A coalescent computational platform to predict strength of association for clinical samples Gabor T. Marth Department of Biology, Boston College Genomic studies and the HapMap March 15-18, 2005 Oxford, United Kingdom

Focal questions about the HapMap CEPH European samples 1. Required marker densityYoruban samples 4. How general the answers are to these questions among different human populations 2. How to quantify the strength of allelic association in genome region 3. How to choose tagging SNPs

Across samples from a single population? (random 60-chromosome subsets of 120 CEPH chromosomes from 60 independent individuals)

Possible consequence for marker performance Markers selected based on the allele structure of the HapMap reference samples… … may not work well in another set of samples such as those used for a clinical study.

How to assess sample-to-sample variability? 1. Understanding fundamental characteristics of a given genome region, e.g. estimating local recombination rate from the data 3. It would be a desirable alternative to generate such additional sets with computational means McVean et al. Science Experimentally genotype additional sets of samples, and compare association structure across consecutive sets directly

Towards a marker selection tool 2. generate computational samples 3. test the performance of markers across consecutive sets of computational samples 1. select markers (tag SNPs) with standard methods

Generating additional computational haplotypes 1. Generate a pair of haplotype sets with Coalescent genealogies. This “models” that the two sets are “related” to each other by being drawn from a single population. 3. Use the second haplotype set induced by the same mutations as our computational samples. 4. In subsequent statistics, weight each such set proportional to the data likelihood calculated in Enforce data-relevance by requiring that the first set reproduces the observed haplotype structure of the HapMap reference samples. Calculate the “degree of relevance” as the data likelihood (the probability that the genealogy does produce the observed haplotypes).

Generating computational samples Problem: The efficiency of generating data- relevant genealogies (and therefore additional sample sets) with standard Coalescent tools is very low even for modest sample size (N) and number of markers (M). Despite serious efforts with various approaches (e.g. importance sampling) efficient generation of such genealogies is an unsolved problem. N M We propose a method to generate “approximative” M-marker haplotypes by composing consecutive, overlapping sets of data-relevant K-site haplotypes (for small K)

Approximating M-site haplotypes as composites of overlapping K-site haplotypes 1. generate K-site sets 2. build M-site composites M

Piecing together neighboring K-site sets hope that constraint at overlapping markers preserves for long-range marker association

Building composite haplotypes

Initial results: 3-site composite haplotypes a typical 3-site composite 30 CEPH HapMap reference individuals (60 chr)

3-site composite vs. data

3-site composites: the “best case” the “best-case” 3-site scenario: composite of exact 3-site sub- haplotypes “short-range” “long-range”

Variability across sets The purpose of the composite haplotypes sets … … is to model sample variance across consecutive data sets. But the variability across the composite haplotype sets is compounded by the inherent loss of long-range association when 3-sites are used.

4-site composite haplotypes 4-site composite

“Best-case” 4 site composites Composite of exact 4-site sub-haplotypes

Variability across 4-site composites

… is comparable to the variability across data sets.

Technical/algorithmic improvements 3. dealing with uninformative markers 1. un-phased genotypes 2. markers with unknown ancestral state (AC)(CG)(AT)(CT) A G A C C C T T AC ? taking into account local recombination rare

Software engineering aspects: efficiency Currently, we run fresh Coalescent simulations at each K-site (several hours per region). This discards most Coalescent genealogies as irrelevant. Total # genotyped SNPs is ~ 1 million -> 1 million different K-sites to match. Any given Coalescent genealogy is likely to match one or more of these. Haplotype sets resulting from matches can be loaded into, stored in, and retrieved from a database efficiently. 4 HapMap populations x 1 million K-sites x 1,000 comp sets x 50 bytes < 200 Gigabytes

Acknowledgements Eric Tsung Aaron Quinlan Ike Unsal Eva Czabarka (Dept. Mathematics, William & Mary)

Testing markers with composite sets

Using the HapMap 1. genotype a set of reference samples 2. compute strength of association 4. use these markers in clinical studies 3. select a smaller set of markers that capture most of the information present in the complete set of markers

Allele structure varies among populations CEPH European samples Yoruban samples

Data probability for composite haplotypes (motivation from composite likelihood methods for recombination rate estimation e.g. by Hudson, Clark, Wall) Pr(composite) = Pr(K-site 1 ) Pr(K-site 1 ~ K-site 2 )Pr(K-site 2 ) Pr(K-site 2 ~ K-site 3 )Pr(K-site 3 )

Generating K-site haplotypes reference data 1 match / 100 – 10,000 Coalescent genealogies K=3,4

Example: CFTR gene Hinds et al. Science, 2005

4-site composite haplotypes 4-site composite #14-site composite #2 HapMap data

4-site composites vs. data

Why should this work? tease apart two questions: (1) to what degree K-site composites preserve long-range correlations between markers (really, the quality of the approximation) and (3) the variability across different sets (what we are interested in).

Example: 4-site approximation 4-site composite #1 4-site composite #2 4-site composite #3 4-site composite #4