Linkage analysis of a complex disease through use of admixed populations

Linkage disequilibrium arising from the recent admixture of genetically distinct populations can be potentially useful in mapping genes for complex diseases. McKeigue has proposed a method that conditions on parental admixture to detect linkage. We show that this method tests for linkage only under specific assumptions, such as equal admixture in the parental generation and admixture that occurs in a single generation. In practice, these assumptions are unlikely to hold for natural populations, resulting in an inflation of the type I error rate when testing for linkage by this method. In this article, we generalize McKeigue's approach of testing for linkage to allow two different admixture models: (1) intermixture admixture and (2) continuous gene flow. We calculate the sample size required for a genomewide search by this method under different disease models: multiplicative, additive, recessive, and dominant. Our results show that the sample size required to obtain 90% power to detect a putative mutant allele at a genomewide significance level of 5% can usually be achieved in practice if informative markers are available at a density of 2 cM.     

Dissection of genomewide-scan data in extended families reveals a major locus and oligogenic susceptibility for age-related macular degeneration

To examine the genetic basis of age-related macular degeneration (ARMD), a degenerative disease of the retinal pigment epithelium and neurosensory retina, we conducted a genomewide scan in 34 extended families (297 individuals, 349 sib pairs) ascertained through index cases with neovascular disease or geographic atrophy. Family and medical history was obtained from index cases and family members. Fundus photographs were taken of all participating family members, and these were graded for severity by use of a quantitative scale. Model-free linkage analysis was performed, and tests of heterogeneity and epistasis were conducted. We have evidence of a major locus on chromosome 15q (GATA50C03 multipoint P=1.98x10-7; empirical P< or =1.0x10-5; single-point P=3.6x10-7). This locus was present as a weak linkage signal in our previous genome scan for ARMD, in the Beaver Dam Eye Study sample (D15S659, multipoint P=.047), but is otherwise novel. In this genome scan, we observed a total of 13 regions on 11 chromosomes (1q31, 2p21, 4p16, 5q34, 9p24, 9q31, 10q26, 12q13, 12q23, 15q21, 16p12, 18p11, and 20q13), with a nominal multipoint significance level of P< or =.01 or LOD > or =1.18. Family-by-family analysis of the data, performed using model-free linkage methods, suggests that there is evidence of heterogeneity in these families. For example, a single family (family 460) individually shows linkage evidence at 8 loci, at the level of P<.0001. We conducted tests for heterogeneity, which suggest that ARMD susceptibility loci on chromosomes 9p24, 10q26, and 15q21 are not present in all families. We tested for mutations in linked families and examined SNPs in two candidate genes, hemicentin-1 and EFEMP1, in subsamples (145 and 189 sib pairs, respectively) of the data. Mutations were not observed in any of the 11 exons of EFEMP1 nor in exon 104 of hemicentin-1. The SNP analysis for hemicentin-1 on 1q31 suggests that variants within or in very close proximity to this gene cause ARMD pathogenesis. In summary, we have evidence for a major ARMD locus on 15q21, which, coupled with numerous other loci segregating in these families, suggests complex oligogenic patterns of inheritance for ARMD.     

Tests for a Disease-susceptibility Locus allowing for an Inbreeding Coefficient (F)

We begin by discussing the false positive test results that arise because of cryptic relatedness and population substructure when testing a disease susceptibility locus. We extend and evaluate the Hardy-Weinberg disequilibrium (HWD) method, allowing for an inbreeding coefficient (F) in a similar way that Devlin and Roeder (1999) allowed for inbreeding in a case-control study. Then we compare the HWD measure and the common direct measure of linkage disequilibrium, both when there is no population substructure (F = 0) and when there is population substructure (F not = 0), for a single marker. The HWD test statistic gives rise to false positives caused by population stratification. These false positives can be controlled by adjusting the test statistic for the amount of variance inflation caused by the inbreeding coefficient (F). The power loss for the HWD test that arises when controlling for population structure is much less than that which arises for the common direct measure of linkage disequilibrium. However, in the multiplicative model, the HWD test has virtually no power even when allowing for non-zero F.     

A robust numerical algorithm for studying biomolecular transport processes

We present a numerical algorithm that is well suited for the study of biomolecular transport processes. In the algorithm a continuous Markov process is discretized as a jump process and the jump rates are derived from local solutions of the continuous system. Consequently, the algorithm has two advantages over standard numerical methods: (1) it preserves detailed balance for equilibrium processes, (2) it is able to handle discontinuous potentials. The formulation of the algorithm also allows us to calculate the effective diffusion coefficient or, equivalently, the randomness parameter. We provide several simple examples of how to implement the algorithm. All the MATLAB functions files needed to reproduce the results presented in the article are available from www.amath.unc.edu/Faculty/telston/matlab_functions.     

A whole-genome screen of a quantitative trait of age-related maculopathy in sibships from the Beaver Dam Eye Study

Age-related maculopathy (ARM) is a leading cause of visual impairment among the elderly in Western populations. To identify ARM-susceptibility loci, we genotyped a subset of subjects from the Beaver Dam (WI) Eye Study and performed a model-free genomewide linkage analysis for markers linked to a quantitative measure of ARM. We initially genotyped 345 autosomal markers in 325 individuals (N=263 sib pairs) from 102 pedigrees. Ten regions suggestive of linkage with ARM were observed on chromosomes 3, 5, 6, 12, 15, and 16. Prior to fine mapping, the most significant regions were an 18-cM region on chromosome 12, near D12S1300 (P=.0159); a region on chromosome 3, near D3S1763, with a P value of.0062; and a 6-cM region on chromosome 16, near D16S769, with a P value of.0086. After expanding our analysis to include 25 additional fine-mapping markers, we found that a 14-cM region on chromosome 12, near D12S346 (located at 106.89 cM), showed the strongest indication of linkage, with a P value of.004. Three other regions, on chromosomes 5, 6, and 15, that were nominally significant at P< or =.01 are also appropriate for fine mapping.     

Genome-wide linkage scan for genes affecting longitudinal trends in systolic blood pressure

Only one genome scan to date has attempted to make use of the longitudinal data available in the Framingham Heart Study, and this attempt yielded evidence of linkage to a gene for mean systolic blood pressure. We show how the additional information available in these longitudinal data can be utilized to examine linkages for not only mean systolic blood pressure (SBP), but also for its trend with age and its variability. Prior to linkage analysis, individuals treated for hypertension were adjusted to account for right-censoring of SBP. Regressions on age were fitted to obtain orthogonal measures of slope, curvature, and residual variance of SBP that were then used as dependent variables in the model-free linkage program SIBPAL. We included mean age, gender, and cohort as covariates in the analysis. To improve power, sibling pairs were weighted for informativity using weights derived from both the marker and trait. The most significant results from our analyses were found on chromosomes 12, 15, and 17 for mean SBP, and chromosome 20 for both SBP slope and curvature.     

An audit of 'equivocal' (C3) and 'suspicious' (C4) categories in fine needle aspiration cytology of the breast

An audit of 'equivocal' (C3) and 'suspicious' (C4) categories in fine needle aspiration cytology of the breast
We have audited the frequency of use and outcome of the 'equivocal/atypia probably benign' (C3) and 'suspicious of malignancy' (C4) category for breast cytology in our Unit. A total of 14 935 cytological specimens were reported by at least one of the three pathologists with a special interest in breast pathology, according to five categories of the NHSBSP guidelines for cytology reporting, 1992; 3.7% (555 cases) and 3.9% (587 cases) of cases were classified as equivocal (C3) and suspicious (C4), respectively, giving a total rate (C3 + C4) of 7.6%. Of the C3 cases, 68% were subsequently benign and 32% were malignant. Of the C4 cases, 19% were subsequently benign and 81% malignant. The commonest benign lesions in both categories were fibroadenomas (7.6% of C3 and 19.8% of C4), fibrocystic change (14.3% of C3 and 12.5% of C4), radial scars (6.2% of C3 and 10.4% of C4) and papillomas (6.2% of C3 and 6.3% of C4). Of the malignant lesions (particularly those classified as C3), a high proportion were low grade or special type cancers. The categories of atypia probably benign (C3) and suspicious of malignancy (C4) in breast cytology provide a strategy for classification of problematic or uncertain cases; this maintains the predictive value of the benign (C2) and malignant (C5) categories, and allows separation of these difficult cases into clinically useful groups with differing probabilities of malignancy.     

The finite polygenic mixed model: An alternative formulation for the mixed model of inheritance

This paper presents a mixed model of inheritance with a finite number of polygenic loci. This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, likelihood profiles were obtained for the finite polygenic mixed model, the usual mixed model, with exact and approximate calculations, and for a class D regressive model. The profiles for the finite polygenic mixed model were closest to the profiles for the usual mixed model with exact calculations.     

Staging breast cancer: role of bone scanning.

Bone scans using technetium-99m phosphate complexes and a rectilinear scanner were carried out on 192 women with primary operable breast cancer four to six weeks after operation. The lymph node status of all these patients was assessed histologically from triple node biopsy specimens. Only nine patients had positive scans, although 94 patients had histological evidence that the tumour had already spread beyond the confines of the breast. Bone scanning, although accurate as a prognostic guide, is helpful only in a very few cases, and serves mainly to confirm prognostic information obtained more simply and less extensively by histological examination of lymph node biopsy specimens.