On selecting markers for association studies: patterns of linkage disequilibrium between two and three diallelic loci.

Association studies depend on linkage disequilibrium (LD) between a causative mutation and linked marker loci. Selecting markers that give the best chance of showing useful levels of LD with the causative mutation will increase the chances of successfully detecting an association. This report examines the variation in the extent of LD between a disease locus and one or two diallelic marker loci (termed single nucleotide polymorphisms or SNPs). We use a simulation method based on the neutral coalescent in a population of variable size to find the distribution of LD as a function of allele frequencies, the recombination rate, and the population history. Given that LD exists, the allele frequencies determine if a site will be useful for detecting an association with the disease mutation. We show that there is extensive variation in LD even for closely linked loci, implying that several markers may be needed to detect a disease locus. The distribution of LD between common variants is strongly influenced by ancestral population size. We show that in general, best results will be obtained if the frequencies of marker alleles are at least as large as the frequency of the causative mutation. Haplotypes of two or more SNPs generally have a higher probability than individual SNPs of showing useful LD with a disease mutation, although exceptions are described.

Garner C ，Slatkin M 《GENETIC EPIDEMIOLOGY》

Further investigation of linkage disequilibrium SNPs and their ability to identify associated susceptibility loci.

North BV ，Curtis D ，Martin ER ，Lai EH ，Roses AD ，Sham PC ... -  《ANNALS OF HUMAN GENETICS》

Detailed analysis of the relative power of direct and indirect association studies and the implications for their interpretation.

Genetic association studies are usually based upon restricted sets of 'tag' markers selected to represent the total sequence variation. Tag selection is often determined by some threshold for the r(2) coefficients of linkage disequilibrium (LD) between tag and untyped markers, it being widely assumed that power to detect an effect at the untyped sites is retained by typing the tag marker in a sample scaled by the inverse of the selected threshold (1/r(2)). However, unless only a single causal variant occurs at a locus, it has been shown [Eur J Hum Genet 2006;14:426-437] that significant power loss can occur if this principle is applied. We sought to investigate whether unexpected loss of power might be an exceptional case or more general concern. In the absence of detailed knowledge about the genetic architecture at complex disease loci, we developed a mathematical approach to test all possible situations. We derived mathematical formulae allowing the calculation of all possible odds ratios (OR) at a tag marker locus given the effect size that would be observed by typing a second locus and the r(2) between the two loci. For a range of allele frequencies, r(2) between loci, and strengths of association at the causal locus (OR from 0.5 to 2) that we consider realistic for complex disease loci, we next determined the sample sizes that would be necessary to give equivalent power to detect association by genotyping tag and causal loci and compared these with the sample sizes predicted by applying 1/r(2). Under most of the hypothetical scenarios we examined, the calculated sample sizes required to maintain power by typing markers that tag the causal locus at even moderately high r(2) (0.8) were greater than that calculated by applying 1/r(2). Even in populations with apparently similar measurements of allele frequency, LD structure, and effect size at the susceptibility allele, the required sample size to detect association with a tag marker can vary substantially. We also show that in apparently similar populations, associations to either allele at the tag site are possible. Indirect tests of association are less powered than sizes predicted by applying 1/r(2) in the majority of hypothetical scenarios we examined. Our findings pertain even for what we consider likely to be larger than average effect sizes in complex diseases (OR = 1.5-2) and even for moderately high r(2) values between the markers. Until a substantial number of disease genes have been identified through methods that are not based on tagging, and therefore biased towards those situations most favourable to tagging, it is impossible to know how the true scenarios are distributed across the range of possible scenarios. Nevertheless, while association designs based upon tag marker selection by necessity are the tool of choice for de novo gene discovery, our data suggest power to initially detect association may often be less than assumed. Moreover, our data suggest that to avoid genuine findings being subsequently discarded by unpredictable losses of power, follow up studies in other samples should be based upon more detailed analyses of the gene rather than simply on the tag SNPs showing association in the discovery study.

Moskvina V ，O'Donovan MC 《HUMAN HEREDITY》

On the advantage of haplotype analysis in the presence of multiple disease susceptibility alleles.

We investigated the effect of multiple susceptibility alleles at a single disease locus on the statistical power of a likelihood ratio test to detect association between alleles at a marker locus and a disease phenotype in a case-control design. Using simplifying assumptions to obtain the joint frequency distribution of marker and disease locus alleles, we present numerical results that illustrate the impact of historical variation of initial associations between marker alleles and susceptibility alleles on the power of a likelihood ratio test for association. Our results show that an increase in the number of susceptibility alleles produces a decrease in power of the likelihood ratio test. The decrease in power in the presence of multiple susceptibility alleles, however, is less for markers with multiple alleles than for markers with two alleles. We investigate the implications of this observation for tests of association based on haplotypes made up of tightly linked single-nucleotide polymorphisms (SNPs). Our results suggest that an analysis based on haplotypes can be advantageous over an analysis based on individual SNPs in the presence of multiple susceptibility alleles, particularly when linkage disequilibria between SNPs is weak. The results provide motivation for further development of statistical methods based on haplotypes for assessing the potential for association methods to identify and locate complex disease genes.

Morris RW ，Kaplan NL 《GENETIC EPIDEMIOLOGY》

Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between markers and QTL.

Zhao H ，Nettleton D ，Soller M ，Dekkers JC ... -  《Genetics Research》