Experimental Designs for Reliable Detection of Linkage Disequilibrium in Unstructured Random Population Association Studies

Abstract

A method is given for design of experiments to detect associations (linkage disequilibrium) in a random population between a marker and a quantitative trait locus (QTL), or gene, with a given strength of evidence, as defined by the Bayes factor. Using a version of the Bayes factor that can be linked to the value of an F -statistic with an existing deterministic power calculation makes it possible to rapidly evaluate a comprehensive range of scenarios, demonstrating the feasibility, or otherwise, of detecting genes of small effect. The Bayes factor is advocated for use in determining optimal strategies for selecting candidate genes for further testing or applications. The prospects for fine-scale mapping of QTL are reevaluated in this framework. We show that large sample sizes are needed to detect small-effect genes with a respectablesized Bayes factor, and to have good power to detect a QTL allele at low frequency it is necessary to have a marker with similar allele frequency near the gene.T HE advent of dense maps of single-nucleotide polydesign. Then we discuss measures of statistical evidence or criteria for "detecting" associations. We argue that morphisms (SNPs) covering the genome with 300,000 or more markers offers new opportunities to find and there are problems with commonly used P-values as a measure of evidence and advocate the Bayes factor (see, identify genes, by testing for population-level associations e.g., Spiegelhalter and Smith 1982) as a replacement between the SNP and disease or other trait of interest.measure. Further information including relationships Associations occur because of linkage disequilibrium between Bayes factors, posterior probabilities, type I error between the marker and trait. "Linkage disequilibrium rates, P-values, power, and false discovery rates as evi-(LD) mapping" aims to detect and locate genes relative dence for gene effects is given in appendix b. Then, we to a map of existing genetic markers. Location informareview and correct the deterministic power calculation tion is obtained because the distance between the gene from Luo (1998) (with technical details in appendix and a marker on a chromosome is one factor influenca) and the classical approach to power of experiments ing the closeness of association between the gene and and then introduce a generic Bayes factor (Spiegelhalmarker. In a population, recombinations affecting the ter and Smith 1982) for comparing linear models, in association between a gene and marker may occur over the absence of prior information. This is linked to the many generations. This potentially gives a much finer classical power calculation, to give designs with a given resolution than pedigrees used for quantitative trait loci probability to detect an effect with a given Bayes factor. (QTL) mapping. Finer resolution comes at a cost, howResults are presented for sample sizes ranging from ever. More genotyping is needed per individual and as 600 to 4800 and Bayes factors ranging from 1 ⁄20 to 20 and we shall show, larger sample s...

Mapping determinants of human gene expression by regional and genome-wide association

“…The proportion of outcomes with P-value ,0.05/770,000 was taken as the power. Second, this procedure was checked by comparing results with those from a published equivalent 21 . Luciferase reporter assay.…”

The distribution of SNP marker effects for faecal worm egg count in sheep, and the feasibility of using these markers to predict genetic merit for resistance to worm infections

“…Thus, it may be thought of as assessing the repeatability of the results. The power to detect polymorphisms using K. E. Kemper et al 208 LD was calculated using the ' ldDesign ' package in R 2.6.1 (R Development Core Team, 2007 ;Luo, 1998 ;Ball, 2005 Hill & Robertson (1968), where p is the frequency of the first allele at the marker, t is the frequency of the first variant at the QTL or polymorphism and r HR 2 is the LD between the allele and the QTL variant. The level of LD between the marker allele and the QTL variant, and the effect size of the QTL have the greatest impact on estimated power, with the frequency of the marker allele and QTL variant of lesser (relative) importance (Luo, 1998).…”

Experimental Designs for Robust Detection of Effects in Genome-Wide Case–Control Studies

“…There are two main approaches to power calculations for GWAS: frequentist (e.g., Purcell et al 2003;Menashe et al 2008) and Bayesian (Ball 2004(Ball , 2005. We briefly review frequentist and Bayesian measures of evidence with reference to recent GWAS.…”

“…Even (in fact, especially) with large sample sizes, power and spurious associations are important considerations. While larger and larger samples will eventually detect any effect of given size, there will be more and more possibly spurious effects "detected" at or near the threshold of significance.There are two main approaches to power calculations for GWAS: frequentist (e.g., Purcell et al 2003;Menashe et al 2008) and Bayesian (Ball 2004, 2005. We briefly review frequentist and Bayesian measures of evidence with reference to recent GWAS.…”

“…Results of GWAS to date suggest that the traits of interest are governed by many small effects (e.g., Wellcome Trust Case Control Consortium 2007; Diabetes Genetics Initiative of Broad Institute of Harvard and MIT 2007;Gudbjartsson et al 2008;Lettre et al 2008;Weedon et al 2008;Lango Allen et al 2010). Previously, we gave Bayesian power calculations for genome-wide association studies for quantitative traits (Ball 2005). This approach ensures power to detect effects of a specified size with a given Bayes factor, where the Bayes factor is chosen large enough to overcome the low prior odds for effects.…”