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.
Simple algorithm
Figures 1B and 2B show linkage analysis results using the simple algorithm at each cut point with ungenotyped parents. We observed substantial reduction of the inflated LOD score, especially with lower cut points. The average of the maximum LOD score over the 100 replicates ranges from 10.5 (SD = 2.8) at D' of 0.7 with 453 SNPs to 5.9 (SD = 2.8) at D' of 0.1 with 41 SNPs (Figure 1B). A similar pattern of reduced LOD score inflation of was observed with r2 cut points (Figure 2B). The range of the average maximum LOD score was 6.5 (SD = 2.7), with an average 54 SNPs and 13.9 (SD = 3.4) with an average of 857 SNPs. The simple algorithm performed better with D' threshold as indicated by lower amount of LOD score inflation in this region of no linkage.
SNPLINK
Using SNPLINK with ungenotyped parents, a similar trend of reduction of LOD score inflation was observed with lowest D' cut point showing the greatest reduction (Figure 1C). However, the average maximum LOD scores across all cut points fell in a narrow range of 2.9 (SD = 1.5) and 3.9 (SD = 1.7) for D' of 0.1 and 0.7, respectively. At the highest D', an average of 160 SNPs were evaluated. Using r2 threshold shown by Figure 2C, such reduction of LOD score inflation with decreasing cut points remained, but with a wider range of average maximum LOD scores of 3.7 (SD = 1.6) and 11.7 (SD = 3.1). At r2 cut point of 0.01, an average of 164 SNPs were evaluated compared to 695 SNPs at the highest cut point. SNPLINK performed better with D' threshold, as was observed for the simple algorithm.
MERLIN LD
Figure 2D shows summary ASP linkage results using MERLIN-LD from families with no parental genotypes. We observed a tangibly reduced LOD score inflation across all cut points compared to the unadjusted (Figure 2A) and other approaches (Figure 2B and 2C). The range of average maximum LOD scores was 2.8 (SD = 1.5), with 51 clusters at r2 = 0.01 and 5.3 (SD = 1.8) with 446 clusters at r2 = 0.5 evaluated in linkage analysis. Although the lowest average maximum LOD score was below 3, it was still slightly higher than the value of 1.9 obtained with full parental information shown in Figure 2E.