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Impact of marker density on the accuracy of association mapping
© Zhang et al; licensee BioMed Central Ltd. 2007
Published: 18 December 2007
We studied the impact of marker density on the accuracy of association mapping using Genetic Analysis Workshop 15 simulated dense single-nucleotide polymorphism (SNP) data on chromosome 6. A total of 1500 cases and 2000 unaffected controls genotyped for 17,820 SNPs were analyzed. We applied the approach that combines information from multiple SNPs under the framework of the Malecot model and composite likelihood to non-overlapping regions of the chromosome. We successfully detected the associations with disease Loci C and D and predicted their locations as small as zero distance to Locus C when it was "typed" and 112 kb from the untyped rare Locus D. Reducing marker density decreased the accuracy of location estimates. However, the predicted locations were robust to variations in the number of SNPs. Generally, the linkage disequilibrium (LD) map reflecting distances between markers in relation to LD produced higher accuracy than the physical map. We also demonstrated that SNP selection based on equal LD distance outperforms that based on equal physical distance or SNP tagging. Furthermore, ignoring rare SNPs diminished the ability to detect rare causal variants.
As the cost of genotyping decreases, genome-wide association (GWA) mapping of the predisposition genes for complex diseases is becoming a common study design in genetic epidemiology. As the huge number of single-nucleotide polymorphisms (SNPs) in the human genome is still prohibitive for exhaustive investigation, subsets of SNPs have often been selected for large scale studies. Morton et al. developed a novel GWA mapping approach based on the Malecot model and composite likelihood combining multiple marker information from non-overlapping genomic regions to predict the locations of disease variants . We applied this approach to the Genetic Analysis Workshop (GAW) 15 Problem 3 simulated dense chromosome 6 data with the knowledge of the answers and we studied the effect of SNP density on the accuracy of association mapping.
The simulated data set contained 1500 families with a sib pair affected with rheumatoid arthritis (RA) and a random sample of 2000 unrelated and unaffected individuals. To form a case-control study, we selected the first sibling per family as a case. A total of 1500 cases and 2000 controls from Replicate 1 were analyzed. There are three simulated disease loci. HLA-DR is at the same location of 32484.648 kb as Locus C, where a SNP denseSNP6_3437 lies, so we considered this SNP the disease variant C. Locus D is at 37233.784 kb, in very weak linkage disequilibrium (LD) with Locus C. The minor allele frequency (MAF) for the C allele was 0.4055 in control samples. The D allele has a population frequency of 0.0083, but the variant was not typed.
Genotype data were composed of 17,820 SNPs on chromosome 6, mimicking a 300 K GWA scan with no missing values. Fifty-eight SNPs showing departure from Hardy-Weinberg equilibrium (HWE) in control samples (χ21 ≥ 10 for either Pearson's or likelihood ratio chi-square tests) were discarded . Following convention, 2061 rare SNPs with MAF < 5% were further removed except when otherwise indicated. The main data set (1) was thus composed of a total number of 15,701 SNPs. In another experiment we retained all SNPs but removed 26 SNPs showing departure from HWE by the likelihood-ratio test and this generated 17,794 SNPs (data set 2).
The physical map length was 170,813 kb. LD maps expressed in LD units (LDUs) were constructed based on pair-wise LD for multiple markers in control samples . LDU is the product of ε and kb distance for an interval of two adjacent SNPs and is additive, where ε represents the exponential decline of LD with distance for that interval. We used the LDMAP-cluster, a parallel version of LDMAP program that rapidly constructs the maps of equally divided chromosome segments http://www.som.soton.ac.uk/research/geneticsdiv/epidemiology/ldmap/. For each segment, an overall ε value was also estimated. The LD map length was 1311.225 LDUs for the main data set and 1237.923 LDUs for data set 2. SNPs can have the same LDU if they are in an LD block. Therefore, we also made tilted LD maps by reassigning LDU locations for the SNPs with the same LDU by linear interpolation.
A chromosome is divided into non-overlapping consecutive regions of a minimum number of 30 SNPs and a minimum length of 10 LDUs by default without breaking LD blocks. Each genomic region was then analyzed separately. Association between SNP alleles and disease status in the Malecot model is a function of several parameters. Composite likelihood combines information of all marker-disease association in a genomic region. The parameters were estimated through fitting the model to the data with a map in LDU or kilobases and by minimizing -2 natural log composite likelihood (denoted as Λ) . The estimated location S of the disease locus is converted to a kilobase scale. The significance test is performed by contrasting two hierarchical models. Model A assumes no association with the disease, therefore S is not estimated. Model D assumes an association with the disease and S and two other parameters are estimated and ε is specified. The difference in Λ between models A and D (ΛA - ΛD) is monotonic to the magnitude of chi-square with three degrees of freedom (χ23). Permutation by shuffling case-control status for each region was performed to obtain empirical p-values . The algorithms were implemented in the CHROMSCAN program. A parallel version, CHROMSCAN-cluster, deployed on a local Beowulf cluster http://www.som.soton.ac.uk/research/geneticsdiv/epidemiology/chromscan/ was used for computing 1000 replicates.
The values of ε were obtained by averaging over eight segments in LD map construction, which were 1.14472 and 0.00568 for LD and kilobase maps, respectively, for the main data set, and 1.14386 and 0.00544 over nine segments for data set 2. Theoretically, a more accurate ε may be obtained by fitting the maps to the whole chromosome data, but the extensive computing power required for the task is impractical to implement and beyond the current computing resource. Also, slightly altered ε values did not appear to have an appreciable effect (data not shown).
For comparison, a single SNP χ21 was obtained by the 2 × 2 allelic count table and the most significant SNP (msSNP) showing maximal χ21 in each region was identified. Location error (in kilobases) was defined as the difference between S or the location of the msSNP and the true location of disease variant. Accuracy refers to the precision of the predicted location S. The smaller the error, the higher the accuracy.
To generate different SNP density, we selected every ith SNP (i = 2, 3, ..., 20, 25, 30) in the order of their physical locations from the full data set, representing 1/i the number of SNPs in the original set. For a candidate region spanning Loci C and D with rare SNPs included, we used Tagger implemented in the Haploview software to select tagging SNPs that optimally capture allelic variation among SNPs at a given r2 threshold based on pairwise LD in control samples . For comparison, we selected the same number of SNPs as Tagger but in equal LDU or kilobase distance. To do this we used the tilted LD map in which every SNP had a unique LDU location. We also studied the impact of region length and sample size.
Results and discussion
Association mapping of disease loci in full data set
Association mapping of disease Loci C and D on chromosome 6
ΛA - ΛD
Candidate regions of disease Loci C and D with rare SNPs included
Location error with rare SNPs
ΛA - ΛD
Occasionally or under high marker density, the kilobase map performed better than the LD map, presumably because every SNP has a unique physical location, whereas several SNPs could have the same LDU location in LD blocks. The tilted LD map improved the location accuracy for Locus C, although not for Locus D (Table 2).
In practice, the phenomenon in this simulated data set may be too extreme. On the other hand, it is possible that several disease loci can be closely located. To distinguish such loci is a challenge to genetic epidemiologists. Under this circumstance, single SNP association plus a gene functional study may be useful.
SNP density based on the order
Density and accuracy for Locus C – SNP selection by order
Location error by the composite likelihood approach
Causal SNP out
Causal SNP in
SNP density (kb/SNP)
Although mapping accuracy decreases with marker density, even with 1/30 the number of SNPs, corresponding to a 10 K GWA scan, we could still detect Locus C (Table 3). Single SNP tests depend heavily on whether the disease variant is typed. It has less predictive value for accuracy because the SNP with maximal χ2 is not necessarily the closest SNP to the disease variant. In contrast, methods that combine information from multiple markers predict the location of the disease variant better than single SNP tests because the location is less influenced by any single SNP effects. A multi-marker approach may therefore be more robust to genotyping errors.
We expect that the mapping accuracy will be improved further in maps with higher marker density than that assessed in this paper, such as the commercially available 500 K or more genotyping platforms for GWA studies.
SNP density based on tagging or equidistance
Density and accuracy – SNP selection by tagging or equidistancea
R2 (LDU, kb)
No. SNPs (kb/SNP)
Sample size and region length
We analyzed different sample sizes based on the combination of 500, 1000, 1500, and 2000 cases or controls. Despite variations in location errors for Locus C, there was no clear trend to draw any meaningful conclusion. For Locus D, however, a high degree of accuracy appeared to be maintained when the data sets had over 1000 cases and 1500 controls. Therefore, large samples are needed for detecting rare disease loci.
With Locus C being centred, we studied region lengths from 0.2 up to 30 LDUs, with the latter starting in region 27 and ending in region 30. The location error was relatively stable but extremely small or large LDU lengths resulted in increased error. The region lengths in LDUs (location errors in kilobases) were 0.2 (107), 1 (5), 2 (82), 4 (5), 6 (5), 8 (5), 10 (5), 12 (-10), 14 (-10), 16 (-13), 18 (-14), 20 (-14), and 30 (-68). We therefore recommend 10-LDU for the maximal length while maintaining minimal error. Increasing the number of SNPs also linearly increases the computing load .
Fixing region length had no appreciable impact on location accuracy at high density, but the errors were greater than let-the-program-decide regions at low density (data not shown).
We successfully detected disease Loci C and D in the simulated dense chromosome 6 data using the Malecot model and composite likelihood approach. Decreasing SNP density compromises accuracy of association mapping. This multi-marker approach has many advantages. Firstly, it markedly decreases the number of tests in GWA studies, avoiding heavy penalty for multiple testing. Secondly, it predicts the disease loci more accurately than single SNP association tests. We also demonstrated that SNP selection by equal LD distance outperforms that by tagging or equal kilobase distance in the accuracy of association mapping. Finally, we conclude that excluding rare SNPs significantly decreases the power and accuracy in mapping rare disease loci.
WZ was supported by the Institute of Cancer Research, Sutton, Surrey, UK. WL, CH, and T-YK were supported by Ph.D. studentships funded by the University of Southampton, Shanghai Jiaotong University, and the Taiwan Ministry of Education, respectively.
This article has been published as part of BMC Proceedings Volume 1 Supplement 1, 2007: Genetic Analysis Workshop 15: Gene Expression Analysis and Approaches to Detecting Multiple Functional Loci. The full contents of the supplement are available online at http://www.biomedcentral.com/1753-6561/1?issue=S1.
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