Estimating haplotype frequencies and standard errors for multiple single nucleotide polymorphisms

Abstract

Estimating haplotype frequencies becomes increasingly important in the mapping of complex disease genes, as millions of single nucleotide polymorphisms (SNPs) are being identified and genotyped. When genotypes at multiple SNP loci are gathered from unrelated individuals, haplotype frequencies can be accurately estimated using expectation-maximization (EM) algorithms (Excoffier and Slatkin, 1995; Hawley and Kidd, 1995; Long et al., 1995), with standard errors estimated using bootstraps. However, because the number of possible haplotypes increases exponentially with the number of SNPs, handling data with a large number of SNPs poses a computational challenge for the EM methods and for other haplotype inference methods. To solve this problem, Niu and colleagues, in their Bayesian haplotype inference paper (Niu et al., 2002), introduced a computational algorithm called progressive ligation (PL). But their Bayesian method has a limitation on the number of subjects (no more than 100 subjects in the current implementation of the method). In this paper, we propose a new method in which we use the same likelihood formulation as in Excoffier and Slatkin's EM algorithm and apply the estimating equation idea and the PL computational algorithm with some modifications. Our proposed method can handle data sets with large number of SNPs as well as large numbers of subjects. Simultaneously, our method estimates standard errors efficiently, using the sandwich-estimate from the estimating equation, rather than the bootstrap method. Additionally, our method admits missing data and produces valid estimates of parameters and their standard errors under the assumption that the missing genotypes are missing at random in the sense defined by Rubin (1976).

Ovarian Cancer Risk and Polymorphisms Involved in Estrogen Catabolism

“…To analyze haplotypes, we used HPlus software version 2.1 (Fred Hutchinson Cancer Research Center, Seattle, WA), which infers haplotypes based on expectationmaximization with a modified progressive ligation computational algorithm (18). Diplotype (haplotype pair) analysis was done using PHASE software version 2.0 (University of Washington, Seattle, WA), which, based on a Bayesian coalescence theory, generates all possible haplotype pairs and the probability of that pair for each individual (19).…”

DNA Repair Polymorphisms and Risk of Colorectal Adenomatous or Hyperplastic Polyps

“…Haplotype frequencies were estimated using the expectation maximization algorithm as implemented in the program Hplus (54). Based on the results (see Table 2), the MGMT and XPD combined genotypes were collapsed into homozygous wild type, heterozygous, and homozygous variant.…”

Leptin Concentrations, Leptin Receptor Polymorphisms, and Colorectal Adenoma Risk

“…28,29). The most common haplotype was selected as the reference group with all others being compared with it.…”