Handling linkage disequilibrium in linkage analysis using dense single-nucleotide polymorphisms

With rapid development of high-throughput genotyping technologies, more researchers have begun genome-wide searches for genes associated with complex diseases using dense single-nucleotide polymorphisms (SNPs). These dense SNPs create clusters of SNPs in linkage disequilibrium (LD) along each chromosome. The underlying assumption of linkage equilibrium (LE) between markers in many multipoint linkage methods is violated among dense SNPs where LD may exist. Such violation can lead to incorrect pedigree haplotype inference [1], especially with missing parental genotypes, resulting in bias in linkage analysis. Huang and colleagues [2] have shown that LE assumption among tightly linked markers induces false-positive evidence for linkage in qualitative trait linkage analysis with missing parental genotypes. This bias may be influenced by SNPs in LD, which can cause apparent oversharing of multipoint identity by descent (IBD). Thus, appropriate LD modeling or adjusting for markers in LD is needed to avoid potential bias in linkage in the case of missing parental genotypes. In our study, we sought to examine and compare three different approaches of handling LD in both affected sib-pair (ASP) and quantitative trait locus (QTL) linkage analysis using dense SNPs on chromosome 6 from the Genetic Analysis Workshop 15 (GAW15) simulated data without prior knowledge of the answers. The methods include a simple algorithm, SNPLINK [3], and MERLIN-LD [4].

Using the original data with complete parental genotypes, we observed no substantial linkage evidence (average maximum LOD = 2.0, SD = 1.2) over the selected sub-region in ASP linkage analysis of the RA dichotomous phenotype (last panels in Figures 1 and 2). However, ignoring LD combined with missing parental genotypes, we observed LOD score inflation shown in the panel A of Figures 1 and 2 (average maximum LOD = 17.1, SD = 3.6). Even with just one ungenotyped parent, large LOD scores were observed [average maximum of 8.5 (SD = 2.7)]. In contrast, no such inflation was observed when ignoring LD using either MERLIN-regress or the robust score statistic in QTL linkage analysis; the average maximum LOD scores for the two approaches were 0.3 and 0.2, respectively, without parental genotypes. Consequently, no inflation in LOD score was observed regardless of approaches and conditions applied in QTL analysis. Thus, we only present results from ASP linkage analysis in what follows. In general, with complete parental genotype information, all methods for handling LD with various LD thresholds yielded maximum LOD scores similar to the original linkage results (last panels in Figures 1 and 2).

As a note, in this selected sub-region, the mean, median, and mode of D' are 0.13, 0.06, and 1.0, respectively. On the other hand, most pairwise r² values are below 0.01 (median and interquartile range of 0.001 and 0.002, respectively). Of the 438,516 SNP pairs formed by 937 SNPs, there were 28,703 SNP pairs on average with r² greater than 0.01. Consequently, this resulted in most SNPs being omitted from the analysis after applying the algorithms at such threshold. In general, the number of SNPs included in each analysis decreased as the cut points decreased. In some cases, especially with the lower cut points, only 20 to 50 SNPs remained to be analyzed within our selected 15-cM region; however, this still offered a fairly dense coverage (1 to 3 SNPs per cM) and served our attempt to present a trend and magnitude of LOD score inflation due to LD among dense SNPs.

We examined and compared three approaches of handling LD using dense SNPs on chromosome 6 from the GAW15 simulated data. We performed ASP and QTL linkage analyses on a selected sub-region with low evidence of linkage (170 to 185 cM) that contains 937 SNPs. We observed inflation of LOD scores with missing parental genotypes only in ASP linkage analysis of the RA phenotype. In QTL linkage analysis, we observed no inflation in LOD scores even with missing parental genotypes using the unascertained data with respect to severity categories.

In ASP analysis across the LD thresholds (D' or r²), all three methods showed a similar pattern of less LOD score inflation as the LD cut points decreased. Using r² threshold, MERLIN-LD outperformed other approaches across all cut points; however, the reduction by the lowest threshold did not quite reach the LOD score with full parental genotypes available. With D' threshold, both SNPLINK and simple algorithm performed at a similar level; however, SNPLINK showed further reduction of LOD scores, especially with lower cut points. SNPLINK and the simple algorithm performed better with D' with low r², but this result may not be generalizable to regions with high r².

Overall, MERLIN-LD approach worked well even with the skewed r² distribution observed in the selected region in our sample. However, because clusters are determined based on r², its usage is limited if D' is a more appropriate measure of LD. In addition, this approach assumes no recombination within clusters and no LD between clusters. SNPLINK appears to be flexible, with the option of using D', r², or both combined. However, implementation takes some preparation and modification of the script is challenging. The simple algorithm is intuitive to implement but the results still contained highest inflated LOD scores at the lowest cut points compared to other approaches.

In measuring LD, r² provides the correlation between two SNPs and depends on the allele frequency and D' captures the ancestral history over time. Even with low r², large D' will create bias in the probability of IBD sharing, which may lead to LOD score inflation. Therefore, applying D' threshold will remove more SNPs in handling of LD because it is generally larger than r². In our selected region, small r² values reflect negligible measures of LD in practice, and thus D' measures appear to be more applicable in the analysis.

The resulting inflation with missing parental genotypes could be partially due to the decreased number of SNPs being analyzed because the information content is higher with more available parental genotypes. However, comparing the results from unadjusted data without parental data (Figs. 1A and 2A) and the original complete data (Figs. 1D and 2E) with the same number of SNPs analyzed, we see that increased information content with complete data resulted in no inflation in our study. Thus, it is more plausible to believe that the inflation is mainly due to LD in this sample rather than the decreased information content. Further, removing large number of SNPs and thus reducing the information content may affect the location accuracy and power of linkage mapping.

In conclusion, our findings reiterate the importance of properly modeling or adjusting for LD among dense markers because it gives false evidence of linkage when the parental genotypes are missing. In cases with missing parental genotypes in ASP analysis, all three approaches of adjusting for LD substantially reduced the false-positive linkage signals. The results from our study further bolster efforts to improve and develop approaches to handle linkage disequilibrium in linkage analysis using dense markers.