1	Backward Haplotype Transmission Association (BHTA) Algorithm — A Fast Multi-point Screening Method for Complex Traits Tian Zheng Department of Statistics Columbia University
2	Acknowledgements This is a joint work with Professor Shaw-Hwa Lo at Columbia University.
3	Outline Introduction BHTA-based methods Algorithm details Marker selection procedures Examples Summary and Future efforts
4	Example of Complex Traits: BBS syndrome
5	Screening for Complex Traits Complex diseases —“… are caused by multiple genes interacting with each other and with environmental factors to create a gradient of genetic susceptibility to disease.” (Weeks and Lathrop 1995) “…there seems to be a great need for the development of multilocus tests of association that make use of haplotype information, since these might prove to be much more efficient.”—J. Pritchard and M. Przeworski (June 2001). Am. J. Hum. Genet. 69: 1-14
6	Current Multi-locus Approaches for complex traits Marker-by-marker strategies Sums of single-marker statistics Hoh, J et al (2001) Genome Res. 11: 2115-2119 Multifactor-dimensionality reduction (MDR) Richie, MD et al (2001) Am. J. Hum. Genet. 69:138-147
7	Ideal Marker Screening Method Start with a large set of candidate genetic markers; Screen out the markers with little information regarding the disease traits; Take into account of possible interactions among the disease genes; Time and Memory efficient.
8	BHTA—Introduction Backward Haplotype Transmission Association (BHTA) algorithm—A fast multi-point screening algorithm based on haplotypic transmission disequilibrium. Multipoint Screening Fast and memory-efficient Use haplotypic transmission information—taking into account interactions among disease susceptibility loci Automatically select a set of important markers as screening result
9	BHTA Algorithm Details Notations & statistics formulations Screening mechanisms Two-step marker selection procedure based on BHTA algorithm
10	Haplotype Transmission Disequilibrium Assume a parent of a patient has two haplotypes:
11	Haplotype Transmission Disequilibrium (continued)
12	Notation for Case-Parent Trio Haplotype Data Data: a random sample of n patients and their parents. 2n parent-patient transmission pairs; Each pair consists of two haplotypes; one transmitted and the other untransmitted. For pair, let be the haplotype transmitted to the diseased child, and be the untransmitted
13	Information Measure: Haplotype transmission Disequilibrium (HTD) Define counts: HTD is defined to measure the amount of linkage/LD information contained in the set of markers being tested
14	Idea of screening Assume m markers are being screened; The marker is to be evaluated; Consider (the -deleted set) The amount of information contributed by can be evaluated using the HTD difference—the information drop, which can used to measure the importance of to current marker set.
15	Marker Importance Measure Mathematical inference and formulation of Haplotype Transmission Association (HTA) where is the haplotype risk ratio.
16	Properties of HTA Statistic
17	BHTA Screening algorithm Backward Haplotype Transmission Association algorithm: Step0: Start with Step1: Calculate HTA for each retained in Step2: If all HTA are negative, stop; otherwise delete the marker with highest HTA; Step3: If , stop; otherwise continue to step1; Stop: return all markers retained in as selected markers
18	Example 1: a model with no marginal effects (Simulated)
19	Information Flow during BHTA
20	Issue of sparseness If the number of possible haplotypes is significantly larger than the number of observations, markers are deleted randomly. This is because the counts of haplotype transmissions are mostly 0's or 1's, hence the HTA scores based on these counts all cluster around zero, which makes the selection non-informative.
21	Two-step BHTA-based marker selection procedure Step 1: Randomly select k (15, for instance) markers out of the original set of K markers. Run BHTA on the selected markers and record the markers returned. Step 2: Repeat step 1 B times (e.g. B=5000). Selection: Markers whose returning frequencies are more than the quartile plus 1.5 times IQR (inter-quartile range) will be selected in the resulting set.
22	Relative Chance of Deletion During BHTA
23	Two-Step Selection Procedure Results on Example 1
24	Example 2: Simulated BBS-type Complex Traits
25	Summary BHTA based marker selection methods are haplotype-based so that they are capable of handling possible complicated interaction among disease loci; are formulated without specific disease model pre-assumed; can be applied to large-scale studies with hundreds of candidate markers; are time efficient—algorithm complexity is on the order of nm. (n is the number of patients, and m is the number of markers).
26	Current Efforts Variance of HTA and corresponding adjustments to the screening algorithm; Extension to genotype data; Extension to mapping of quantitative trait loci; Extension to gene expression data analysis.