Summary: Aw ebsite for performing power calculations for the design of linkage and association genetic mapping studies of complex traits. Availibility: The package is made available at http://

Genetic Power Calculator: design of linkage and association genetic mapping studies of complex traits

An Introduction to Genetic Statistics.

The relationship between increased risk in relatives over population prevalence (lambda R = KR/K) and probability of sharing zero marker alleles identical by descent (ibd) at a linked locus (such as HLA) by an affected relative pair is examined. For a model assuming a single disease-susceptibility locus or group of loci tightly linked to a marker locus, the relationship is remarkably simple and general. Namely, if phi R is the prior probability for the relative pair to share zero marker alleles identical by descent, then P (sharing 0 markers/both relatives are affected) is just phi R/lambda R. Alternatively, lambda AR, the increased risk over population prevalence to a relative R due to a disease locus tightly linked to marker locus A, equals the prior probability that the relative pair share zero A alleles ibd divided by the posterior probability that they share zero alleles ibd, given that they are both affected. For example, for affected sib pairs, P (sharing 0 markers/both sibs are affected) = .25/lambda S. This formula holds true for any number of alleles at the disease locus and for their frequencies, penetrances, and population prevalence. Similar formulas are derived for sharing one and two markers. Application of these formulas to several well-studied HLA-associated diseases yields the following results: For multiple sclerosis, insulin-dependent diabetes mellitus, and coeliac disease, a single-locus model of disease susceptibility is rejected, implying the existence of additional unlinked familial determinants. For all three diseases, the effect of the HLA-linked locus on familiality is minor: for multiple sclerosis, it accounts for only a 2.5-fold increased risk to sibs over the population prevalence, compared to an observed value of 20; for coeliac disease, it accounts for approximately a 5.25-fold increased risk to sibs, while the observed value is on the order of 60; for insulin-dependent diabetes mellitus, it accounts for a 3.42-fold increased risk in sibs, while the observed value is 15. In all cases, the secondary determinants must be outside the HLA region. For tuberculoid leprosy, an unlinked familial determinant is also implicated (increased risk to sibs due to HLA = 1.49; observed value = 2.38). For hemochromatosis and Hodgkin's disease, there is little evidence for HLA-unlinked familial determinants. With this formula, it is also possible to examine the hypothesis of pleiotropy versus linkage dis-equilibrium by comparing lambda AS with the increased risk to sibs due to the associated allele(s).(ABSTRACT TRUNCATED AT 400 WORDS)

Assessing the role of HLA-linked and unlinked determinants of disease

Multiple sclerosis (MS) has, since the 1970s, been known to be associated with the HLA-Dw2 and -DR2 specificities in Caucasian Europeans and North Americans. By the use of genomic typing techniques, the association has been specified to be with the DRw15,DQw6,Dw2, i.e. the DRB1*1501-DQA1*0102-DQB1*0602 haplotype. A significant DPw4 association in Scandinavian MS patients has been described in one report. However, this association has not been confirmed in several subsequent studies with patients from the same and other ethnic groups. During the last few years several reports, based on serological, RFLP and PCR-SSO data, have suggested that the HLA class II-associated MS susceptibility gene(s) may be more closely associated with the DQ than with the DR subregion. The observations that the HLA-DQB1 genes of MS patients share long stretches of sequence motifs and also carry DQA1 alleles encoding glutamine at position 34 of the DQ alpha chain have received considerable attention. It has been suggested that the susceptibility to develop MS might be determined by the corresponding DQ alpha-beta heterodimers either encoded in cis or in trans. We have investigated these issues in a large group of Swedish MS patients (n = 179). We found that the associations with the suggested DQB1 sequences and position 34 of the DQ alpha chain were due to linkage disequilibrium and secondary to the association with the DRw15,DQw6,Dw2 haplotype (p less than 10(-9) and p less than 10(-8), respectively). No overrepresentation of the implicated DQ alpha-beta heterodimers was observed in DRw15,DQw6,Dw2-negative patients.(ABSTRACT TRUNCATED AT 250 WORDS)

Hla class ii-associated genetic susceptibility in multiple sclerosis : a critical evaluation

An analytical study is conducted of the properties of statistical tests to detect linkage between a disease locus and a very polymorphic marker locus when data on sib pairs are available. In most instances the most powerful test is the test based on the mean number of marker alleles shared identical by descent by the two members of a sib pair, and the most efficient sampling strategy is almost always to sample only pairs with both sibs affected. We show it is valid to use the information from all possible sib pairs as though they came from separate families when data on sibships of size three or larger are available, though more power may be obtained if different weights are given to the different sibship sizes.

A comparison of sib-pair linkage tests for disease susceptibility loci

The distribution of marker locus identity-by-descent scores in affected sib pairs provides a powerful tool for detecting the presence of a linked non-Mendelian disease susceptibility locus. This basic approach is here extended to include a trio of sibs. A special type of sib trio consisting of two affected and one unaffected sib is investigated. It is shown that compared to affected-sib-pairs, trios with the above configuration are less efficient in detecting the presence of a linked disease susceptibility locus.



When the generalized two-allele single locus model is fitted to sib pairs affected with multiple sclerosis, an estimate of the recombination fraction of 0.21 between the putative disease susceptibility locus and the HLA complex is obtained. However, this transmission model is deemed inadequate since a recombination fraction this large is inconsistent with the variety of HLA associations observed at the population level.

Paul Van Eerdewegh

Papers

Power of the affected-sib-pair method to defect disease susceptibility loci of small effect: an application to multiple sclerosis.