Gene-gene Interaction Analysis by IAC

(Interaction Analysis by Chi-Square)

A Novel Biological Constraint-based Interaction Analysis Framework

Sidney K. Chu

, Samuel Guanglin Xu

, Feng Xu

and Nelson L. S. Tang

1,4,5

Department of Chemical Pathology, Faculty of Medicine, The Chinese University of Hong Kong, Hong Kong SAR, China

Shanghai American School (Pudong), Shanghai, China

Department of Biochemistry & Centre of Genomic Science, LKS Faculty of Medicine,

The University of Hong Kong, Hong Kong SAR, China

Li Ka Shing Institute of Health Sciences, Faculty of Medicine, The Chinese University of Hong Kong, Hong Kong, China

School of Biomedical Sciences, Faculty of Medicine, The Chinese University of Hong Kong, Hong Kong, China

Keywords: Genome Wide Association Study, SNP-SNP Interaction, Genetic Susceptibility, Statistical Modelling.

Abstract: In the recent years of the GWAS era, large-scale genotyping of million polymorphisms (SNPs) among

thousands of patients have identified new disease predisposition loci. However, these conventional

GWAS statistical models only analyse SNPs singularly and cannot detect significant SNP-SNP (gene-

gene) interaction. Studies of interacting genetic variants (SNPs) are useful to elucidate a disease’s

underlying biological pathway. Therefore, a powerful and efficient statistical model to detect SNP-

SNP interaction is urgently needed. We hypothesize that among all the exhaustive model patterns of

interaction (>100), only limited patterns are plausible based on the principle of protein-protein

interaction (in the context of GWAS data analysis). The production of proteins by the process of

translation of DNA predicts that gene-gene interaction resulting in a phenotype should only occur in

classical genetic epistasis models, such as dominant-dominant, and recessive-recessive models. We

developed a statistical analysis model, IAC (Interaction Analysis by Chi-Square), to examine such

interactions. We then exhausted different population and statistical parameters, upon a total of 532

simulated case-control experiments to study the effects of these parameters on statistical power and

type I error of using an interaction vs. singular SNP analysis. Our method has also detected potential

pairwise interactions associated with Parkinson's disease that were previously undetected in

conventional methods. We showed that the detection of SNP-SNP interaction is actually feasible using

typical sample sizes found in common GWAS studies. This approach may be applied in

complimentarily with other models in two-stage association tests to efficiently detect candidate SNPs

for further study.

1 INTRODUCTION

1.1 Recent Progress in GWAS

Advances in Genome-Wide Association Studies

(GWAS) have been successful in identifying genetic

variation carrying predisposition to diseases.

Prostate cancer, breast cancer, ovarian cancer,

colorectal cancer and many other diseases have all

shown to have predisposition loci by GWAS

(Musani et al., 2007). Polymorphic sites are present

every 2000 to 3000 bp in the human genome. In the

past five years, studies have detected many disease

associated SNPs and genes which enhanced our

understanding of cancer-related genetic variants

(Visscher et al., 2012). For example, single

nucleotide polymorphisms (SNPs) of more than 50

genes are related to cancer susceptibility (Stadler et

al., 2010). This era of GWAS and Haplotype

analysis have helped researches to understand

contribution of genetic variation in predisposition of

most cancers (such as breast cancer) (Figure 1).

GWAS greatly contribute to our understanding of

disease predisposition.

142

Chu, S., Xu, S., Xu, F. and Tang, N.

Gene-gene Interaction Analysis by IAC (Interaction Analysis by Chi-Square) - A Novel Biological Constraint-based Interaction Analysis Framework.

DOI: 10.5220/0005654601420150

In Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2016) - Volume 3: BIOINFORMATICS, pages 142-150

ISBN: 978-989-758-170-0

1.2 Current Limitations in GWAS

While GWAS was successful to find thousands of

predisposition SNPs, a large portion of heritability is

still unexplained and this problem of missing

heritability has generated a large interest within the

scientific community. Little progress in both

analysis method of interaction and outcomes has

been made so far. Interaction among genes and

variants may account for this unexplained

heritability, hence it may yield new insights into the

details of complex traits.

So far, less than 30% of heritability in breast

cancer, colorectal cancer, and prostate cancer can be

explained by predisposition genes and SNPs that

have been discovered (Stadler et al., 2010)

(Figure

1). Although conventional single SNP analyses can

be preformed quickly nowadays (Purcell et al.,

2007), it is not designed to detect interactions

between variants (Wan et al., 2010). As a result,

researchers solely rely on increasing sample size (up

to tens of thousands) to increase statistical power

(Manolio et al., 2009). On the other hand, an

efficient and universally acceptable statistical model

would make detecting SNP-SNP interaction a more

efficient and reliable process. Researchers had

proposed a stage-wise approach, by accurately

selecting subsets of SNPs during the first stage of an

association test, such SNPs may be linked to higher

order interactions or may further understand the

phenotypic variance of cancer subsets and other

diseases (Musani et al., 2007).

Figure 1: [Data from: “Genome-Wide Association Studies

of Cancer by Zsofia K. Stadler et al. 2010”] This is a

representation of discovered genes and their affect on the

genetic susceptibility of different cancer subsets. GWAS

SNPs found with contribution to the predisposition of the

respective cancer subset is marked in red.

Even with SNP-SNP interaction analysis (in 3x3x2

contingency table), of a typical GWAS microarray

of 500,000 SNPs, a large number of 2-SNP pairs

(125 billion tests) will be generated from the

genotyping array; this large number of analyses

makes the detection process over-exhaustive

(Schüpbach et al., 2010). Currently all these analysis

approaches, exhaustively exploit all possible

interaction pattern enumerations in each of the 3x3

genotype interaction table.

In short, the search space for interaction is too

large and will result in reduced statistical power,

leading to an increased false positive rate (type I

error). Although potential statistical solutions to

exhaust all these models have been proposed (Wan

et al., 2010) it may not be the most efficient and

appropriate analytical approach. The need for an

appropriate analysis method is exacerbated by

failure to replicate results from other association

studies.

1.3 Our Solution

Here, based on the biological principles of Protein-

Protein Interaction (PPI), we propose that 8

interaction patterns (4 dominant-dominant, 4

recessive-recessive) (Figure 3) are plausible in it's

biological context; this contrasts to the exhaustive

models from exhaustive enumerations, many of

which have their biological plausibility questioned

(Figure 8). Ultimately, these unnecessary and

biologically implausible exhaustive searches would

increase computational burdens and would

subsequently be counterproductive

(Li and Reich,

2000).

Studies of model organisms (saccharomyces

cerevisiae) have shown that interactions occur

frequently and have strong effects on certain

phenotypes (Raval and Ray, 2013). These studies

have shown the presence of dominant-dominant and

recessive-recessive interactions (Segrè et al., 2005)

(Venturi et al., 2000) from PPI analysis through the

two-hybrid screening. The presence of underlying

biological epistasis in model organisms suggests a

need to base statistical analysis on biological

constraints of protein interactions (Emily et al.,

2009).

Interaction Analysis by Chi-Square (IAC)

applies classical epistasis models (dominant-

dominant, recessive-recessive) as biological

constraints to reduce search space and computational

intensity commonly associated with interaction

testing in GWAS. Apart from applying our

framework on 532 case-control simulations, we were

also able to detect one pair of interacting SNPs

associated with Parkinson's disease that was

previously undetected with conventional analysis.

Using a reduced dimension chi-square test, we have

Gene-gene Interaction Analysis by IAC (Interaction Analysis by Chi-Square) - A Novel Biological Constraint-based Interaction Analysis

Framework

143

found interaction patterns and parameters that

present strong SNP-SNP interaction which

conventional single SNP analyses fail to detect. For

the simulations, we used parameters that are realistic

and similar to those of GWAS and have studied

statistical power in the computational analysis. The

results have demonstrated benefits of analysing the

generated datasets with IAC along with focused

searches amongst plausible interaction patterns in

light of PPI. Statistical power was determined by

using 60,000 emulated case-control datasets under

varying sample sizes and parameters. This chi-

square test with reduced dimensions may be useful

for the identification of SNP-SNP interaction in

GWAS.

2 MODELS AND METHODS

2.1 Biological Plausibility of

Interaction Model

Great deals of research efforts in the past have

attempted to screen for all possible interaction

patterns in GWAS. In order to be exhaustive,

investigators enumerated all possible patterns of

interaction that is feasible in a 3x3x2 (Genotype A x

Genotype B x Case-control) contingency table.

Under such exhaustive searches, 100+ non-

redundant patterns have been defined. Our insight

into this problem suggests that a majority of these

investigation patterns are not biologically plausible.

We base our hypothesis on the central dogma of

biology in which the gene translation and protein-

protein interactions occur in one of the recognized

patterns implemented directly to its statistical

augmentation.

Protein-protein interactions occur either as

ligand-receptor pair or as polymeric subunits of a

protein complex, which must have corresponding

biochemical characteristics in order to interact (it is

also applicable to a ligand and receptor pair)

(Jones and Thornton, 2009) (Figure 2).

Wet-laboratory experiments support the notion

of limited ways of interaction between proteins.

Studies in the past have shown that protein inter-

allelic complementation has the ability to produce

enough biochemical activity to express or regulate a

multi-protein complex (Steingrimson et al., 2003).

The physical interaction of mutated protein subunits

(Figure 2) only occurs under certain circumstances

(for example facilitated by the particular allele of a

polymorphism) due to biochemical constraints. To

show this, Bondos et al. (2004) used the yeast two-

hybrid assay to assess which proteins interact with a

Hox protein and found that only a few out of the

Figure 2: (opposite page). This shows the flow of information from the central dogma to statistical augmentation in the 3x3

genotypic interaction table. Uniform transcription leads to a number of possible random interactions (depending on if the

protein is a monomer or dimer) at the subunit level. In this case, the "healthy" subunit pair is assigned at random (recessive-

recessive) depending on its role in the multi-protein complex. Biological action scores(~) are then calculated by the

probability a interaction will yield the assigned "healthy" protein by the specific genotype.

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many proteins tested were able to physically interact

with each other. Conformational epistasis (Ortlund

et al., 2009) describes the theory that proteins may

interact in many possible ways, but only a few

biochemical pathways are functionally plausible as

there are many constraints due to evolutionary

recourses.

The models are based on the assumption that the

constraints of PPI are based on three biochemical

principles:

(I) Protein A (encoded by gene A with 2 alleles

A or a) and protein B (encoded gene B with allele B

or b) interacts as subunits of a protein complex or a

ligand and receptor pair.

(II) Uniform transcriptions of both copies of the

gene (both paternal and maternal copies)

(III) Random pairing of subunits from translated

products of the two copies.

We confined the statistical analysis of interaction

to biologically plausible model patterns that is 4

dominant-dominant and 4 recessive-recessive

configurations.

Figure 3: Eight biologically plausible interaction patterns.

Supported by studies from Dummer et al. (2015),

Phillips (2008) and Emily et al. (2009), we are

convinced that these constraints based on biological

epistasis are essential; however, very few existing

algorithms have taken them into account.

2.2 Reduced Dimension Chi-Square

Test for Interaction

We used 266 simulation settings that are based on

the simulated genotype counts of the bi-allelic 3x3x2

contingency table. Conventional univariate analysis,

such as the ones used in PLINK (Purcell et al.,

2007), are often unable to detect interacting SNP

pairs; hence, specific analyses for modelling

interaction needs to be preformed. The power to

detect interaction by our method is characterized by

the simulated counts within the table for detecting

SNP-SNP interaction. A chi-square test is done by

pooling high-risk interaction counts (dominant-

dominant) and low risk (recessive-recessive)

interaction counts to calculate the genotype

frequency distributions. It efficiently reduces a

3x3x2 table to a series of 2x2 tables (Figure 4). This

statistical approach is shown to be a balanced

solution for data sparsity and computational burdens

(Schwarz et al., 2010).

Figure 4: In this illustration, a model of dominant-

dominant interactions is shown; the four genotype

interactions (aa-bb, Aa-bb, aa-Bb, Aa-BB) are considered

to have many similar biological activities, hence they are

combined and collapsed as the high-risk interactions in the

2x2 table. The four other recessive-recessive interactions

are combined in the same fashion as the low risk

interaction. In conventional interaction analyses, each cell

is considered separated.

2.3 Dataset Generation

We generate a genotype distribution for a population

of a given sample size to generate 60,000 datasets

(studies) with genotype counts of assigned

parameters (sample size, MAF, odds ratio) for

different simulations. Based on the Hardy-Weinberg

principle, we first generate genotype frequencies of

2 SNPs based on 2 given MAF’s. Then,

combinations of given Minor Allele Frequency

(MAF) of SNP A and SNP B, disease relative risk,

one of the eight biologically plausible interaction

patterns, sample sizes, proportions and counts may

be generated in each of the cells in the 3x3x2 table

using a multinomial distribution.

IAC converts GWAS data from 9 genotype

counts into high risk and low risk counts (2 counts)

(along with reducing the observed 3x3x2 into 2x2

contingency table). This allows for clear illustrations

in interaction pattern, improving our assessment of

the model's biological plausibility.

2.4 IAC Dataset Analysis

From each collection of simulation datasets of

different population parameters and settings, the

constraints were applied when determining statistical

Gene-gene Interaction Analysis by IAC (Interaction Analysis by Chi-Square) - A Novel Biological Constraint-based Interaction Analysis

Framework

145

power of the interaction analysis and marginal

singular SNP analysis. The Bonferroni correction

was used to correct for multiple testing.

We approached all the analyses conservatively

by placing the Bonferroni corrected P-value for false

discovery rates at a global level of 0.05,which

ensures that the probability of having false positives

does not exceed the nominal significance level.

While calculating the power and type I error with

IAC, a conventional single SNP analysis is also run

for the same dataset. In the results, the average type

I errors for the conventional method analysis results

barely reached the nominal false positive

significance level of global 5%, thus deeming the

setup for the conventional method to be accurate and

conservative as well. The same datasets are

spontaneously converted using the same genotype

distributions and probabilities to fit two

conventional 2x3 single SNP association tests for

determining the statistical significance if the Single

SNP analysis is applied. To handle possible data

sparsity, the observed and expected values for the

modified setup are calculated once again for

statistical power. In order to ensure fairness in

comparison of the two models, both models are

analysed by their p-values using the same

significance filters and other SPC. Our

supplementary data (included in the website)

includes the records for all the simulations and the

analysis setup.

3 RESULTS

3.1 Simulation Results

We have exhausted many parameter configurations

and have arrived at several important conclusions:

We have focused the search amongst the 8

interaction patterns instead of the exhaustive search

of over 100 interaction patterns commonly used

nowadays in various algorithms) and have shown

that the IAC analysis is more efficient in detecting

interaction than conventional single SNP analyses.

We are certain that on top of these 8 pathologically

feasible patterns other patterns may exist and have

not been investigated. However, these 8 models

should be most representative of the biological

nature of gene-gene interaction.

Both IAC and the conventional single SNP

analysis show that type I error levels do not (or

barely) exceed the nominal significance number for

false positives. As the management of false positives

is a common factor in computational burdens

(Visscher et al., 2012) our controlled type I error

rates suggested our approach is conservative. As we

approach the data conservatively, we deem all power

percentages >80% to have enough power to detect

underlying significant SNP-SNP interaction. The

simulation analysis is comprised of many

population-based variables such as Odds Ratio,

Sample Size, disease distribution pattern and Minor

Allele Frequency. The prevalence of the disease

does not affect the statistical power since it does not

affect the population proportions or genotype

frequencies. Below we summarize the effects of

sample size, MAFs and interaction patterns on the

ability to detect significant interaction in GWAS.

We exhaustively analyse our method under many

parameter settings (table 1). The 532 mass-

simulation comparisons (266 by IAC, 266 by Single

SNP analysis) have contained the empirical power

and type I error for 60,000 simulations each.

Table 1: The exhaustive simulations in this study used

these parameters interchangeably for different

investigations. Please note that this table only depicts the

types of parameters we have tested (not the quantity of the

simulations); many of these settings were repeated with

other parameters for other specific investigations.

3.2 Effect of Sample Size

As the sample size (n) increases, the p-value

decreases accordingly (Spencer et al., 2009). A large

sample size, though preferred, is extremely difficult

to acquire in GWAS databases for the detection of

statistically significant interactions

(Bush and Moore,

2012). Using the results from our simulation, our

method clearly shows a dramatic improvement of

power (along with conservative type I error rates)

compared to the 2x3 single SNP analysis. IAC not

only requires less sample size to detect interaction,

but it is also has greater power to detect interactions

with recessive-recessive patterns (Figure 5). By

setting the MAF of both SNPs at 0.5 (the best-case

scenario), the dominant-dominant patterns are able

to detect interaction at only 4000 individuals with

IAC, while the conventional method requires

approximately 8000 individuals. IAC is able to

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detect recessive low-risk patterns at about 14000

individuals, while the conventional method requires

unrealistic sample sizes (more than 20,000).

Figure 5: The results from using IAC (top graph) and the

conventional single SNP analysis (bottom graph) with

sample sizes ranging from 2000-15000. The MAF (SNP

A=0.5, SNP B=0.5), odds ratio and all other simulation

parameter settings (besides sample size) remained the

same throughout. The statistical power for SNP A and

SNP B for the single SNP analysis was averaged for the

trend line.

As all the plausible dominant and recessive patterns

exhibit extremely similar trends in statistical power,

we have decided to use only one of each to simplify

the graphs for viewing (Figure 5). Our results

conclude that significant interaction may be detected

using the sample sizes commonly implemented

amongst current GWAS studies.

3.3 Odds Ratio

A disease’s odds ratio can significantly impact the

genotype frequencies observed in patients and thus

Figure 6: The results from using IAC and the conventional

single SNP analysis with varying odds ratios. The

interaction pattern (dominant-dominant), sample size

(4000) and SNP A MAF (0.1) remained constant

throughout.

greatly influence the power of statistical tests. We

based our primary analysis on two common disease

odds ratios of 1.5 and 2 and to compare the power of

both methods. In this scenario (Figure 6), it is clear

that IAC may detect significant interaction as long

as the MAF is above 0.2.

3.4 Minor Allele Frequency (MAF)

Like the odds ratio, the MAF greatly affects the

power of the analysis (Lettre et al., 2007). Though

most of the trends exhibit constant or exponential-

like growth of power with increasing MAF.

Sometimes, unexpected power curves may still

occur when using MAF as a variable. Computing the

genotypic distributions on the interaction table

allows us to use the population disease

characteristics to consider behaviours of interacting

proteins (Moore and Williams, 2005), which

conventional methods may not detect.

Figure 7: A relationship between Minor Allele

Frequencies and statistical power is shown with dominant-

dominant interaction patterns at a sample size of 4000.

MAF of SNP A remains at 0.5.

3.5 Parkinson's Disease Dataset

Analysis

Parkinson's disease is a neurodegenerative disorder

that affects an estimated seven to 10 million people

worldwide. Fung et al. (2006) genotyped 408,803

unique SNPs for 267 Parkinson's disease patients

and 270 neurologically normal controls. In their

analysis of the data, they did not identify any

significant associations using the single SNP

analysis. Different Bayesian models, such as the

ones implemented in Tang et al. (2009), were also

not able to detect any interaction effect. After

running the dataset with IAC, we were able to

replicate and confirm one dominant-dominant

Gene-gene Interaction Analysis by IAC (Interaction Analysis by Chi-Square) - A Novel Biological Constraint-based Interaction Analysis

Framework

147

interaction between SNPs rs849523 (chromosome 2)

and rs10519435 (chromosome 5) with a raw p-value

of 1.79x10

-3

. Although it did not reach a genome-

wide level of statistical significance, it serves here as

a demonstration of feasibility of our approach. The

SNPs are located in the NRP2 and LVRN genes

respectively. NRP2 is related to axon degeneration

and LVRN has been associated with level of very

long chain fatty acid. Both of them are relevant to

neuronal function. However, more experiment and

validation are needed to confirm this preliminary

finding.

4 DISCUSSION

The results indicated better efficiency of the IAC

analysis approach compared to conventional analysis

in many aspects, including; the detection of

interaction under plausible interaction patterns, the

detection of interaction under a given sample size or

relative risk and the detection of interaction under

unexpected power fluctuations. We believe that this

is an ideal search approach for future interaction

studies to increase efficiency when selecting subsets

of SNPs for further validation. Our results have

shown that most trends are biologically multivariate

(Turner and Bush, 2011) and thus IAC does not

require any multiplicative model to conduct high

capacity genome wide scans. Two-stage association

tests are becoming increasingly popular for

interaction analysis, in which the first stage is crucial

for selecting interactions with high power for in-

depth analysis (Feng et al., 2007).

For datasets with genetic interaction, which

results in no main marginal effect, univariate tests

are not able to exhibit power in conventional single

SNP analysis (Goodman et al., 2006). Several

univariate models such as FastEpistasis (Schüpbach

et al., 2010), TEAM (Zhang et al., 2010)and

EPIBLASTER (Kam-Thong et al., 2011) can be

computationally intensive when handling datasets

with complicated interaction patterns and difficult

sample sizes

(Moore and Williams 2005). In fact,

parametric models such as linear and logistic

regression fail to perform well when population

characteristics cannot be known a priori (Moore et

al., 2006). With Bayesian models, the process is too

computationally intensive. Furthermore, the

computationally efficient model BOOST (Wan et

al., 2010) has no consideration of biological

assumptions. IAC can work complementarily with

network-based approaches (Emily et al., 2009). By

filtering potential SNP pairs associated with certain

known protein-protein interactions, the biological

plausibility of the test for statistical epistasis will

substantially improve.

The advantage of IAC is that biologically

redundant patterns are excluded, reducing search

space and enhancing power, also promoting lower

false positive rates. Biologically plausible

interactions rarely exhibit univariate and/or linear

trends in statistical power (Boulesteix et al., 2012),

and have biochemical constraints in PPI (Emily et

al., 2009), hence more studies need to transverse the

disunity between the biological principles of

association and pure statistical reasoning to increase

productivity in exploiting SNP-SNP interactions.

Our results not only showed the efficiency of our

statistical distributions (using IAC) but have also

proposed evidence that detecting significant SNP-

SNP interaction should be feasible in the common

settings of GWAS studies. We have also shown

those scenarios in which the detection of SNP-SNP

interaction is not possible due to lack of statistical

power (eg. extremely low power in recessive-

recessive interaction patterns).

5 CONCLUSIONS

This investigation shows that by using biological

principles of PPI to constrain statistical analysis,

interaction tests become more effective. Once we are

able to understand the behaviour of biochemical

interactions, we may further enhance the practicality

of computational genetic analysis. Thornton-wells et

al., (2004) also believed that “the real power of

existing and yet-to-be-developed methods lies in our

ability to marry them into a comprehensive approach

to genetic analysis, so that their relative strengths

and weaknesses can be balanced and few alternative

hypotheses are left uninvestigated”. Through this

experiment, we were also able to detect two-locus

interaction in GWAS.

ACKNOWLEDGEMENTS

NLST received grant support from Health and

Medical Research Fund 14130282 of the HKSAR

Government.

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SUPPLEMENTARY

INFORMATION

Additional materials can be found at our website:

www.interactionanalysisbychisquare.com

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