Two-locus Disease Models Research Articles

HiSSI: high-order SNP-SNP interactions detection based on efficient significant pattern and differential evolution

BackgroundDetecting single nucleotide polymorphism (SNP) interactions is an important and challenging task in genome-wide association studies (GWAS). Various efforts have been devoted to detect SNP interactions. However, the large volume of SNP datasets results in such a big number of high-order SNP combinations that restrict the power of detecting interactions.MethodsIn this paper, to combat with this challenge, we propose a two-stage approach (called HiSSI) to detect high-order SNP-SNP interactions. In the screening stage, HiSSI employs a statistically significant pattern that takes into account family wise error rate, to control false positives and to effectively screen two-locus combinations candidate set. In the searching stage, HiSSI applies two different search strategies (exhaustive search and heuristic search based on differential evolution along with χ2-test) on candidate pairwise SNP combinations to detect high-order SNP interactions.ResultsExtensive experiments on simulated datasets are conducted to evaluate HiSSI and recently proposed and related approaches on both two-locus and three-locus disease models. A real genome-wide dataset: breast cancer dataset collected from the Wellcome Trust Case Control Consortium (WTCCC) is also used to test HiSSI.ConclusionsSimulated experiments on both two-locus and three-locus disease models show that HiSSI is more powerful than other related approaches. Real experiment on breast cancer dataset, in which HiSSI detects some significantly two-locus and three-locus interactions associated with breast cancer, again corroborate the effectiveness of HiSSI in high-order SNP-SNP interaction identification.

Neural networks for modeling gene-gene interactions in association studies

BackgroundOur aim is to investigate the ability of neural networks to model different two-locus disease models. We conduct a simulation study to compare neural networks with two standard methods, namely logistic regression models and multifactor dimensionality reduction. One hundred data sets are generated for each of six two-locus disease models, which are considered in a low and in a high risk scenario. Two models represent independence, one is a multiplicative model, and three models are epistatic. For each data set, six neural networks (with up to five hidden neurons) and five logistic regression models (the null model, three main effect models, and the full model) with two different codings for the genotype information are fitted. Additionally, the multifactor dimensionality reduction approach is applied.ResultsThe results show that neural networks are more successful in modeling the structure of the underlying disease model than logistic regression models in most of the investigated situations. In our simulation study, neither logistic regression nor multifactor dimensionality reduction are able to correctly identify biological interaction.ConclusionsNeural networks are a promising tool to handle complex data situations. However, further research is necessary concerning the interpretation of their parameters.

PHCR: a Parallel Haplotype Configuration Reduction algorithm for haplotype interaction analysis

Finding gene interaction models is one of the most important issues in genotype-phenotype association studies. This paper presents a model-free nonparametric statistical interaction analysis known as Parallel Haplotype Configuration Reduction (pHCR). This technique extends the original Multifactor Dimensionality Reduction (MDR) algorithm by using haplotype contribution values (c-values) and a haplotype interaction scheme instead of analyzing interactions among single-nucleotide polymorphisms. The proposed algorithm uses the statistical power of haplotypes to obtain a gene-gene interaction model. pHCR computes a statistical value for each haplotype, which contributes to the phenotype, and then performs haplotype interaction analysis on the basis of the cumulative c-value of each individual haplotype. To address the high computational complexity of pHCR, this paper also presents a scalable parallel computing solution. Nine common two-locus disease models were used to evaluate the algorithm performance under different scenarios. The results from all cases showed that pHCR shows higher power to detect gene-gene interaction in comparison with the results obtained from running MDR on the same data set. We also compared pHCR with FAMHAP, which mainly considers haplotype in the association analysis. For every experiment on the simulated data set, pHCR correctly produced haplotype interactions with much fewer false positives. We also challenged pHCR with a real data set input of beta-thalassemia/Hemoglobin E (HbE) disease. The result suggested the interaction between two previously reported quantitative trait loci of the fetal hemoglobin level, which is a major modifying factor, and disease severity of beta-thalassemia/HbE disease.

A conditional synergy index to assess biological interaction

In genetic studies of complex diseases, a crucial task is to identify and quantify gene-gene interactions which are often defined as deviance from genetic additive effects. This statistical definition, however, does not need to reflect the biological interactions of genes. We propose a new method to detect gene-gene interactions. This new approach exploits the concept of synergy and antagonism that is appropriate to capture biological relationships. The conditional synergy index (CSI) describes the extent of interaction on the penetrance scale. We develop the CSI for two-locus disease models and cohort data. The index assumes genotypes to be dichotomized into risk-genotypes (exposed) and non-risk-genotypes (unexposed) but it does not assume the loci to be in linkage equilibrium. We investigate the performance of the CSI and compare it to classical epidemiological interaction measures like Rothman's synergy index (S) and the attributable proportion due to interaction (AP). In addition, the performance of an estimator of this new parameter is illustrated in a practical example.

Generating samples for association studies based on HapMap data

BackgroundWith the completion of the HapMap project, a variety of computational algorithms and tools have been proposed for haplotype inference, tag SNP selection and genome-wide association studies. Simulated data are commonly used in evaluating these new developed approaches. In addition to simulations based on population models, empirical data generated by perturbing real data, has also been used because it may inherit specific properties from real data. However, there is no tool that is publicly available to generate large scale simulated variation data by taking into account knowledge from the HapMap project.ResultsA computer program (gs) was developed to quickly generate a large number of samples based on real data that are useful for a variety of purposes, including evaluating methods for haplotype inference, tag SNP selection and association studies. Two approaches have been implemented to generate dense SNP haplotype/genotype data that share similar local linkage disequilibrium (LD) patterns as those in human populations. The first approach takes haplotype pairs from samples as inputs, and the second approach takes patterns of haplotype block structures as inputs. Both quantitative and qualitative traits have been incorporated in the program. Phenotypes are generated based on a disease model, or based on the effect of a quantitative trait nucleotide, both of which can be specified by users. In addition to single-locus disease models, two-locus disease models have also been implemented that can incorporate any degree of epistasis. Users are allowed to specify all nine parameters in a 3 × 3 penetrance table. For several commonly used two-locus disease models, the program can automatically calculate penetrances based on the population prevalence and marginal effects of a disease that users can conveniently specify.ConclusionThe program gs can effectively generate large scale genetic and phenotypic variation data that can be used for evaluating new developed approaches. It is freely available from the authors' web site at .

The power of two‐locus affected sib‐pair linkage analysis to detect interacting disease loci

It has been shown that two-locus linkage analysis can, for some two-locus disease models, be used to detect effects at disease loci that do not reach significance in a genome scan. However, few examples exist where two-locus linkage has been successfully used to map genes. We study the possible gain in power of affected sib-pair nonparametric two-locus linkage analysis for two-locus models which fulfil the two-locus triangle constraints. Using a new parameterization of the two-locus joint identity-by-descent sharing probabilities we can, for fixed marginal sharing at both of two unlinked disease loci, derive a two-locus distribution such that the power of a two-locus analysis is maximized. In a simulation study we look at two test statistics, the two-locus maximum likelihood score and the correlation between nonparametric linkage scores, and study power as a function of marginal sharing. We show that in a best-case scenario two-locus linkage can have considerable power to detect pairs of interacting loci if there is a moderate increase in allele sharing at one of the two loci, even if there is a very small increase in allele sharing at the other locus. But we also show that the power to detect interacting loci in a two-locus analysis decreases as the marginal sharing at the two loci decreases and for any distribution with a small increase in allele sharing at both loci the power of a two-locus analysis is always low.

Efficient intermediate fine mapping: confidence set inference with likelihood ratio test statistic

In positional cloning of disease causing genes, identification of a linked chromosomal region via linkage studies is often followed by fine mapping via association studies. Efficiency can be gained with an intermediate step where confidence regions for the locations of disease genes are constructed. The confidence set inference [CSI; Papachristou and Lin, 2006b] achieves this goal by replacing the traditional null hypothesis of no linkage with a new set of null hypotheses where the chromosomal position under consideration is in tight linkage with a trait locus. This approach was shown to perform favorably compared with several competing methods. Using the duality of confidence sets and hypothesis testing, CSI was proposed for the Mean test statistics with affected sibling pair data (CSI-Mean). We postulate that more efficient confidence sets will result if more efficient test statistics are used in the CSI framework. One promising candidate, the maximum LOD score (MLS) statistic, makes maximum use of available identity by descent information, in addition to handling markers with incomplete polymorphism naturally. We propose a procedure that tests the CSI null hypotheses using the MLS statistic (CSI-MLS). Compared with CSI-Mean, CSI-MLS provides tighter confidence regions over a range of single and two-locus disease models. The MLS test is also shown to be more powerful than the Mean test in testing the CSI null over a wide range of disease models, the advantage being most pronounced for recessive models. In addition, CSI-MLS is computationally much more efficient than CSI-Mean.

Test for Interaction between Two Unlinked Loci

Despite the growing consensus on the importance of testing gene-gene interactions in genetic studies of complex diseases, the effect of gene-gene interactions has often been defined as a deviance from genetic additive effects, which is essentially treated as a residual term in genetic analysis and leads to low power in detecting the presence of interacting effects. To what extent the definition of gene-gene interaction at population level reflects the genes' biochemical or physiological interaction remains a mystery. In this article, we introduce a novel definition and a new measure of gene-gene interaction between two unlinked loci (or genes). We developed a general theory for studying linkage disequilibrium (LD) patterns in disease population under two-locus disease models. The properties of using the LD measure in a disease population as a function of the measure of gene-gene interaction between two unlinked loci were also investigated. We examined how interaction between two loci creates LD in a disease population and showed that the mathematical formulation of the new definition for gene-gene interaction between two loci was similar to that of the LD between two loci. This finding motived us to develop an LD-based statistic to detect gene-gene interaction between two unlinked loci. The null distribution and type I error rates of the LD-based statistic for testing gene-gene interaction were validated using extensive simulation studies. We found that the new test statistic was more powerful than the traditional logistic regression under three two-locus disease models and demonstrated that the power of the test statistic depends on the measure of gene-gene interaction. We also investigated the impact of using tagging SNPs for testing interaction on the power to detect interaction between two unlinked loci. Finally, to evaluate the performance of our new method, we applied the LD-based statistic to two published data sets. Our results showed that the P values of the LD-based statistic were smaller than those obtained by other approaches, including logistic regression models.

Optimal two-stage strategy for detecting interacting genes in complex diseases

BackgroundThe mapping of complex diseases is one of the most important problems in human genetics today. The rapid development of technology for genetic research has led to the discovery of millions of polymorphisms across the human genome, making it possible to conduct genome-wide association studies with hundreds of thousands of markers. Given the large number of markers to be tested in such studies, a two-stage strategy may be a reasonable and powerful approach: in the first stage, a small subset of promising loci is identified using single-locus testing, and, in the second stage, multi-locus methods are used while taking into account the loci selected in the first stage. In this report, we investigate and compare two possible two-stage strategies for genome-wide association studies: a conditional approach and a simultaneous approach.ResultsWe investigate the power of both the conditional and the simultaneous approach to detect the disease loci for a range of two-locus disease models in a case-control study design. Our results suggest that, overall, the conditional approach is more robust and more powerful than the simultaneous approach; the conditional approach can greatly outperform the simultaneous approach when one of the two disease loci has weak marginal effect, but interacts strongly with the other, stronger locus (easily detectable using single-locus methods in the first stage).ConclusionGenome-wide association studies hold the promise of finding new genes implicated in complex diseases. Two-stage strategies are likely to be employed in these large-scale studies. Therefore we compared two natural two-stage approaches: the conditional approach and the simultaneous approach. Our power studies suggest that, when doing genome-wide association studies, a two-stage conditional approach is likely to be more powerful than a two-stage simultaneous approach.

A two‐step procedure for constructing confidence intervals of trait loci with application to a rheumatoid arthritis dataset

Preliminary genome screens are usually succeeded by fine mapping analyses focusing on the regions that signal linkage. It is advantageous to reduce the size of the regions where follow-up studies are performed, since this will help better tackle, among other things, the multiplicity adjustment issue associated with them. We describe a two-step approach that uses a confidence set inference procedure as a tool for intermediate mapping (between preliminary genome screening and fine mapping) to further localize disease loci. Apart from the usual Hardy-Weiberg and linkage equilibrium assumptions, the only other assumption of the proposed approach is that each region of interest houses at most one of the disease-contributing loci. Through a simulation study with several two-locus disease models, we demonstrate that our method can isolate the position of trait loci with high accuracy. Application of this two-step procedure to the data from the Arthritis Research Campaign National Repository also led to highly encouraging results. The method not only successfully localized a well-characterized trait contributing locus on chromosome 6, but also placed its position to narrower regions when compared to their LOD support interval counterparts based on the same data.

Haplotype interaction analysis of unlinked regions

Genetically complex diseases are caused by interacting environmental factors and genes. As a consequence, statistical methods that consider multiple unlinked genomic regions simultaneously are desirable. Such consideration, however, may lead to a vast number of different high-dimensional tests whose appropriate analysis pose a problem. Here, we present a method to analyze case-control studies with multiple SNP data without phase information that considers gene-gene interaction effects while correcting appropriately for multiple testing. In particular, we allow for interactions of haplotypes that belong to different unlinked regions, as haplotype analysis often proves to be more powerful than single marker analysis. In addition, we consider different marker combinations at each unlinked region. The multiple testing issue is settled via the minP approach; the P value of the "best" marker/region configuration is corrected via Monte-Carlo simulations. Thus, we do not explicitly test for a specific pre-defined interaction model, but test for the global hypothesis that none of the considered haplotype interactions shows association with the disease. We carry out a simulation study for case-control data that confirms the validity of our approach. When simulating two-locus disease models, our test proves to be more powerful than association methods that analyze each linked region separately. In addition, when one of the tested regions is not involved in the etiology of the disease, only a small amount of power is lost with interaction analysis as compared to analysis without interaction. We successfully applied our method to a real case-control data set with markers from two genes controlling a common pathway. While classical analysis failed to reach significance, we obtained a significant result even after correction for multiple testing with our proposed haplotype interaction analysis. The method described here has been implemented in FAMHAP.

Identifying SNPs predictive of phenotype using random forests

There has been a great interest and a few successes in the identification of complex disease susceptibility genes in recent years. Association studies, where a large number of single-nucleotide polymorphisms (SNPs) are typed in a sample of cases and controls to determine which genes are associated with a specific disease, provide a powerful approach for complex disease gene mapping. Genes of interest in those studies may contain large numbers of SNPs that classical statistical methods cannot handle simultaneously without requiring prohibitively large sample sizes. By contrast, high-dimensional nonparametric methods thrive on large numbers of predictors. This work explores the application of one such method, random forests, to the problem of identifying SNPs predictive of the phenotype in the case-control study design. A random forest is a collection of classification trees grown on bootstrap samples of observations, using a random subset of predictors to define the best split at each node. The observations left out of the bootstrap samples are used to estimate prediction error. The importance of a predictor is quantified by the increase in misclassification occurring when the values of the predictor are randomly permuted. We extend the concept of importance to pairs of predictors, to capture joint effects, and we explore the behavior of importance measures over a range of two-locus disease models in the presence of a varying number of SNPs unassociated with the phenotype. We illustrate the application of random forests with a data set of asthma cases and unaffected controls genotyped at 42 SNPs in ADAM33, a previously identified asthma susceptibility gene. SNPs and SNP pairs highly associated with asthma tend to have the highest importance index value, but predictive importance and association do not always coincide.

Detecting Gene-Gene Interactions Using Affected Sib Pair Analysis with Covariates

Interest has recently focussed on allowing for interactions between loci as a way to increase power to detect linkage. In this paper, a simplified logistic regression method was used to perform affected sib pair analyses allowing for the inclusion of data from other loci. A systematic search of two-locus disease models was carried out to determine the situations in which this was advantageous. If IBD information is available (e.g. from a genome scan), it is unlikely that allowing for interactions will give a large lod score in the absence of linkage evidence from sinlge-locus analysis. Furthermore, allowing for interactions rarely gave a significant increase in power to detect linkage over a single-locus analysis, except for heterogeneity models with low K_P. Conversely, the availability of disease-associated genotypes may greatly increase the power both to detect linkage to a second locus and interaction between the loci. These results indicate that when only IBD information is available, two-locus analysis of genome scan data should be restricted to regions giving peaks under single-locus analysis. If disease-associated genotypes are available, it may be worth re-analysing the whole genome.

Systematic search for disease loci for complex genetic traits: a study based on simulated population data.

Simulated family data were analyzed using one- and two-locus disease models to detect linkage. Regions of interest, found on chromosomes 3 and 5, were then further analyzed to look for evidence of locus interaction and/or genetic heterogeneity. Methods described by Falk [1993] were used to separate families into subsets likely to be genetically homogeneous. Based on the results, it was concluded that there were at least two distinct disease loci, one on chromosome 3 and one on chromosome 5, and that these loci were probably not interacting but were expressing two distinct forms of the disease. The identification of these loci was in agreement with the generating model. However, the analysis did not show any indication of a two-locus form of the disease or detect a disease locus on chromosome 1. This could be due to lack of power and/or too small a sample size for the method of analysis.

Comparison of Nonparametric Statistics for Detection of Linkage in Nuclear Families: Single-Marker Evaluation

We have evaluated 23 different statistics, from a total of 10 popular software packages for model-free linkage analysis of nuclear-family data, by applying them to single-marker data simulated under several two-locus disease models. The statistics that we examined fall into two broad categories: (1) those that test directly for increased identity-by-state or identity-by-descent sharing (by use of the programs APM, Genetic Analysis System [GAS] SIBSTATE and SIBDES, SAGE SIBPAL, ERPA, SimIBD, and Genehunter NPL) and (2) those that are based on likelihood-ratio tests and that report LOD scores (by use of the programs Splink, SIBPAIR, Mapmaker/Sibs, ASPEX, and GAS SIBMLS). For each of eight two-locus disease models, we analyzed six data sets; the first three data sets consisted of two-child families with both sibs affected and zero, one, or both parents typed, whereas the other three data sets consisted of four-child families with at least two affected sibs and zero, one, or both parents typed. We report false-positive rates, overall rank by power, and the power for each statistic. We give rough recommendations regarding which programs provide the most powerful tests for linkage, as well as the programs to be avoided under certain conditions. For the likelihood-ratio-based statistics, we examined the effects of various treatments of sibships with multiple affected individuals. Finally, we explored the use of some simple two-of-three composite statistics and found that such tests are of only marginal benefit over the most powerful single statistic.

Linkage analysis under "random" and "genetic" reduced penetrance.

We examined whether the results of linkage analysis are affected by the reasons for so-called "reduced penetrance". We simulated linkage data with random reduced penetrance and contrasted that with data that were simulated under inheritance controlled by two loci interacting epistatically. For the two-locus disease models, one of those loci was linked to the marker. All data, irrespective of how the data were simulated, were analyzed under the assumption of a single-locus genetic model with random reduced penetrance. We found that there appears to be little bias in the results of linkage analysis whether the "reduced penetrance" was caused by random (usually interpreted as environmental) factors or by strictly genetic factors. We also illustrate that when the trait or disease is influenced by more than one locus, the inheritance of the trait at the linked locus is the important consideration, not the inheritance of the trait per se.