Abstract
Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise linkage disequilibrium, r2. A complete derivation of this relationship from a general disease model is shown. Quite interestingly, this relationship holds across all modes of inheritance. Extensive Monte Carlo simulations using a disease genetics model applied to chromosomes subjected to a standard model of recombination are employed to better understand the variation around this fine mapping theorem due to sampling effects. We also use this relationship to provide a framework for estimating properties of a non-interrogated causal site using data at closely linked markers. Lastly, we apply this way of examining association data from high-density genotyping in a large, publicly-available data set investigating extreme BMI. We anticipate that understanding the patterns of disease association decay with declining linkage disequilibrium from a causal site will enable more powerful fine mapping methods and provide new avenues for identifying causal sites/genes from fine-mapping studies.
Highlights
Genetic markers closely linked to disease-causing sites will exhibit association with disease through linkage disequilibrium (Lai et al, 1994; Weiss and Clark, 2002; Morton, 2005; Slatkin, 2008)
Several groups have described the relationship of statistical power at a marker site in linkage disequilibrium with a causal site
In 1999, using the coalescent process to investigate the density of markers necessary for adequate coverage across the genome to detect disease-associated regions, Kruglyak presented the outline of an argument that the sample size necessary to detect association at a marker locus in linkage disequilibrium with a causal site is approximately S/d2, where S is the number of samples required to detect disease association at the causal site with a given level of power and d2 = q 1 − q p−1 1 − p −1 r2, such that r2 is the standard measure of linkage disequilibrium between the causal site and the marker site and q and p are the allele frequencies at the marker and causal sites, respectively (Kruglyak, 1999)
Summary
Genetic markers closely linked to disease-causing sites will exhibit association with disease through linkage disequilibrium (Lai et al, 1994; Weiss and Clark, 2002; Morton, 2005; Slatkin, 2008).
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