Searching for genotype-phenotype structure: using hierarchical log-linear models in Crohn disease.

There has been considerable recent success in the detection of gene-disease associations. We consider here the development of tools that facilitate the more detailed characterization of the effect of a genetic variant on disease. We replace the simplistic classification of individuals according to a single binary disease indicator with classification according to a number of subphenotypes. This more accurately reflects the underlying biological complexity of the disease process, but it poses additional analytical difficulties. Notably, the subphenotypes that make up a particular disease are typically highly associated, and it becomes difficult to distinguish which genes might be causing which subphenotypes. Such problems arise in many complex diseases. Here, we concentrate on an application to Crohn disease (CD). We consider this problem as one of model selection based upon log-linear models, fitted in a Bayesian framework via reversible-jump Metropolis-Hastings approach. We evaluate the performance of our suggested approach with a simple simulation study and then apply the method to a real data example in CD, revealing a sparse disease structure. Most notably, the associated NOD2.908G-->R mutation appears to be directly related to more severe disease behaviors, whereas the other two associated NOD2 variants, 1007L-->FS and 702R-->W, are more generally related to disease in the small bowel (ileum and jejenum). The ATG16L1.300T-->A variant appears to be directly associated with only disease of the small bowel.

Bayesian meta-analysis of genetic association studies with different sets of markers.

Robust assessment of genetic effects on quantitative traits or complex-disease risk requires synthesis of evidence from multiple studies. Frequently, studies have genotyped partially overlapping sets of SNPs within a gene or region of interest, hampering attempts to combine all the available data. By using the example of C-reactive protein (CRP) as a quantitative trait, we show how linkage disequilibrium in and around its gene facilitates use of Bayesian hierarchical models to integrate informative data from all available genetic association studies of this trait, irrespective of the SNP typed. A variable selection scheme, followed by contextualization of SNPs exhibiting independent associations within the haplotype structure of the gene, enhanced our ability to infer likely causal variants in this region with population-scale data. This strategy, based on data from a literature based systematic review and substantial new genotyping, facilitated the most comprehensive evaluation to date of the role of variants governing CRP levels, providing important information on the minimal subset of SNPs necessary for comprehensive evaluation of the likely causal relevance of elevated CRP levels for coronary-heart-disease risk by Mendelian randomization. The same method could be applied to evidence synthesis of other quantitative traits, whenever the typed SNPs vary among studies, and to assist fine mapping of causal variants.

Analysis of multiple SNPs in a candidate gene or region.

We consider the analysis of multiple single nucleotide polymorphisms (SNPs) within a gene or region. The simplest analysis of such data is based on a series of single SNP hypothesis tests, followed by correction for multiple testing, but it is intuitively plausible that a joint analysis of the SNPs will have higher power, particularly when the causal locus may not have been observed. However, standard tests, such as a likelihood ratio test based on an unrestricted alternative hypothesis, tend to have large numbers of degrees of freedom and hence low power. This has motivated a number of alternative test statistics. Here we compare several of the competing methods, including the multivariate score test (Hotelling's test) of Chapman et al. ([2003] Hum. Hered. 56:18-31), Fisher's method for combining P-values, the minimum P-value approach, a Fourier-transform-based approach recently suggested by Wang and Elston ([2007] Am. J. Human Genet. 80:353-360) and a Bayesian score statistic proposed for microarray data by Goeman et al. ([2005] J. R. Stat. Soc. B 68:477-493). Some relationships between these methods are pointed out, and simulation results given to show that the minimum P-value and the Goeman et al. ([2005] J. R. Stat. Soc. B 68:477-493) approaches work well over a range of scenarios. The Wang and Elston approach often performs poorly; we explain why, and show how its performance can be substantially improved.

Detecting association using epistatic information.

Genetic association studies have been less successful than expected in detecting causal genetic variants, with frequent non-replication when such variants are claimed. Numerous possible reasons have been postulated, including inadequate sample size and possible unobserved stratification. Another possibility, and the focus of this paper, is that of epistasis, or gene-gene interaction. Although unlikely that we may glean information about disease mechanism, based purely upon the data, it may be possible to increase our power to detect an effect by allowing for epistasis within our test statistic. This paper derives an appropriate "omnibus" test for detecting causal loci whist allowing for numerous possible interactions and compares the power of such a test with that of the usual main effects test. This approach differs from that commonly used, for example by Marchini et al. [2005], in that it tests simultaneously for main effects and interactions, rather than interactions alone. The alternative hypothesis being tested by the "omnibus" test is whether a particular locus of interest has an effect on disease status, either marginally or epistatically and is therefore directly comparable to the main effects test at that locus. The paper begins by considering the direct case, in which the putative causal variants are observed and then extends these ideas to the indirect case in which the causal variants are unobserved and we have a set of tag single nucleotide polymorphisms (tag SNPs) representing the regions of interest. In passing, the derivation of the indirect omnibus test statistic leads to a novel "indirect case-only test for interaction".

One degree of freedom for dominance in indirect association studies.

Usual tests of association using tag single nucleotide polymorphisms (SNPs) assume that the alleles of the causal locus act additively and that these alleles are then predicted indirectly via a set of tag SNPs. In the presence of strong dominance effects this model is not correct and an extra term needs to be included, which uses the tag SNPs to predict the heterozygosity of the causal locus. Assuming this scenario of a strong dominance effect, we present an appropriate test statistic and investigate how much power, if any, we gain by adding this single degree of freedom for dominance.

Improved power offered by a score test for linkage disequilibrium mapping of quantitative-trait loci by selective genotyping.

Selective genotyping is used to increase efficiency in genetic association studies of quantitative traits by genotyping only those individuals who deviate from the population mean. However, selection distorts the conditional distribution of the trait given genotype, and such data sets are usually analyzed using case-control methods, quantitative analysis within selected groups, or a combination of both. We show that Hotelling's T(2) test, recently proposed for association studies of one or several tagging single-nucleotide polymorphisms in a prospective (i.e., trait given genotype) design, can also be applied to the retrospective (i.e., genotype given trait) selective-genotyping design, and we use simulation to demonstrate its improved power over existing methods.

No evidence of association or interaction between the IL4RA, IL4, and IL13 genes in type 1 diabetes.

Attempts to identify susceptibility loci that, on their own, have marginal main effects by use of gene-gene interaction tests have increased in popularity. The results obtained from analyses of epistasis are, however, difficult to interpret. Gene-gene interaction, albeit only marginally significant, has recently been reported for the interleukin-4 and interleukin-13 genes (IL4 and IL13) with the interleukin-4 receptor A gene (IL4RA), contributing to the susceptibility of type 1 diabetes (T1D). We aimed to replicate these findings by genotyping both large family and case-control data sets and by using previously published data. Gene-gene interaction tests were performed using linear regression models in cases only. We did not find any single-locus associations with T1D and did not obtain evidence of gene-gene interaction. Additional support from independent samples will be even more important in the study of gene-gene interactions and other subgroup analyses.

Use of unphased multilocus genotype data in indirect association studies.

It is usually assumed that detection of a disease susceptability gene via marker polymorphisms in linkage disequilibrium with it is facilitated by consideration of marker haplotypes. However, capture of the marker haplotype information requires resolution of gametic phase, and this must usually be inferred statistically. Recently, we questioned the value of the marker haplotype information, and suggested that certain analyses of multivariate marker data, not based on haplotypes explicitly and not requiring resolution of gametic phase, are often more powerful than analyses based on haplotypes. Here, we review this work and assess more carefully the situations in which our conclusions might apply. We also relate these analyses to alternative approaches to haplotype analysis, namely those based on haplotype similarity and those inspired by cladistics.

Detecting disease associations due to linkage disequilibrium using haplotype tags: a class of tests and the determinants of statistical power.

In the 'indirect' method of detecting genetic associations between a trait and a DNA variant, we type several markers in a gene or chromosome region of linkage disequilibrium. If there is association between markers and the trait, we presume the existence of one or more causal polymorphisms in the region. In order to obtain a sufficiently dense set of markers it will almost always be necessary to use single nucleotide polymorphisms (SNPs). Although there is an emerging literature on methods for choosing an optimal set of 'haplotype tag SNPs' (htSNPs) to detect association between a genetic region and a trait, less attention has been given to the problem of how such studies should be analysed when completed, and how the initial data which was used to select the htSNPs should be incorporated into the analysis. This paper discusses this problem for both population- and family-based association studies. The role of the R2 measure of association between a causal locus and various methods of scoring of marker haplotypes is highlighted. In most cases, the simplest method of scoring (locus coding), which does not require phase resolution, is shown generally to be more powerful than scoring methods that include haplotype information. A new 'multi-locus TDT' is also proposed.