Introduction Efforts to fine map the causal variants responsible for genome-wide association studies (GWAS) signals have been largely predicated on the common disease common variant theory, postulating a common variant as the culprit for observed associations. This has led to extensive resequencing efforts that have been largely unsuccessful [1]–[5]. Here, we explore the possibility that part of the reason for this may be that the disease class causing an observed association may consist of multiple low-frequency variants across large regions of the genome—a phenomenon we call synthetic association. For convenience, these less common variants will be referred to here as “rare,” but we emphasize that we use this term loosely, only to refer to variants less common than those routinely studied in GWAS. The basic idea of how synthetic associations emerge in this model is illustrated in Figure 1, which shows how rare variants, by chance, can occur disproportionately in some parts of a gene genealogy. Any variant “higher up in the genealogy” that partitions those parts of the genealogy containing more disease variants than average will be identified as disease-associated. It is well appreciated that a noncausal variant will show association with a causal variant if the two are in strong linkage disequilibrium (LD). We use the previously introduced term synthetic association [6], however, to describe how such indirect association can occur between a common variant and at least one and possibly many rarer causal variants. Using the term synthetic as opposed to indirect emphasizes that the properties of the association signal are very different when the responsible variant or variants are much less frequent than the marker that carries the signal, as we detail below. 10.1371/journal.pbio.1000294.g001 Figure 1 Example genealogies showing causal variants and the strongest association for a common variant. (A) A genealogy with 10,000 original haplotypes was generated with 3,000 cases and 3,000 controls, genotype relative risk (γ) = 4, and nine causal variants. The branches containing the strongest synthetic association are indicated in blue. The branches containing the rare causal variants are in red. (B) A second genealogy was generated using the same parameters. These genealogies demonstrate two scenarios with genome-wide significant synthetic associations: the first (upper genealogy) had a high risk allele frequency (RAF = 0.49), and the second (lower genealogy) had a low RAF (0.08). To assess the tendency of rare disease-causing variants to create synthetic signals of association that are credited to single polymorphisms that are much more common in the population than the causal variants, we have simulated 10,000 haplotypes based on a coalescent model in a region either with or without recombination (Materials and Methods). We assumed that gene variants that influence disease have an allele frequency between 0.005 and 0.02, which is generally below the range of reliable detection (either by inclusion or indirect representation) using the genome-wide association platforms currently in use. We assumed a baseline probability of disease of φ for individuals with none of the rare genetic risk factors. The presence of at least one rare risk allele at the locus increased the probability of disease from φ to γ. We considered two values of φ (0.01, 0.1) and chose values of the penetrance γ such that the genotypic relative risk (GRR) of the rare causal variants varied incrementally between 2 and 6, where GRR is the ratio γ/φ. These values were chosen to explore the space around a GRR of 4, a threshold above which consistent linkage signals would be expected [7]. We simulated scenarios with one, three, five, seven, and nine rare causal variants. Results Across the conditions we have studied, not only is it possible to achieve genome-wide significance for common variants when one or more rare variants are the only contributors to disease, it is often the likely outcome (Figure 2). Overall, 30% of the simulations were able to detect an association with a common SNP at genome-wide significance (p 5%, Hardy-Weinberg equilibrium p-value >1×10−6, SNP call rate >95%), using the PLINK software [40]. For the sickle cell anemia GWAS, we compared 194 cases and 7,407 controls of inferred African ancestry via multidimensional scaling, with a genomic control inflation factor of 1.01. For hearing loss, we performed a GWAS on 418 cases and 6,892 control subjects, all of whom were of genetically inferred European ancestry via multidimensional scaling, with a genomic control inflation factor of 1.02.
