Introduction

A large number of single nucleotide polymorphisms (SNPs) can now be used to look for an association between a disease and a candidate gene. These markers can either be studied one at a time or jointly in haplotypes. The advantages of haplotypic versus single-marker methods have been widely debated in the literature: some studies show that haplotypic tests are more powerful,1, 2, 3 whereas others conclude that single-site analysis should be preferred.4, 5, 6 However, the relative power of these two approaches depends on whether the disease contributing SNPs are among the investigated SNPs or not,7, 8 on the number of disease susceptibility sites,8 on the disease susceptibility model and on the type of interactions between disease contributing sites.9, 10 The number of SNPs that are considered jointly in haplotypes is also an important parameter since the number of haplotypes increases with the number of investigated SNPs and, consequently, increase the degrees of freedom of tests comparing cases and controls, thus reducing their power. Moreover, as some haplotypes would only be carried by a few individuals, there could be statistical problems owing to small sample sizes making difficult the evaluation of their possible effect on the susceptibility. To face this problem, different strategies have been developed for the grouping of haplotypes. The method of Templeton et al11 consists in building a cladistic phylogenetic tree of the haplotypes and statistically comparing the number of cases and controls carrying haplotypes from the different nested clades. Recently, Durrant et al12 have proposed a different method in which the grouping of haplotypes is based on a distance metric and the association in the different groups is tested by a regression analysis. The method allows the study of large number of SNPs through a sliding window approach and is implemented in the software CLADHC. It differs from the method of Templeton11 since trees are reconstructed by simple group average linkage (clustering) and rooted, instead of being reconstructed by a parsimony method and unrooted. It also allows the analysis of long haplotypes, whereas the method of Templeton focuses on few SNPs. Based on simulations, Durrant et al12 showed that their clustering method may considerably increase the power to detect an association with a genomic region including a single disease susceptibility locus as compared to single-site or classical haplotype analysis. To perform these simulations, Durrant et al12 considered the haplotype data observed in Caucasians in a 10 Mb region of chromosome 20. To determine if their conclusions remain valid with different genes and linkage disequilibrium (LD) patterns, we present here the results of simulations using real haplotype data from five different genomic regions.

Materials and methods

Description of the data

Data from the Variation Discovery Resource Project13

Various genes are sequenced in 23 unrelated European individuals. SNPs are identified within these genes and the most likely haplotypes are reconstructed using Phase v2.0.14, 15 Three genes are studied here:

  • Interleukine 13 (IL13): 6919 base pairs (bp) on the chromosome 5q31: 12 bi-allelic loci are kept, defining 14 different haplotypes;

  • Plasminogen Activator Urokinase (PLAU): 9274 bp on the chromosome 10q24: 16 bi-allelic loci are kept, defining 10 different haplotypes;

  • Tumor Necrosis Factor (TNF): 4830 bp on the chromosome 6p21.3: 10 bi-allelic loci are kept, defining six different haplotypes.

Data from chromosome 20 (HapMap project)

A 500 kb region of chromosome 20 sequenced for 30 CEPH trios is randomly chosen (from position 48362908 to 48862907). The most likely haplotypes are reconstructed using Phase v2.0.14, 15 Two different sets of SNPs are studied:

  • CHR20_1 (461 kb): 13 randomly chosen SNPs, defining 37 different haplotypes

  • CHR20_2 (442 kb): 12 randomly chosen SNPs, defining 38 different haplotypes

Data on the CARD15 region

The data set16 includes 232 families with two affected children and their parents genotyped for 13 SNPs covering 140 kb in the CARD15 region. Haplotypes were reconstructed using GENEHUNTER 2.0b.17 Haplotypes with missing data were removed and 531 control haplotypes (parental haplotypes non-transmitted to the children) were kept for the analysis. These data include 88 different haplotypes.

The pairwise LD (r2 value) for these six data sets obtained with GOLD software18 are presented as a Supplementary figure.

The three tests

The data were analyzed using the CLADHC software,12 kindly provided by Caroline Durrant. This program considers overlapping sliding windows of SNPs across the haplotypes. In each window, three association tests are performed:

  • A single-locus allele-based analysis using Pearson's χ2 test.

  • An haplotype-based logistic regression without grouping of haplotypes referred to as T[h].

  • An haplotype-based logistic regression analysis with clustering of haplotypes: a tree of the haplotypes is reconstructed using a distance method and a statistics is calculated at each level of the tree. The statistics at the level maximizing the evidence of a disease-marker association is then retained. This test is referred to as T[MAX].

For each window, the program also provides a significant threshold calculated using the Bonferroni correction. The single-locus test is corrected for the number of SNPs, T[h] is corrected for the number of windows and T[MAX] is corrected for the number of windows and for the number of levels in the tree.

The simulation process

We start by selecting a site as the disease susceptibility (DS) site in the studied gene. In the following, we will assume that the minor allele at this locus is the one that confers the highest risk of disease (DS allele). To generate the genotype of each individual, pairs of haplotypes are randomly sampled with replacement and the disease status is obtained by applying the penetrance f2, f1 and f0 associated to the different genotypes (2, 1 or 0 DS alleles) at the DS locus. The chosen penetrance values correspond to an heterozygote genotype relative risk (GRR) of 1.5 and to homozygote GRRs of 2, 5 and 10, respectively. We keep sampling with replacement until we obtain 1000 cases and 1000 controls. This constitutes a replicate and 1000 such replicates are simulated for each of the studied penetrance vectors. CLADHC12 was applied on the simulated data either with the DS site being kept or removed. The powers of the three tests (single-locus, T[h] and T[MAX]) to detect an association are compared as in Durrant et al.12 Windows of six markers are considered for T[h] and T[MAX] tests. Type I errors were evaluated by simulations under the null hypothesis of no association, assigning identical values of the penetrances to all three genotypes (f2=f1=f0=0.50) for both cases and controls. However, since the number of performed tests vary from one method to another, different type I errors are obtained. Therefore, to compare the powers of the methods, the data were reanalyzed with different nominal values, until the observed type I errors equal 1% for all the three tests.

For IL13, PLAU, TNF, CHR20_1 and CHR20_2, all the SNPs are considered as the susceptibility site in turn, except when two sites are in complete LD. In this latter case, only one of the two sites is studied. For the CARD15 region, as the computation time is really longer due to the larger haplotypic diversity in the data set, only nine SNPs out of the 13 are analyzed.

Results

Results of the power computations are presented in Table 1 and in Figures 1 and 2. In Table 1, the power to detect an association is presented for site 13 of the CARD15 region. As expected, the power of the three tests is higher when the homozygote GRR is high, and when the susceptibility site is included in the analysis. The same results are obtained for all the sites on the four genes.

Table 1 Power of the three tests obtained over 1000 simulations for different penetrance vectors in the CARD15 region. The chosen susceptibility site is SNP13
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Figure 1
figure 1

Power of the three tests (S: single-locus test, B: T[h] test, C: T[MAX]) test according to the frequency of the DS allele and to the LDmax between the DS site and another site. The DS site is kept in the analysis. (a) CHR20_1, (b) CHR20_2, (c) CARD15, (d) IL13, (e) PLAU, (f) TNF.

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Figure 2
figure 2

Power of the three tests (S: single-locus test, B: T[h] test, C: T[MAX]) test according to the frequency of the DS allele and to the LDmas between the DS site and another site. The DS site is removed before analysis, (a) CHR20_1, (b) CHR20_2, (c) CARD15, (d) IL13, (e) PLAU, (f) TNF.

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The power of the three tests for an homozygote GRR of 2 is presented in Figures 1 and 2 for different values of DS allele frequency and for different maximum linkage disequilibrium (LDmax, based on the r2 values) between the susceptibility site and another site. Whatever the test, we can see that the power increases when the DS allele frequency and the LDmax increase.

The difference in power for the three tests can be tested by a Friedman two-way analysis of variance. As our data sets are heterogeneous, we test separately the data sets corresponding to long sequences (CHR20_l, CHR20_2 and CARD15) and to short sequences (IL13, PLAU and TNF). The two groups are referred to as LS and SS, respectively. When the susceptibility site is present (Figure 1), we find that the power of the three tests is statistically different at the 1% level for LS and SS. As expected in this case, the single-locus test is more powerful than the two others since the use of haplotypes increases the number of tests without adding any information. The difference in power between the two haplotypic tests is not significant at the 5% level for both LS and SS. When the susceptibility site is removed (Figure 2), the difference in power between the three tests is significant at the 1% level for LS and at the 5% level for SS. The pairwise comparisons of the three tests show that T[h] and T[MAX] are not significantly different at the 5% level for both LS and SS and that the single-locus test is more powerful than the two other tests. The power of the single-locus test is particularly high when LDmax is high. However, it should be noted that for the haplotypic tests, the results in the overlapping windows are highly correlated. Thus, they may suffer a greater loss of power due to the Bonferroni correction than the single-locus test. With a less conservative correction for multiple testing, the difference of power between the single-locus test and the haplotypic tests should be reduced.

For an homozygote GRR of 5, the powers are very high for all the three tests (around 100% for 66% of the tested sites), and no significant difference is observed between the three tests.

In this study, as in Durrant et al,12 we assume that haplotypes can be reconstructed without ambiguity. If this is not the case, haplotype uncertainty should be taken into account in the haplotypic tests and their power will be reduced. The power of the single-locus test will not be affected and thus the difference in power between the tests will be increased.

Discussion

The results obtained in this study turn out to be very different from those published by Durrant et al,12 although the same software is used. For the same GRR values, our power estimates are definitively higher than theirs. A possible explanation may be the large size of their analyzed region (10 Mb region, 5216 markers): although they do not specify the number of markers included in the ‘flanking region’ used to evaluate the power, we can assume that they are numerous and that a strong correction for multiple testing is used, thus decreasing the power of all the three methods. Our results show that the method of Durrant et al does not generally lead to a statistically significant gain in power compared to both single-locus and T[h] tests, T[MAX] being the most powerful test only for six sites out of the 57 sites tested. One must note that CLADHC is designed to analyze long sequences (several Mb), and thus, in our simulations, we may not be under the optimal conditions, especially for the three short sequences IL13, PLAU and TNF. For the CHR20 data for which distances between markers are close to the ones in the example given by Durrant et al12 (17 of their 23 studied markers are in a 600 kb region of the CFTR gene) we indeed find that the performance of T[MAX] compared to T[h] and to the single-locus test is better than in the other studied regions. However, even then, T[MAX] has the highest power for only five sites out of 25. For the remaining 20 sites, there is a lack of power when using T[MAX] instead of T[h] or a single-locus test. The relative power of the three tests seems to vary with the LDmax and with the frequency of the DS allele: all sites but one for which T[MAX] performs better than the two other tests have moderate LDmax (<0.6) and moderate frequency of the DS allele (<0.27). The difference between our results and Durrant et al's may be explained by the simulation process they use to generate their sample of haplotypes: they are obtained after a particular processing of the observed data that might lead to extreme LD patterns. In our simulations, whole haplotypes are sampled from real data sets, thus keeping the observed LD between the studied locus.

The power of another phylogeny-based association test has also been investigated by Seltman et al19 who extended the method of Templeton11 to case-parent trios data. However they use a simulation process different from the one used here and in Durrant et al.12 Indeed, rather than choosing a susceptibility site, Seltman et al19 choose groups of at-risk haplotypes on the tree and assume that all the other haplotypes are only carried by control individuals. This may give an advantage to the evolutionary-based method, especially when the at-risk haplotypes are all grouped in a clade.

To conclude, the distance-based grouping of haplotypes as described in Durrant et al12 will usually result in a lack of power as compared to other association tests except for very particular patterns of LD and DS frequency where a slight gain in power may be obtained. However, as suggested in Durrant et al,12 in Seltman et al19 and in Bardel et al,20 the various clustering or phylogeny-based methods might be more powerful when more than one susceptibility site are involved in the disease and be more efficient to precisely localize these susceptibility sites along the haplotypes. Further investigations should confirm these points.