • Efficient and approximate computations Merlin - Multipoint Engine for Rapid Likelihood Inference

5. Merlin – Getting Started • Input consists of 3 files: • Pedigree file • Data file (elaborated later) • Map file (contains marker data) Merlin - Multipoint Engine for Rapid Likelihood Inference

6. Merlin Input – Pedigree Example Family Person Parent1 Parent2 Sex Diabetes Glucose HLA-DR HLA- DQ 1 1 0 0 1 1 x 3 3 4 3 1 2 0 0 2 1 3.000 4 4 1 1 1 3 0 0 1 1 8.000 1 2 x x 1 4 1 2 2 1 3.500 4 3 1 4 1 5 3 4 2 2 1.234 1 3 3 4 1 6 3 4 1 2 4.321 2 4 1 1 1 7 0 0 1 1 5.500 1 2 4 2 1 8 7 4 2 1 6.231 1 4 4 1 2 1 0 0 1 1 6.000 4 3 1 4 2 2 0 0 2 2 7.000 3 4 5 3 2 3 0 0 1 1 7.700 1 2 2 4 2 4 1 2 2 1 4.000 4 3 1 5 2 5 0 0 2 1 3.600 3 5 2 4 2 6 3 4 1 2 1.234 1 3 1 4 2 7 3 4 1 2 3.321 2 4 2 5 2 8 3 4 2 1 5.175 1 4 1 5 2 9 5 6 2 2 0.512 3 3 4 4 Merlin - Multipoint Engine for Rapid Likelihood Inference

7. Merlin Input – Data file • Link column name to type. • A diabetes (A =Affected/Not Affected) • T glucose (T = Trait) • M HLA-DR (M = Marker) • M HLA-DQ • It’s possible to encode twins status Merlin - Multipoint Engine for Rapid Likelihood Inference

8. Advantages and Disadvantages • Pros: • Merlin is VERY fast. • Multipoint IBD calculations are exact. • Cons: • Can’t handle very large pedigrees (but still better than Genehunter!) Merlin - Multipoint Engine for Rapid Likelihood Inference

9. Merlin is fast! – Example pedigrees Merlin - Multipoint Engine for Rapid Likelihood Inference

10. Merlin is fast! – Results Merlin - Multipoint Engine for Rapid Likelihood Inference

11. Merlin needs less memory • Due to the smart storage of inheritance vectors, less memory is consumed in compare to Genehunter. • Example pedigree: Genehunter – 1024MB • Exact Merlin: 100MB • Approximate Merlin: 4MB-54MB • Automatic disk-swapping. Merlin - Multipoint Engine for Rapid Likelihood Inference

12. Pedigree Simplifications • Tear families apart… 2 1 1 3 4 5 6 7 Merlin - Multipoint Engine for Rapid Likelihood Inference

13. More Pedigree Simplifications • Remove unneeded people… 2 1 3 4 5 Merlin - Multipoint Engine for Rapid Likelihood Inference

14. Input Error Correction C/D A/B • Discovers impossible genotypes. • Report of unlikely recombinations. • Mistakes are ambiguous  reports the most likely mistake. A/C A/B Merlin - Multipoint Engine for Rapid Likelihood Inference

15. From IV to packed tree Inheritance Vector: 0 1 . . . n 1st Meiosis 0 0 1 Packed Tree: 1 1 2nd Meiosis 0 1 0 1 2 2 2 2 Merlin - Multipoint Engine for Rapid Likelihood Inference

16. From packed trees to sparse trees • Idea: Prune unneeded sub trees. • Sub-trees with zero likelihood • Symmetric nodes – Seeing one is like seeing the rest • Pruning at level i removes a sub tree of size O(2n-i). • IV order is important! Merlin - Multipoint Engine for Rapid Likelihood Inference

17. 0 1 . . . . Case 1: Zero Likelihood a/A A/A Any IV with IV[0]=0 is of zero likelihood! A/A Merlin - Multipoint Engine for Rapid Likelihood Inference

18. 1 1 . . . . Case 2: Symmetric Nodes a/A A/A A vector with a IV[1]=0 have a twin with IV[1]=1 A/A Merlin - Multipoint Engine for Rapid Likelihood Inference

19. L L L L L L L L 1 2 1 2 1 2 1 2 Sparse: Legend Node with zero likelihood Node identical to sibling L L L L 1 2 Likelihood for this branch 1 2 From Packed tree to Sparse Trees Packed: Merlin - Multipoint Engine for Rapid Likelihood Inference

20. H1 H2 Hi X1 X2 Xi Every member in the matrix is of the form: {step i} P(x1,…,xi,hi) =  P(x1,…,xi-1, hi-1) P(hi | hi-1 ) P(xi | hi) hi-1 Reminder: The forward algorithm Note that in Step i of the forward algorithm, we multiply a transition matrix of size 22n x 22n with vectors of size 22n. Merlin - Multipoint Engine for Rapid Likelihood Inference

21. 1 2 3 4 5 6 1 1 1 2 1 1 1 3 1 11 4 1 1 5 1 1 6 1 1 Transition matrix is a bottleneck • Matrix-Vector Multiplication: θ(N2) • In our case, N=22n. • If the matrix was sparse (k<<N2), it was easy. Trivial Implementation: List of lists Merlin - Multipoint Engine for Rapid Likelihood Inference

22. Multipoint analysis in dense maps • Idea: Close markers  Negligible chance for consecutive recombination. • Used for approximate solutions. • Allowing <3 recombinants give an almost exact solution. • But 3 times faster, and with half the memory. Merlin - Multipoint Engine for Rapid Likelihood Inference

23. Summary • Detects data errors and unlikely data. • Simplifies pedgirees. • Use sparse trees to exploit symmetries and impossible data. • Use sparse matrix to ease matrix-vector multiplication. • Open source. Merlin - Multipoint Engine for Rapid Likelihood Inference

24. More info • http://bioinformatics.well.ox.ac.uk/Merlin • “Merlin - rapid analysis of dense genetic maps using sparse gene flow trees", Gonçalo R. Abecasis, Stacey S. Cherny, William O. Cookson, and Lon R. Cardon. Nat Genet. 2002 Jan;30(1):97-101 Merlin - Multipoint Engine for Rapid Likelihood Inference

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