A new method of fine-scale mapping of susceptibility genes with multiple ancestral haplotypes and allelic heterogeneity

The current emphasis of association study has shifted toward locating genes for common complex diseases. Whole-genome-association studies are proposed to search for complex disease susceptibility genes. Risch and Merikangas [1996] suggest that LD mapping can be a screening tool in general population for complex disease genes. Terwilliger and Weiss [1998] point out three models for a complex disease: (1) allelic homogeneity: a single disease allele with a single ancestral haplotype; (2) allelic heterogeneity: multiple unique but functionally equivalent alleles at a single disease gene; and (3) multiple alleles at multiple disease genes. Effective LD mapping methods for the second and the third disease models have not yet been developed. The existing association measures depend on marker allele frequencies under these models. The assumption of a single ancestral haplotype, i.e. the assumption that, when the disease gene was first introduced into the general population, all chromosomes carrying the disease gene have the same haplotype, is quite unrealistic. Closer to the reality may be for a rare Mendelian disease in an isolated population stemming from a small number of ancestors. It is definitely unrealistic for a common complex disease in general populations. Guo [1997] points out that under the more realistic assumption of multiple ancestral haplotypes, all measures for LD depend on marker allele frequencies and do not perform well. For many different methods of mapping disease genes, finding ancestral haplotypes is an essential and difficult step. The most general model for a complex disease will involve multiple disease alleles at multiple unlinked disease genes. Terwiliger [1995], Xiong and Guo [1997], and Collins and Morton [1998] propose likelihood methods using information across markers. McPeek and Strahs [1999] proposed a maximum likelihood multipoint method based on the decay of haplotype sharing. Rannala and Reeve [2001], Liu et al. [2001], and Morris et al. [2002] proposed Bayesian multipoint methods. Some of the methods assume independence of the markers, and many of these methods consider only a single ancestral haplotype case. Although multiple ancestral haplotypes sometimes are allowed, the number of ancestral haplotypes cannot be too large and the number has to be predetermined. Using non-parametric methods will avoid making false assumptions on models. But if there are multiple disease alleles at the disease locus, there will be multiple ancestral haplotypes. In this case, many fine-scale mapping measures are not monotonic decreasing functions of the distance between the marker locus and the disease locus. If a measure has a larger value at marker locus one than at marker locus two, it does not necessarily mean marker locus one is closer to the disease locus than marker locus two. Suppose that a region contains a disease locus, and several markers span the region. If a measure has a maximum at one of the markers, it does not mean the disease locus is near that marker. If one of the chosen marker loci is exactly the disease locus, the above problem can be avoided. However, it is not practical to assume that one of the chosen marker loci is indeed the disease locus. In this paper we propose to solve the problem in the following way. We will use pexcess (see (1) for definition) as a fine-mapping measure. Instead of using it on individual markers, we use it on an interval consisting of several closely related markers. The region in concern is divided into several intervals. The above mentioned problem can be avoided because we can always assume that one of the intervals contains the disease locus. If one of the interval contains the disease locus, pexcess will have a maximum at that interval. Our method will work well for diseases with multiple ancestral haplotypes and diseases with multiple disease alleles (allelic heterogeneity). Joint Statistical Meetings Section on Statistics in Epidemiology