Plot of the density function of beta distributions parameterized by mean and heterogeneity factor .

<p>On each subplot the density is shown for two choices of namely  = 0.2 (solid line) and  = 0.25 (dotted lines).</p

Principal components plots of AABC and selected HapMap samples.

<p>Principal components plots of AABC and selected HapMap samples.</p

Quantile-quantile plot of p-values from association tests in the hypothesized case-control study in which cases from the CBCS and controls from the MEC are used.

<p>The plotted values indicate adjustment for 0 (uncorrected heavy solid line), 1 (dashed line), 10 (dotted line) and 200 (thin solid line) eigenvectors, by using these components in the calculation of .</p

Plot of estimate of proportion of African ancestry from STRUCTURE by participating AABC study.

<p>Plot of estimate of proportion of African ancestry from STRUCTURE by participating AABC study.</p

Plot of non-centrality parameter for the Bourgain test for a case-control study using two incompletely admixed populations as sources of cases and controls respectively.

<p>The parameters chosen refer to a test of a variant associated with disease which has 40 percent overall allele frequency and which is associated with a 10 percent difference in frequency between cases and controls (OR = 1.5 per copy). Cases are assumed to have average admixture percentage of 20 percent and controls 25 percent. The within population heterogeneity is specified by a single common heterogeneity parameter as used in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1001096#pgen-1001096-g001" target="_blank">Figure 1</a>.</p

A Genome-Wide Scan for Breast Cancer Risk Haplotypes among African American Women

<div><p>Genome-wide association studies (GWAS) simultaneously investigating hundreds of thousands of single nucleotide polymorphisms (SNP) have become a powerful tool in the investigation of new disease susceptibility loci. Haplotypes are sometimes thought to be superior to SNPs and are promising in genetic association analyses. The application of genome-wide haplotype analysis, however, is hindered by the complexity of haplotypes themselves and sophistication in computation. We systematically analyzed the haplotype effects for breast cancer risk among 5,761 African American women (3,016 cases and 2,745 controls) using a sliding window approach on the genome-wide scale. Three regions on chromosomes 1, 4 and 18 exhibited moderate haplotype effects. Furthermore, among 21 breast cancer susceptibility loci previously established in European populations, 10p15 and 14q24 are likely to harbor novel haplotype effects. We also proposed a heuristic of determining the significance level and the effective number of independent tests by the permutation analysis on chromosome 22 data. It suggests that the effective number was approximately half of the total (7,794 out of 15,645), thus the half number could serve as a quick reference to evaluating genome-wide significance if a similar sliding window approach of haplotype analysis is adopted in similar populations using similar genotype density.</p> </div

Two known breast cancer risk regions 10p15 and 14q24 exhibit putative haplotype effects.

<p>(A) 5.67–6.17 Mb region at 10p15; (B) 67.84–68.34 Mb region at 14q24. Black circles denote individual haplotypes, the sizes of which are proportional to their haplotype frequencies. Red dots denote genotyped SNPs within the same region. Blue dot shows the most significant SNP. Cyan dot denotes the known breast cancer risk SNP identified by previous GWAS.</p

The most significant individual haplotypes in 10p15 and 14q24.

a<p>the p-value of LR test of the haplotype specific effect after adjustment for both the known breast cancer risk SNP and the best SNP contained in that haplotype.</p>b<p>the rs number, risk allele and its frequency, Odds Ratios and 95% CI, and the p-value for the SNP adjusted in the LR test are presented. For the regions with known breast cancer risk hits, both the known hit and the locally best SNP were adjusted for in the LR test for the independence of haplotype signals.</p

Fitting the minimum p-values from 1,000 permutations of chromosome 22 data to theoretical beta distributions beta(a,b).

<p>Fitting the minimum p-values from 1,000 permutations of chromosome 22 data to theoretical beta distributions beta(a,b).</p

Comparison of the significance of individual haplotypes with imputed SNPs in regions on chromosomes 1, 4 and 18.

<p>Contrast of the haplotype effects with the effects of the 1000 Genome Project imputed SNPs in these three regions, namely, (A) chr1∶8,309,317-8,318,147; (B) chr4∶122,325,743- 122,363,114; and (C) chr18∶35,670,316-35,683,522 are shown. Black circles denote individual haplotypes, the sizes of which are proportional to their haplotype frequencies. Red dots denote imputed SNPs within the same region. Blue dot shows the most significant imputed SNP.</p