INTRODUCTION

TOP ABSTRACT INTRODUCTION DISCUSSION REFERENCES

The current emphasis on searching for disease susceptibility genes is carried out by association to tens of thousands of SNP markers (Collins et al. 1998). Such association analyses may be carried out in a variety of data designs, for example, by testing for differences in SNP allele frequencies between affected and unaffected individuals (case-control studies), or by comparing whether a SNP allele is transmitted to an affected offspring more or less often than expected by chance (the transmission disequilibrium test, TDT; Spielman and Ewens 1996). Because complex traits presumably arise from multiple interacting genes located throughout the genome, it would be appropriate to search for sets of marker loci in different genes and to analyze these markers jointly rather than testing each marker in isolation. Forming haplotypes over multiple neighboring markers in one gene can increase the power of gene mapping studies (Fallin et al. 2001), as can scan statistics (Hoh and Ott 2000); but these methods only work locally in a given genomic region.

Most current approaches essentially evaluate one SNP marker at a time, that is, by focusing on its marginal effect on disease. Those SNPs with a significant association to disease are taken to be close to or within susceptibility genes. Testing each SNP for association with disease leads to a locus-specific probability of a false-positive result (type I error). Such a type I error can easily be inflated when large numbers of SNPs are tested simultaneously and treated independently (Risch and Merikangas 1996); the problems involving such multiple testing and its effect on the genomewide type I error are the subject of a presently ongoing debate (Lin et al. 2001). For genomewide linkage analysis, appropriate measures have been developed to keep this problem under control (Lander and Kruglyak 1995). For genomewide association analysis, however, no general treatment exists because the interactions between markers do not follow a known pattern. But apart from these problems of multiple testing, this marker-by-marker approach completely ignores the multigenic nature of complex traits and does not take into account possible interactions between susceptibility genes.

Although various authors have postulated the need for investigating multiple disease genes jointly, few viable approaches in this direction exist. Looking at all possible pairs of marker loci in the genome and evaluating the significance level of each pair may not be the answer because of the high number of tests required (Dupuis et al. 1995), although, for a small number of candidate marker loci, this method does seem to have merit (Cordell et al. 1995). Conditional approaches, in which a new locus is searched for, given good evidence for an existing locus or set of loci, appear more promising (Dupuis et al. 1995; Cordell et al. 2000).

In addition to a small number of multilocus approaches (Stoesz et al. 1997; Blangero et al. 2000), an intriguing method has recently been proposed to allow for the joint analysis of multiple marker loci (Nelson et al. 2001). This combinatorial partitioning method (CPM) works by evaluating all possible partitions of marker loci and retaining only those partitions fulfilling certain optimality criteria. Of course, the possible number of partitions is astronomical. Focusing on partitions comprising two marker loci each, Nelson et al. (2001) showed that this approach identified biological interactions between loci. Unfortunately, the CPM may not easily reach genomewide statistical significancein an application to candidate genes for coronary heart disease, the overall significance level was 0.14 (Nelson et al. 2001).

In this paper, we introduce an alternative approach, set-association, to evaluate sets of SNP markers at various positions in the genome (in particular, in different susceptibility genes). This method performs a simultaneous significance test on several sets of loci while keeping the overall type I error in control. To increase the power of the test, that is, to limit the false-negative error rate, we combine relevant sources of information for a given SNP: allelic association (AA), Hardy-Weinberg disequilibrium (HWD), and evidence for genotyping errors. Contributions from multiple SNPs in different genomic regions are combined by forming a sum of single-marker statistics, which results in a single genomewide test statistic with high power. The principle of summing over single-locus statistics is based on an extension of Tukey's compound covariates in a linear regression setting (Tukey 1993). In Tukey's case, covariates were summed to form a new compound covariate, and the association between such a compound covariate and the dependent variable was evaluated via regression analysis. In our case, a trait-association statistic for each marker is suitably chosen, sets of such statistics are summed, and the significance levels are evaluated via computer-based randomization (permutation) procedures. Our set-association method for detecting a set of possibly interacting trait-associated SNP markers has an accurate and small overall false-positive rate but does not incur the penalty of low power. And, most importantly, this method is easily implemented in a computer algorithm.

Set-Association Approach

Previous work has shown that deviations from Hardy-Weinberg equilibrium (Crow 2001) in affected individuals may be indicative of the presence of susceptibility loci (Feder et al. 1996; Nielsen et al. 1999). On the other hand, it is allelic association (due to proximity of an SNP to a susceptibility gene) that measures overrepresentation of genomic variants in cases versus controls. For this reason, we consider both of these effects, AA and HWD, where each may be expressed by a -square statistic. The extent of AA is measured, for example, by the -square in a 2 × 2 table with rows corresponding to cases and controls, and columns corresponding to SNP alleles 1 and 2; a simpler measure is the mean difference in the number of 1 alleles between cases and controls. HWD is defined as the -square for deviation from Hardy-Weinberg equilibrium, which may be obtained with one of our utility programs (http://linkage.rockefeller.edu/ott/linkutil.htm#HWE). As outlined in detail below, we combine these two sources of information for a given SNP by simply forming the product of the corresponding two statistics.

Trimming

HWD As an Association Measure

Weighting

Grouping

Significance Tests

View larger version (50K): [in this window] [in a new window]   Figure 1   Flow diagram illustrating the algorithm implemented in the set-association approach.

Application

The set-association approach worked successfully on the following case-control study (R. Zee, pers. comm.). In 779 heart disease patients, 6 mo after angioplasty, 342 showed restenosis ("cases"), the rest being "controls." All individuals were genotyped for 89 SNP markers in 62 candidate genes. Clearly, this study is not a genomewide association study, but it serves the purpose of showing our method. The results of this study have not yet been published, which is why we report marker ID numbers rather than marker names below.

For trimming, we considered HWD values exceeding the 99th percentile of ² (= 6.6, 1 df) in control individuals as unusually large. Among the 89 SNPs, under the hypothesis of Hardy-Weinberg equilibrium, <1 SNP is expected to be in this region. Here we have four HWD values larger than 6.6, corresponding to SNPs #13 (HWD = 29.4), #50 (HWD = 21.7), #22 (HWD = 12.6), and #23 (HWD = 6.9). Therefore, we decided to trim the d = 4 largest HWD -square values in observed and randomized data.

For the AA statistic, t_i, we simply chose the absolute difference in mean frequencies of the 1 allele between cases and controls for the ith SNP. Initially, we computed HWD values, u_i, for association in case individuals. With this, we used t_i × u_i as the single-marker statistic for the ith SNP, with the d = 4 largest values of u_i to be trimmed. Testing up to N = 20 sums furnished the smallest P-value, min_np_n = 0.061, for a sum comprising n = 12 SNPs. The corresponding associated global significance level was obtained as p_min = 0.101, that is, a nonsignificant result.

As all individuals are heart disease patients ("affected"), it makes sense to consider the combined -square for HWD in cases and controls as the measure indicative for association, the idea being that HWD may pick up SNPs correlated with restenosis and heart disease. Therefore, we computed u_i as the sum of HWD for cases and HWD for controls, again trimming the four largest of these summed values, and tested up to N = 20 sums, S_n, as above. This furnished min_np_n = 0.021 for a sum comprising n = 10 SNPs (a subset of the 12 SNPs identified above), with an associated global significance level of p_min = 0.040. Of the n = 10 SNPs, only 2 are in the same gene. Therefore, we conclude that the g = 9 genes identified through the SNPs are likely to confer susceptibility to restenosis. The significance level of S_n as a function of the number n of SNPs included in S_n is shown in Figure 2. Note that the (global) significance level associated with testing the single best marker (#23) is 0.129. This value is much higher than the significance level, p_min = 0.040, for our minimum-p-value statistic, which shows the power of our set-association approach. Because with four clearly inflated HWD ² values the trimming was obvious, there was no need to evaluate p_min-min.

View larger version (23K): [in this window] [in a new window]   Figure 2   Significance level of Sn statistic as a function of the number n of SNPs in different genes that are included at each step. The smallest significance level, minnpn, occurs with 10 SNPs included in Sn. The 10 SNPs represent 9 different genes.

	DISCUSSION

TOP ABSTRACT INTRODUCTION DISCUSSION REFERENCES

Our set-association approach furnishes a list of SNP markers that presumably are in the vicinity or within susceptibility genes. One of the main features of our method is that it furnishes a clearly defined genomewide significance level. Of course, SNPs identified this way must be scrutinized to see whether the genes implicated make biological sense for the trait under study, for example, whether genes identified by these SNPs are reasonable candidate genes. We present our approach as an alternative to other multilocus methods of gene mapping, in particular, the partitioning methods of Nelson et al. (2001). Each of these approaches presumably looks at the data from a different angle, and each has its advantages and disadvantages. We believe that we have a found a way to control the genomewide significance level with excellent power for detecting disease-causing genes.

Application of our method worked well for the restenosis data in the sense that it furnished significant results with a global significance below 5%. Of course, there is no absolute guarantee that this method correctly identified loci contributing to restenosis. Trimming and the use of HWD for association were essential elements in the significance of the result. Using only AA without trimming and no HWD for association resulted in a global significance level of 0.38. On the other hand, differences in HWD between case and control individuals are not significant (P-value = 0.69). Therefore, it really is the combined effect of AA and HWD, coupled with quality control through trimming, that gives our method its power.

Trimming could be applied in one of two ways: Either an SNP is eliminated from analysis altogether (removed from observed and permuted data), or the process of trimming is handled in a dynamic way, that is, applied in observed and permuted data. In our experience, the latter approach is more powerful than the former.

Several unresolved questions need to be addressed. For one thing, the method of incorporating SNPs in sums with increasing numbers n of terms rests solely on the test statistic, t × u, for each SNP. However, SNPs in close proximity to each other in the same gene may be correlated, and having one SNP in the sum may make it less desirable to have another that is strongly correlated with it. We are working on finding more sophisticated ways of building these sums. However, the fact that some SNPs may be correlated with each other does not have a negative impact on the significance level. Permutation tests elegantly allow for such substructure in the data. Another discussion point is that, as expected, results of our approach depend on the statistic, t_i, used for measuring association between SNPs and case and control individuals. It will be important to find the most powerful statistic for such studies.

Genotyping errors have deleterious effects on association and linkage disequilibrium analysis (Akey et al. 2001) and thus will also affect our set-association method. If, in addition, errors occur with different frequencies in cases and control individuals, this would lead to different estimates of SNP allele frequencies and HWD in the two groups, which would seriously affect our method. The easiest solution to the error problem is increased quality control in the laboratory. Another avenue to be explored is incorporating error frequencies in the analysis model as it has successfully been done for a specific disequilibrium test (Gordon et al. 2001).

Population admixture (substructure) is a problem in any association study. If cases and controls have different ethnic backgrounds with different SNP allele frequencies, this will adversely affect our set-association method. At this time, our recommendation is to proceed in analogy to previously proposed solutions, which require genotyping of SNPs known to be unrelated to the trait under study (Pritchard and Rosenberg 1999; Bacanu et al. 2000).