On the use of haplotype phylogeny to detect disease susceptibility loci.

BACKGROUND: The cladistic approach proposed by Templeton has been presented as promising for the study of the genetic factors involved in common diseases. This approach allows the joint study of multiple markers within a gene by considering haplotypes and grouping them in nested clades. The idea is to search for clades with an excess of cases as compared to the whole sample and to identify the mutations defining these clades as potential candidate disease susceptibility sites. However, the performance of this approach for the study of the genetic factors involved in complex diseases has never been studied.
RESULTS: In this paper, we propose a new method to perform such a cladistic analysis and we estimate its power through simulations. We show that under models where the susceptibility to the disease is caused by a single genetic variant, the cladistic test is neither really more powerful to detect an association nor really more efficient to localize the susceptibility site than an individual SNP testing. However, when two interacting sites are responsible for the disease, the cladistic analysis greatly improves the probability to find the two susceptibility sites. The impact of the linkage disequilibrium and of the tree characteristics on the efficiency of the cladistic analysis are also discussed. An application on a real data set concerning the CARD15 gene and Crohn disease shows that the method can successfully identify the three variant sites that are involved in the disease susceptibility.
CONCLUSION: The use of phylogenies to group haplotypes is especially interesting to pinpoint the sites that are likely to be involved in disease susceptibility among the different markers identified within a gene.

Background

With the development of molecular techniques to identify genetic polymorphisms, numerous markers and in particular Single Nucleotide Polymorphisms (SNPs) [1,2] are now available within and between genes for establishing their possible role in disease susceptibility. One recurrent question in the literature is the way these markers could be used to test for association with complex diseases [3,4]. Should one focus on one marker at a time and simply compare allele or genotype distributions for the studied markers in cases and controls or should one consider haplotypes formed by several linked markers? Haplotypic methods have been suggested to be more powerful at detecting the role of a given genomic region in disease susceptibility [4-7]. Indeed, disease susceptibility may be due to the combined effects of variants at different markers. Different methods have been proposed to test for association between markers located on the same reconstructed haplotypes and disease susceptibility [4,7-10]. In these tests, the number of haplotypes being large, the degrees of freedom to compare cases and controls are also large, decreasing the power to detect the association. Moreover, as some haplotypes would only be carried by one or two individuals, there could be statistical problems owing to small sample sizes making difficult the evaluation of their possible effect on the susceptibility to the disease.

A solution to reduce these problems is to group haplotypes in order to decrease the degrees of freedom and to increase the number of individuals in the different haplotype groups. The cladistic method as described by Templeton et al. [11] is a method to carry out such groupings of haplotypes and to determine which haplotype or group of haplotypes is likely to be responsible for the phenotypic variation observed among the population. It consists in using parsimony methods to build a phylogeny of the haplotypes, and to group haplotypes according to the clades defined by the phylogenetic tree. When applied to a case/control data set, the proportions of cases and controls in different clades are compared. If a clade shows a significantly larger number of cases than the others, one will conclude, first, that there is an association between the disease and one haplotype or a group of haplotypes belonging to the clade, and, second, that the mutations defining the clade containing an excess of cases are good candidates to be functional gene polymorphisms involved in the disease susceptibility.

The cladistic analysis relies for a large part on the reconstruction of an accurate phylogenetic tree, but recombination is known to bias phylogenetic reconstruction processes [12]. The recent discovery of the haplotype block structure of the human genome [13] now provides an interesting framework for cladistic methods. Indeed, haplotype blocks define regions in which the recombination rate is quite low. Moreover, once a block is found to be associated with a disease, it will not be suitable to use classical methods based on recombination to fine map susceptibility loci. Haplotype phylogenies being based on the history of mutations may then help to identify disease susceptibility loci.

The cladistic method was first described in a series of five articles [11,14-17] and applied in different case-control studies focusing either on quantitative or qualitative data. For example, Haviland et al. used a cladistic analysis to study the association between the apolipoprotein AI-CIII-AIV and plasma lipid, lipoprotein and apolipoprotein levels [18]. Keavney et al. [19] used cladograms to localize the sites that significantly influence Angiotensin-I Converting Enzyme (ACE). Zhu et al. [20] worked on quantitative data simulated for the twelfth Genetic Analysis Workshop (GAW). Using regression analysis and analysis of variance (ANOVA), they were able to find a short region containing the simulated mutation. Wang et al. [21] used a nested linear model to analyze the association between ApoA4 haplotypes and plasma lipid level in the cladistic framework. Among the studies that consider discrete data is the one by Kittles et al. [22] who tested the association between haplotype variations on the Y chromosome and alcohol dependence and related personality traits. Lobos and Todd applied the same cladistic method to four RFLPs in the tyroxine hydroxylase gene [23], and to five SNPs in the dopamine receptor D2 gene [24]. Darlu and Génin [25] applied the method to the GAW 12 simulated data and were able to identify some of the disease susceptibility sites. For a more detailed review on the subject, see [26].

More recently Seltman et al. [27] developed a method that can be applied on family-based data. They proposed a test, the ET-TDT, that combines the transmission disequilibrium test (TDT) and the use of unrooted phylogenetic trees to group haplotypes. They further extended their method to the analysis of qualitative and quantitative data from case-parent trios or population-based studies [28]. Finally, an alternative method where phylogenetic trees are reconstructed by a distance method was proposed by Durrant et al. [29] and implemented in the software CLADHC.

From these different examples, cladistic methods appear to be innovative methods to detect an association between a candidate gene and a disease and to localize disease susceptibility sites. However, the validity and the power of these methods to detect association have only been tested in a very limited number of situations (fixed pattern of linkage disequilibrium, fixed phylogenetic tree) [27,29]. In this paper, we develop a new cladistic test (CT), based on the analysis of a rooted tree, which allows to make hypotheses about functional polymorphisms that are involved in the susceptibility to the disease. Through simulations on ten different tree topologies, we evaluate the conditions in which this cladistic method is efficient and compare it to other methods. Finally, we apply this method to a real data set concerning Crohn disease and the CARD15 gene [30].

Results

Association test

As detailed in the method section, four different tests are performed: a single locus allele-based test referred to as SbST (Site by Site Test), an haplotype-based test referred to as HT (Haplotypic Test), a test based on haplotype phylogenies referred to as CT (Cladistic Test) and a test based on the clustering of haplotypes described by Durrant et al. [29] and referred to as CLADHC. To compare their respective power to detect an association, simulations were performed under three disease models involving one (model 1) or two (model 2 and model 3) susceptibility sites for ten different tree topologies.

Results for model 1 are presented in Table 1 and 2. When the susceptibility site is included in the studied SNPs (Table 1), SbST is the most powerful test for all trees but one (tree 8) (between 99.1% and 99.5% depending on the tree, 99.35% on average), while the other tests have a weaker power (92.9%, 93.7%, and 91.2%, on average, for CT, HT, and CLADHC respectively). CT and CLADHC have almost the same average type I error, slightly but significantly lower than the type I error of HT and SbST. In these simulations, as the type I errors cannot be fixed a priori, powers may be difficult to compare. However, if the type I errors of CT and CLADHC were increased, their power would also be increased and, consequently, the difference in power with HT would be even more pronounced and the difference in power with SbST would be more reduced. In the trees showing comparable type one error (Trees 1, 5, 7), the power of SbST is clearly higher than the power of CT. When the susceptibility site is removed (Table 2), the performances of the four tests are, on average, similar (about 89%), CT being the most powerful test for four trees, SbST for four other trees, HT and CLADHC for one tree each. However, the type I errors being slightly different, by adjusting them one expects that CT and CLADHC could be on average, slightly more powerful than HT and SbST.

Table 1

Power to detect an association, one susceptibility site simulated and included in the analysis

Tree	CT	CLADHC	HT	SbST
1	96.4 (3.3)	88.9 (3.3)	91.1 (5.1)	99.3(3.4)
2	99.0 (4.4)	95.7 (4.1)	91.3 (6.0)	99.5(5.3)
3	86.0 (2.5)	91.1 (4.7)	91.2 (4.6)	99.3(4.4)
4	96.3 (3.8)	95.6 (2.9)	91.5 (4.2)	99.3(4.6)
5	88.8 (4.1)	95.3 (3.3)	90.4 (4.7)	99.1(4.6)
6	84.5 (3.5)	88.8 (2.7)	90.7 (4.4)	99.5(4.4)
7	97.4 (4.0)	96.3 (3.7)	91.9 (4.8)	99.2(4.3)
8	99.7 (3.2)	98.5 (2.4)	91.2 (4.9)	99.4 (4.7)
9	88.1 (3.5)	94.0 (4.4)	91.3 (4.7)	99.4(4.3)
10	92.5 (2.6)	93.0 (2.9)	91.3 (4.7)	99.5(3.6)
Average	92.9 (3.5)	93.7 (3.4)	91.2 (4.8)	99.35(4.4)
Std dev.a	5.63 (0.62)	3.24 (0.76)	0.41 (0.49)	0.13 (0.54)

Sample size: 100 cases and 100 controls, 1000 replicates, penetrance vector: [0.03;0.06;0.3], frequency of the susceptibility allele: 0.205 ± 0.005. The corresponding type I errors are indicated in italics within brackets. For each tree, the method giving the best result is underlined. CT: Cladistic Test, CLADHC: test developed by Durrant et al. [29], HT: Haplotypic Test, SbST: Site by Site Test.

a Standard deviation

Table 2

Power to detect an association, one susceptibility site simulated and removed from the analysis

Tree	CT	CLADHC	HT	SbST
1	94.8 (3.8)	89.1 (3.5)	91.2 (5.6)	89.5 (3.9)
2	94.0 (3.8)	92.7 (4.1)	87.6 (5.6)	98.5 (5.3)
3	79.3 (3.2)	88.9 (4.7)	86.2 (4.7)	94.2 (4.1)
4	88.7 (2.3)	85.7 (3.1)	87.8 (4.6)	93.6 (4.4)
5	85.6 (4.3)	94.4 (4.1)	90.5 (4.5)	94.0 (4.1)
6	78.6 (3.0)	81.6 (3.3)	88.0 (4.2)	67.0 (4.2)
7	92.4 (3.8)	90.5 (3.7)	87.8 (5.2)	92.7 (4.0)
8	99.7 (3.0)	98.6 (2.8)	91.2 (4.7)	99.6 (4.5)
9	91.9 (3.7)	89.2 (4.5)	91.2 (4.8)	89.1 (4.1)
10	88.8 (2.9)	82.8 (3.0)	81.3 (4.1)	79.1 (3.5)
Average	89,38 (3.4)	89.35 (3.7)	88,28 (4.8)	89,73 (4.2)
Std dev.a	6.71 (0.6)	5.2 (0.6)	3.06 (0.5)	9.81 (0.5)

Sample size: 100 cases and 100 controls, 1000 replicates, penetrance vector: [0.03;0.06;0.3], frequency of the susceptibility allele: 0.205 ± 0.005. The corresponding type I errors are indicated in italics within brackets. For each tree, the method giving the best result is underlined. CT: Cladistic Test, CLADHC: test developed by Durrant et al. [29], HT: Haplotypic Test, SbST: Site by Site Test.

a Standard deviation

As expected, the power is higher when the susceptibility site is included than when it is removed. In this latter case, the power depends on the degree of linkage disequilibrium (LD) between the susceptibility site and the other sites as expressed by the maximum value of LD, referred to as LD. Moreover, since the pattern of LD can be different from one tree to another, one expects more differences in power between trees when the susceptibility site is removed. Indeed the standard deviation of the power is larger in this case. This standard deviation is also particularly large for SbST (σ = 9.81). This test, being an allele-based test, is more influenced by LD than the three others tests that are haplotype-based tests, as proved by the high positive correlation observed between the power of SbST to detect association and the LD(Spearman rank correlation ρ equals 0.851, p-value < 0.01). For CT and CLADHC, Spearman rank correlations are not significant (p > 0.1) confirming that LD has a lesser impact on these two tests. Therefore, the high standard deviations observed for these two tests are probably more related to the phylogeny of haplotypes than to the linkage disequilibrium.

The results for model 2 and model 3, differing by the values of the penetrance vector, are presented in Table 3 and in Table 4 respectively. There is no real difference in power between the four tests for model 2 (about 97%). For model 3, the power of the four tests is approximately half the power for model 2 owing to the reduced value of the penetrance for the genotype associated to the highest risk in this model. In this case, SbST and CT are, on average, the most and the less powerful test respectively

Table 3

Power to detect an association for two susceptibility sites simulated under model 2

		Model 2
Tree	CT	CLADHC	HT	SbST
1	97.8 (3.7)	99.3 (3.8)	97.7 (5.0)	99.1 (6.9)
2	95.1 (3.6)	97.7 (2.9)	97.9 (5.6)	95.8 (4.3)
3	94.2 (4.9)	99.4 (4.9)	97.9 (5.1)	98.6 (4.9)
4	97.6 (4.6)	97.8 (4.6)	97.8 (5.5)	98.6 (4.6)
5	98.5 (5.3)	99.5 (4.5)	98.9 (5.7)	98.2 (7.4)
6	98.9 (4.4)	97.9 (3.9)	98.5 (5.7)	96.9 (6.6)
7	93.0 (5.1)	93.5 (4.6)	96.9 (5.6)	95.5 (5.2)
8	95.2 (6.1)	99.0 (5.3)	98.2 (6.2)	95.4 (4.2)
9	96.7 (3.6)	97.3 (3.1)	97.6 (4.1)	97.7 (4.0)
10	99.9 (4.5)	99.5 (4.0)	98.2 (60.)	99.8 (5.8)
Average	96.7 (4.6)	98.06 (4.2)	97.96 (5.45)	97.56 (5.4)
Std dev.a	2.24 (0.8)	1.83 (0.8)	0.54 (0.6)	1.58 (1.2)

Sample size: 200 cases and 200 controls, 1000 replicates, penetrance: 0.9 for the homozygotes carrying the two susceptibility alleles, 0.3 for the other genotypes. The corresponding type I errors are indicated in italics within brackets. For each tree, the method giving the best result is underlined. CT: Cladistic Test, CLADHC: test developed by Durrant et al. [29], HT: Haplotypic Test, SbST: Site by Site Test

a Standard deviation

Table 4

Power to detect an association for two susceptibility sites simulated under model 3

		Model 3
Tree	CT	CLADHC	HT	SbST
1	40.7 (4.7)	54.0 (4.5)	42.0 (5.9)	47.5 (4.7)
2	31.7 (3.4)	32.7 (3.9)	43.0 (5.9)	45.8 (5.3)
3	26.8 (4.2)	47.9 (4.4)	40.7 (6.4)	45.2 (3.5)
4	34.8 (4.8)	39.2 (4.7)	38.9 (7.0)	47.0 (4.4)
5	41.5 (5.6)	49.7 (4.7)	44.2 (6.6)	37.2 (4.6)
6	42.0 (3.6)	34.8 (4.7)	42.4 (5.6)	41.3 (5.3)
7	28.6 (5.2)	32.1 (4.7)	41.6 (6.4)	39.9 (4.3)
8	33.2 (4.3)	47.2 (4.0)	42.9 (6.1)	37.7 (4.0)
9	33.5 (4.4)	39.1 (4.1)	41.2 (7.0)	48.5 (5.3)
10	65.6 (6.6)	48.1 (4.1)	42.1 (7.8)	56.9 (4.2)
Average	37.84 (4.7)	42.48 (4.4)	41.9 (6.5)	44.7 (4.6)
Std dev.a	11.07 (0.9)	7.84 (0.3)	1.45 (0.7)	5.94 (0.6)

Sample size: 200 cases and 200 controls, 1000 replicates, penetrance: 0.6 for the homozygotes carrying the two susceptibility alleles, 0.3 for the other genotypes. The corresponding type I errors are indicated in italics within brackets. For each tree, the method giving the best result is underlined. CT: Cladistic Test, CLADHC: test developed by Durrant et al. [29], HT: Haplotypic Test, SbST: Site by Site Test

a Standard deviation

Localization of the susceptibility site(s)

The efficiency of SbST, CT and CLADHC to localize the susceptibility site(s) when it is included among the SNPs is presented in Figure 1 and 2. The efficiency of CT is plotted against the efficiency of SbST or CLADHC. To correctly interpret these figures, it has to be noted that the criteria used to compare the methods are not strictly identical. Indeed, the identified SNP is always unambiguously detected by the SbST method, since this is the site giving the most significant chi-square and two chi-squares are never exactly identical. On the other hand, the susceptibility site may not be the only one detected by CT because two or more sites could have the same values of the criteria (V, see the Methods section). However, in our simulations, the susceptibility site is the only one detected in from 80% (for 1 tree) to 100% (for 5 trees) of the replicates. When the susceptibility site is not found alone, it is almost always found with only one other site, rarely with two other sites (<0.5% of the replicates).

Figure 1

Comparison of the efficiency to localize the susceptibility site between CT, and SbST or CLADHC. The efficiency to localize the susceptibility site is measured by the percentage of replicates in which the simulated susceptibility site is either uniquely detected or detected among other putative sites. black circles: comparison of CT and SbST, crosses: comparison of CT and CLADHC. Each symbol corresponds to one of the ten tree topologies.

Figure 2

Comparison of the efficiency to localize the two susceptibility sites between CT and SbST. The efficiency to localize the two susceptibility sites is measured by the percentage of replicates in which the two sites are detected (black circles) or at least one of the two sites (white circles) Each symbol corresponds to one of the ten tree topologies. (A): penetrance 0.9 for homozygotes carrying the two susceptibility alleles and 0.3 for all other genotypes; (B): penetrance 0.6 for homozygotes carrying the two susceptibility alleles and 0.3 for all other genotypes.

For model 1 (Figure 1), CT is slightly less efficient than SbST (for 9 trees out of 10) and more efficient than CLADHC (for all 10 trees). For SbST, we note a high negative correlation between the efficiency to localize the susceptibility site and the LDbetween the susceptibility site and the other sites (Spearman rank correlation ρ equal -0.88 with a p-value of 0.008). It shows that the presence of a site in relatively high LD with the susceptibility site disturbs the localization process, increasing the uncertainty of the susceptibility site's identification. Interestingly, there is no such statistically significant correlation with CT and CLADHC (p > 0.08), due to the fact that these last two tests use both the information on the whole haplotypes and on their history through the tree reconstruction. The presence of sites in high LD with the susceptibility site does not prevent these two methods from localizing correctly the susceptibility site.

For model 2 and model 3, (Figure 2A and 2B respectively), CT is more or at least as efficient as SbST to localize the two sites, whatever the penetrance model. For the detection of at least one of the two sites, we can observe that, whatever the tree, CT is always more efficient than SbST under model 2, whereas this is only true for 6 out of the 10 trees under model 3.

Application to CARD15/NOD2 polymorphisms and Crohn disease

The reconstruction of the phylogenetic tree of the 33 haplotypes leads to a very high number of equally parsimonious trees. One thousand of them were retained and analyzed. In table 5, for the two rooting methods mfH and consH, the SNPs are ranked from the least to the most significant (based on the Vparameter, see the Methods section). Association is detected with CT (p= 2 × 10-5, p= 3 × 10-5) and SNP 8 is selected as potential susceptibility site. If haplotypes carrying the susceptibility allele at SNP 8 are removed, an association can still be detected (p= 4 × 10-5, p= 3 × 10-5) and SNP 12 is identified as potential susceptibility site. When removing haplotypes with the susceptibility allele at SNP 12, there is still a remaining association (p= 8 × 10-5, p= 3 × 10-5) and depending on the rooting method either SNP 13 (with consH) or SNP 9 (with mfH) are retained. When haplotypes with the susceptibility allele at SNP 13 are removed, the association test is not significant (p= 2.9 × 10-1, p= 1.1 × 10-1). When haplotypes with the susceptibility allele at SNP 9 are removed, the association test is significant (p= 2 × 10-5, p= 5 × 10-5) and the identified site is SNP 13 for both rooting method. In the end, the combination of SNP 8, SNP 12 and SNP 13 is the most parsimonious combination that can explain the susceptibility to the disease. Moreover, we can note that these 3 SNPs are those showing the highest Von the whole data set. So, we finally have identified three SNPs involved in the susceptibility to Crohn's disease.

Table 5

Cladistic analysis of Crohn's data 1000 equiparsimonious trees are studied. SNPs are ranked from the least to the most significant. In bold, the presumed susceptibility sites previously identified by Hugot et al. [30].

	least significant				-------->	most significant
mfHa	SNP 5	SNP 9	SNP 6	SNP 7		SNP 13	SNP 12	SNP8
consHb	SNP 9	SNP 5	SNP 6	SNP 7		SNP 13	SNP 12	SNP8

a Rooting on the most frequent haplotype

b Rooting on a consensus sequence

Discussion

In this paper, we have presented a method to perform phylogeny-based nested haplotype analysis of case/control data and introduced the cladistic test (CT). We have shown by simulations that the CT test is approximately as powerful to detect an association as a test that compares haplotype distributions in cases and controls with no prior grouping. However, a major advantage of CT towards other haplotypic tests is the possibility of making inferences on potential susceptibility sites. Indeed the method of parsimony used to build the phylogeny allows the reconstruction of character state changes on the tree and thus the identification of the most likely susceptibility sites. Finding the polymorphisms responsible for the susceptibility to a disease is an important issue in genetic epidemiology and in the past few years, different methods have been proposed that use linkage disequilibrium to fine-map candidate genes and to localize disease mutations ([31,32] and [33] for example) These methods are based on the fact that a disease variant arises on a particular haplotype, the haplotype and the disease thus being initially associated. Then, over time, this association is broken by recombination and only a small region of the ancestral haplotype is preserved around the disease variant. In such models, recombination is the event of interest. Other parameters such as mutations can be integrated in the models, but they are considered as nuisance parameters. The cladistic test developed here is different in the sense that it is based on the reconstruction of the evolutionary history of the mutations that occur to form the haplotypes. Contrary to the other fine-mapping methods, the event of interest is mutation, and recombination is a nuisance parameter. Through the simulation study, we have shown that this test is a powerful tool to suggest etiological SNPs. This is also illustrated here on Crohn disease since the cladistic test was able to correctly identify the 3 sites within the CARD15 gene that are already reported to be involved in the disease susceptibility [30].

The cladistic test requires the building of a phylogeny of the different haplotypes present in the sample. Different methods are available to build haplotype phylogenies: distance methods, parsimony methods and maximum likelihood (ML) methods. A parsimony method was chosen here because it allows the reconstruction of apomorphies that can be used to define potential sites involved in the disease susceptibility and because it runs faster than ML methods, thus allowing a simulation study. We have compared CT with another clustering method, CLADHC, a distance-based method that also differs from CT in the statistical analysis (CLADHC performs regression analysis, CT is based on chi-square tests). We have shown that the power of these two tests to detect association is quite similar, CT being slightly more powerful when one site is simulated, and CLADHC when two sites are simulated. For the localization of the susceptibility site, the efficiency of the two methods is difficult to compare because CT directly localizes the site on short sequences while CLADHC localizes a window containing the susceptibility site on longer sequences. The two test should thus be used in different situations. Nevertheless CT appears to be more efficient in our simulation conditions

In the phylogeny reconstruction, one is faced to different problems. The first one is the choice of the ancestral sequence to root the phylogeny. With real data, the ancestral sequence is usually not known, unless at least two outgroups can be postulated (in the parsimony context). In the absence of ancestral sequences, hypotheses have to be made, and they are numerous, like taking the most frequent haplotype, but this haplotype could be different from one population to an other or from one sampling to another, and this most frequent haplotype may not have a significantly different frequency from the next most frequents. Or one can take the consensus haplotype, but this sequence may not be observed in the sample, or not be among the most frequent sequences. In this study, our strategy was to consider the uncertainty of the ancestral sequence as a nuisance parameter, since our goal was not primarily to focus on this problem and because we must be in the same situation for all the performed simulations. Extensive further simulations will be needed to assess the properties of the different rooting methods. However, several ancestral hypotheses should be considered, discussed, and tested on real data, as we have done for the Crohn data. Second, the presence of recombinations would restrict the use of phylogenetic reconstruction. Indeed, phylogenetic reconstruction is known to be biased by recombinations [12] in a manner depending on how and when the recombination events occur in the tree. This context led us to simulate the history of mutations along the haplotypes without introducing recombinations between haplotypes. However, because in our method the reconstructed tree has not to represent the exact history of the haplotypes, but only gives a way to cluster them in an appropriate way, we believe that our method can tolerate some low degrees of recombination, as it is probably the case for the Crohn data. Further simulations would however be required to better assess this point. Third, the choice of the way characters are optimized on the tree is another important point in cladistic analysis. Two classical options can be used to optimize the character state changes along the tree: deltran, (delayed transformation) that favors convergences or acctran(accelerated transformation) that favors reversions. In this paper, only the results performed with the deltran option are presented. Simulations (one susceptibility site) have also been performed with the acctran option. For the association detection, the results are very similar to those obtained with deltran showing that this parameter does not influence the power of the CT method to detect association in our simulation conditions. For the localization of the susceptibility site, the results are different. The method is more efficient with the deltran option than with the acctran option for eight trees out of ten, it is less efficient for one tree and the results are equivalent for the last tree. It is partly due to to the uncertainties of the character S and to the frequency of the disease susceptibility allele. When the frequency of the susceptibility allele is low, as in our simulations, and when S is coded "?" in some nodes of the tree, one expects the change of S from 0 to 1 to occur later in the tree, and the delayed option (deltran) will then be more appropriate. Conversely, when the frequency of the disease is large, the change of S from 0 to 1 has more chances to occur earlier in the tree since the S mutation can then include more cases, and the accelerated option (acctran) will be more appropriate. However, when analyzing a real data set, it is advisable to compare the results obtained with both options.

The variability of the results obtained with the cladistic method is due for a minor part to the LD between the susceptibility site(s) and the other sites and for the major part to parameters specific to the tree. Among these parameters, the position of the mutation in the tree (near the root or the leaves, sample size of the clades near the mutations...) has already been reported to have an influence on the power of cladistic methods to detect association [27]. Apart from the position of the mutation, the presence of sites that co-mutate with the susceptibility site, the degree of multiple mutations of the susceptibility site in the tree, and the existence of one or more reversions for the susceptibility site influence the power of the cladistic test to detect an association, and they have an even greater impact on the efficiency of the cladistic test to localize the susceptibility site. As all these factors are not independent, the evaluation of their own effects remains problematic.

The four methods compared here (CT, HT, SbST and CLADHC) suppose that haplotypic data are available, which is not usually the case. The most likely haplotypes for an individual have to be reconstructed using numerical methods (for a review of these methods, see [34,35]). The availability of familial data may help to determine the phase of the markers and then, to obtain the most likely haplotypes by using the genetic information of the two parents. However, even when these familial data are not available, the numerical methods have been shown to be very efficient to reconstruct haplotypes, except for rare haplotypes that may either be missed or falsely created. In this work, since we choose to focus on the comparison between several methods, the problem of haplotype inference is ignored. Moreover, as the four studied methods are all based on already known or inferred haplotypes carried by the individuals, the uncertainty due to the haplotype inference should not play differently from one method to another. Further extension of the CT method will take this uncertainty into account by using, for example, likelihood-based tests.

Conclusion

In conclusion, as proved by our simulations and the Crohn example, the use of phylogenies to group haplotypes by clades and the nested analysis of case-control data on the basis of these clades turns out to be an interesting and complementary strategy for the genetic study of multifactorial diseases, especially to pinpoint the sites that are likely to be involved in disease susceptibility among the different markers identified within a gene.

Methods

Principle of the method

The material on which the method is based is a sample of haplotypes composed of a combination of SNPs, each haplotype being labeled either as control or as affected depending on the phenotype of the individual. After building the phylogenetic tree of these different haplotypes, a series of nested homogeneity tests are performed to detect differences in the distribution of cases and controls in the different clades. Once an association is detected, a new character is defined according to the proportion of cases carrying an haplotype. Then, it is optimized on the tree and the sites that significantly co-mutate with this new character are putative susceptibility sites for the disease.

Simulation study

To test the power of this method to detect an association and its efficiency to precisely localize the susceptibility site, we performed the following steps : i) simulation of the haplotypes and choice of the susceptibility site(s) (one or two susceptibility sites are considered) ; ii) attribution of a status (case or control) to these haplotypes taking into account the genetic model of the disease; iii) reconstruction of the phylogeny of haplotypes and inference of the character state changes along the branches of the tree; iv) association test: nested analysis of the case/control ratio in the clades; v) localization of the susceptibility site using the equiparsimonious (ie, all the trees that have the minimum number of character state changes) ; vi) estimation, by simulations, of the power to detect the association between haplotypes and the disease and comparison with other methods; vii) estimation of the efficiency to localize susceptibility sites and comparison with other methods.

Haplotype simulation

24 different haplotypes are simulated using the TREEVOLVE software (version 1.32) [36]. An ancestral haplotype sequence of 20 sites is randomly produced, a guide tree is generated using the coalescent model without recombination and the evolution of this ancestral sequence along the tree is simulated to obtain a sample of 24 different haplotypes. Since TREEVOLVE can only simulate the evolution of DNA sequences (4 nucleotides) and not the evolution of bi-allelic markers, we set the frequencies for bases A and T to very low values (A = T = 0.001 and G = C = 0.498) in order to obtain an ancestral sequence composed only of G and C, as an equivalent of SNPs coded by 0/1 character states. The mutation rate is set to 2 × 10-6, and the substitution rates are chosen so that only G-C transversions could occur: A - C = 0.001, A - G = 0.001, A - T = 0.001, C - T = 0.001, G - T = 0.001, G - C = 0.995. No heterogeneity in the substitution rate among sites is specified. The population size was set to 100,000 and its growth was stationary with no subdivision. Once the haplotypes are obtained by simulation, the susceptibility sites are chosen among the 20 sites. For the simulations with only one susceptibility site, the program picks up the first site in the sequence having a minor allele frequency (p) in the sample of haplotypes within the range F