BioMed Research International
Volume 2015 (2015), Article ID 870123, 7 pages
http://dx.doi.org/10.1155/2015/870123

Review Article

Bridging the Gap between Statistical and Biological Epistasis in Alzheimer’s Disease

Mark T. W. Ebbert, Perry G. Ridge, and John S. K. Kauwe

Department of Biology, Brigham Young University, Provo, UT, USA

Received 6 March 2015; Accepted 5 May 2015

Academic Editor: Helen F. K. Chiu

Copyright © 2015 Mark T. W. Ebbert et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Alzheimer’s disease affects millions of people worldwide and incidence is expected to rise as the population ages, but no effective therapies exist despite decades of research and more than 20 known disease markers. Research has shown that Alzheimer’s disease’s missing heritability remains extensive with an estimated 25% of phenotypic variance unexplained by known variants. The missing heritability may be explained by missing variants or by epistasis. Researchers often focus on individual loci rather than epistatic interactions, which is likely an oversimplification of the underlying biology since most phenotypes are affected by multiple genes. Focusing research efforts on epistasis will be critical to resolving Alzheimer’s disease etiology, and a major key to identifying and properly interpreting key epistatic interactions will be bridging the gap between statistical and biological epistasis. This review covers the current state of epistasis research in Alzheimer’s disease and how researchers can bridge the gap between statistical and biological epistasis to help resolve Alzheimer’s disease etiology.

1. Introduction

Alzheimer’s disease is the most common form of dementia and affects as many as 35 million people worldwide [1], and incidence is expected to increase rapidly as the population ages. The reduced cognition and required full-time care that are characteristic of Alzheimer’s disease exact a tremendous emotional and financial burden on family members and the health care system. Developing viable therapies is becoming a worldwide necessity.

To date, more than 20 Alzheimer’s disease markers have been identified (Table 1), but none have led to the development of effective therapies [1–4]. The majority of these markers were identified using genome-wide association studies, and most are common with small effects on disease risk. In the last several years next-generation sequencing has enabled researchers to sequence whole genomes revealing several rare variants in new genes with large effects [5–8]; however, research suggests that Alzheimer’s disease’s missing heritability remains extensive [9]. Alzheimer’s disease’s missing heritability may be explained by missing variants or epistasis, and discovering these genetic factors will require novel study designs [9]. Most studies to date have treated the effect of candidate variants individually. Epistasis in Alzheimer’ disease is largely unexplored, but there is compelling evidence that it could play a role in disease [10–13].

Table 1: Known Alzheimer’s disease associated genes/variants.

Variant
Gene
Abbreviation
Risk/protective

rs744373
Bridging integrator 1
BIN1
Risk

rs11136000
Clusterin
CLU
Protective

rs3764650
ATP-binding cassette, subfamily A (ABC1), member 7
ABCA7
Risk

rs3818361
Complement component (3b/4b) receptor 1
CR1
Risk

rs3851179
Phosphatidylinositol binding clathrin assembly protein
PICALM
Protective

rs610932
Membrane-spanning 4-domain, subfamily A, member 6A
MS4A6A
Protective

rs3865444
CD33 molecule
CD33
Protective

rs670139
Membrane-spanning 4-domain, subfamily A, member 4E
MS4A4E
Risk

rs9349407
CD2-associated protein
CD2AP
Risk

rs9271192
Major histocompatibility complex, class II, DR beta 5
HLA-DRB5
Risk

Major histocompatibility complex, class II, DR beta 1
HLA-DRB1

rs28834970
Protein tyrosine kinase 2 beta
PTK2B
Risk

rs11218343
Sortilin-related receptor, L(DLR class) A repeats containing
SORL1
Protective

rs10498633
Solute carrier family 24 (sodium/potassium/calcium exchanger), member 4
SLC24A4
Protective

Ras and Rab interactor 3
RIN3

rs8093731
Desmoglein 2
DSG2
Protective

rs35349669
Inositol polyphosphate-5-phosphatase, 145 kDa
INPP5D
Risk

rs190982
Myocyte enhancer factor 2C
MEF2C
Protective

rs2718058
NME/NM23 family member 8
NME8
Protective

rs1476679
Zinc finger, CW type with PWWP domain 1
ZCWPW1
Protective

rs10838725
CUGBP, Elav-like family member 1
CELF1
Risk

rs17125944
Fermitin family member 2
FERMT2
Risk

rs7274581
Cas scaffolding protein family member 4
CASS4
Protective

These SNPs are located close to two different genes so both are listed here (as named in the primary publication reporting the association).

Epistasis involves multiple genes contributing to a single phenotype, but the biological nature and implications of epistatic interactions are not always clear. Epistatic interactions are generally discovered in two ways: statistically and biologically. Statistical epistasis is a deviation from additive effects between factors in the model [14], while biological epistasis is a physical interaction between two or more biological components.

Bridging the gap between statistical and biological epistasis is an essential next step towards understanding the genetics of complex phenotypes such as Alzheimer’s disease, since most phenotypes in complex organisms involve epistasis. To bridge the gap, we must first understand the benefits and shortcomings for discovering epistasis both statistically and biologically.

Two major challenges for biological epistasis are resources and interpretation. Experiments to discover physical interactions are challenging and expensive to carry out—generally limiting experiments to candidate interactions identified statistically or by some other means. Regarding interpretation, if a physical interaction is discovered only through biological experiments, the implications across phenotypes are often less obvious because discovering an interaction alone does not indicate which phenotypes the interaction affects, thus ultimately leaving questions regarding the biological significance of the interaction. The potential benefits, however, to discovering biological epistatic interactions are substantial. The discovery that two biological molecules interact physically provides crucial functional and pathway information and enables researchers with phenotype information to interrogate a given interaction’s role in the phenotype.

Statistical epistasis has its own challenges and benefits. The primary challenge for statistical epistasis is that statistical associations are generally based on genetic variations rather than biological molecules, and the association does not give evidence that the corresponding molecules actually interact physically. In fact, many such statistical associations are based on genetic variations that are not even transcribed (e.g., intergenic) and are not believed to be involved in gene regulation, leaving no obvious biological mechanism for their involvement in known pathways. While this is not always the case, these challenges leave to researchers the arduous task of explaining how the genetic variations, or a nearby gene, could play a role in the phenotype. These explanations often require stepping beyond known biology and sometimes seem implausible. Another major limitation of statistically derived epistasis is the frequency of false-positive and false-negative results. False-positive results are common when testing numerous hypotheses, while false negatives are caused by poor statistical power.

Statistical epistasis can, however, provide insights into unknown biology. For example, just because two proteins are not known to physically interact does not mean they do not both affect the same phenotype; the two proteins may be involved in the same pathway and cause different cascading events, or a given phenotype may be determined by multiple pathways. Such an interaction would be missed in studies of biological epistasis but be discoverable using statistical epistasis. Thus, statistical epistasis can provide the foundation for discovering new biology and generating testable hypotheses. Furthermore, using statistics we can explore whether multiple genetic factors have a nonadditive effect on a phenotype. If so, these genetic factors may be coinvolved in the phenotype’s presentation. In this review we discuss the strengths and weaknesses of different approaches for identifying statistical epistasis and review previous studies of epistasis in Alzheimer’s disease. Finally, we make suggestions for future studies of epistasis in Alzheimer’s disease.

2. Methods to Identify Statistical Epistasis: Merits and Limitations

Identifying statistical epistasis is the most common and cost-effective approach to discovering gene-gene interactions, but most studies of genetics in human disease focus on single genetic loci—likely an oversimplification of the underlying biology. To advance our understanding of the genetic architecture of complex phenotypes, we must elucidate the underlying epistatic relationships.

Several analysis methods have been developed specifically to identify gene-gene interactions, including multifactor dimensionality reduction [15–30], log-linear [31] (a form of multifactor dimensionality reduction), logistic regression [10, 11, 32–42], entropy model [43], and the log-likelihood ratio model [44]. Multifactor dimensionality reduction and logistic regression are the two most commonly used methods. Synergy factors are an extension of logistic regression and for the purposes of this discussion are included in that group. Multifactor dimensionality reduction is a nonparametric approach while logistic regression is parametric. Each method has distinct strengths and weaknesses that determine their ability to identify interactions.

Logistic regression has several drawbacks when detecting epistasis: (1) interaction terms grow exponentially as the number of main effects included in the model increases [45]; (2) parameter estimates have large standard errors because the data is high-dimensional—decreasing power to detect interactions [45]; and (3) logistic regression is generally only valid for binary interactions because of limited sample size [12]. Park and Hastie, however, proposed penalized logistic regression as a method to overcome the limitations and showed that penalized logistic regression performs better than multifactor dimensionality reduction in some situations [46].

Many studies have demonstrated the utility of multifactor dimensionality reduction [47–51]. Advantages of multifactor dimensionality reduction include increased power [28, 52] and superior ability to identify high-order interactions even when main effects are statistically insignificant [46]. Multifactor dimensionality reduction, however, is incapable of identifying additive main effects [46] and is less effective if there are missing values in high-dimensional data [45].

Given the complementarity of logistic regression and multifactor dimensionality reduction, combining approaches may be an effective option. For example, multifactor dimensionality reduction could be used to discover complex interactions while logistic regression can be used for main effects.

The prevalence of false positives is a concern for all available methods. According to Page et al. [53], there are four reasons why an allele or interaction between alleles can be associated with a complex disease: (1) it is actually causative; (2) the association is by random chance; (3) a single allele is in disequilibrium with the causative allele; and (4) the association is due to a systematic bias in some portion of the study. Because of the high-dimensionality and small sample size of many studies, there is an increased likelihood of false positives because of the reasons stated by Page et al. “Overfitting” is another potential cause of false positives. Overfitting happens when a complex model is fit to data and is not generalizable beyond the population from which the sample was derived [54]. The cause has commonly been attributed to either genetic or environmental heterogeneity [55], or due to epistasis [14, 56].

There are many approaches designed to prevent false positives and overfitting when studying predictive alleles in a given disease, but they are not foolproof. For instance, protocol when performing multiple comparisons—millions in the case of genome-wide association studies—involves adjusting values to limit the number of false positives due to chance. Similar methods exist to prevent overfitting statistical models to data. Although these methods are useful, researchers mistakenly report false associations.

Even though many weak associations are reported, this practice is not completely wrong. Statistical analyses are limited by the available data, and data is limited by external restraints such as financial support, limited patient availability, genetic material, and even ethical restrictions. Given the various challenges researchers face to produce data, it is not surprising that weak associations are reported. The key to separating true and false associations will be testing in independent data sets if they are large enough, or using meta-analyses across many smaller data sets to determine if the signal is consistent and significant. If a signal is replicable, researchers then need to test associations in cell lines or model organisms.

3. Epistasis in Alzheimer’s Disease

Numerous studies have identified statistical epistasis in Alzheimer’s disease using logistic regression [10, 11, 32–42] and multifactor dimensionality reduction [15–27]. Here we describe studies where results have been replicated in at least two independent samples.

In 2004 Robson et al. identified statistical epistasis between the transferrin (TF) C2 allele and the haemochromatosis (HFE) C282Y allele using logistic regression and synergy factor analysis [33]. These genes were targeted because of their role in metabolizing iron and previous evidence of iron buildup in Alzheimer’s disease patients [57–59]. In 2009, Kauwe et al. replicated the findings from Robson et al. in a separate cohort [34]. There is strong evidence of a biological cascading effect for this statistical interaction, as suggested by Kauwe et al. [34]. HFE binds with transferrin receptor 1 (TfR1), but the C282Y allele has a lesser affinity, allowing TfR1 to bind TF more easily [34, 60]. It was hypothesized that more aggressive binding of TF may cause overabsorption of dietary iron, leading to iron deposits in various tissues [34, 61]. Additionally, Giunta et al. suggested that wild-type TF plays an important role in iron transport and limits amyloid aggregation [34, 62]. All the information supports hypotheses by Robson et al. [33] and Lehmann et al. [63] that this interaction increases Alzheimer’s disease risk through increased redox-active iron and oxidative stress.

Likewise, in 2004 Infante et al. identified statistical epistasis between interleukin-6 (IL-6) and interleukin-10 (IL-10) associated with decreased risk for Alzheimer’s disease based on previous evidence that patients with Alzheimer’s disease produce more proinflammatory interleukin-6 and less anti-inflammatory interleukin-10 [64]. In 2009 Combarros et al. replicated the statistical interaction in a separate cohort [10]. This interaction may play a critical role in Alzheimer’s disease because Remarque et al. demonstrated that Alzheimer’s disease patients have a proinflammatory phenotype and that Alzheimer’s disease patients produce more IL-6 (proinflammatory) and less IL-10 (anti-inflammatory) when compared to controls [65]. It is difficult to determine, however, whether this inflammation is contributing to Alzheimer’s disease or is simply another side effect of the underlying cause.

In 2009, Combarros et al. performed a comprehensive analysis of over 100 reports of statistical epistasis in Alzheimer’s disease, using and introducing their own synergy factor statistic. The synergy factor is a valuable statistic because it relates the expected odds ratio to the observed, summarizing the nonadditive effect of the interaction. This study highlights the innate challenges in discovering statistical epistasis. The authors were only able to support 27 of the originally reported gene-gene interactions using their synergy factor analysis. The challenge with epistatic replication is that there are many factors that influence whether the interaction can be detected in a given data set. Sample size, heterogeneity, and environmental factors are likely the most influential for detecting a real interaction.

In 2014, Gusareva et al. published the first replicable interaction associated with Alzheimer’s disease using an exhaustive, genome-wide screening approach [66]. They identified an interaction between KHDRBS2 (rs6455128) and CRYL1 (rs7989332) using a cohort from France (2,259 cases and 6,017 controls). The interaction was replicated in a cohort from Germany (555 cases and 824 controls). The interaction was further supported by a meta-analysis using five more independent Alzheimer’s disease cohorts. Transcriptome analysis showed decreased expression for both genes in the temporal cortex and cerebellum brain regions. Gusareva et al. hypothesized a biological link between KHDRBS2 and CRYL1 through a potential association with heat-shock proteins and Alzheimer’s disease. KHDRBS2 is believed to affect transcription of heat-shock proteins because of studies in its homologue Slm1 in Saccharomyces cerevisiae [66, 67]. Slm1 was shown to interact with and activate TORC2 [68], a kinase complex that is part of the TOR pathway, which Pierce et al. demonstrated to affect amyloid β and cognitive function in Alzheimer’s disease mouse models [69]. Pierce et al. hypothesized that upregulated heat-shock proteins, resulting from inhibition of the TOR pathway, affect amyloid β and cognition. This study in particular demonstrates an effective approach to elucidate the functional repercussions of epistasis.

4. Epistasis among Top Alzheimer’s Disease Genes

Most epistasis studies in Alzheimer’s disease involve candidate genes, but to date, few studies [13, 70] have addressed combined effects of the top Alzheimer’s disease genes (see Table 1). Verhaaren et al. examined the contribution of the nine AlzGene.org risk alleles to Alzheimer’s disease status prediction [70]. They calculated an additive genetic risk score and compared Alzheimer’s disease status prediction performance of age, gender, and the apolipoprotein E (APOE)ε4 allele using logistic regression with and without the additive genetic risk score. The genetic risk score did not improve prediction performance significantly, suggesting that the nine alleles may not be diagnostically useful when constrained to an additive relationship. The assumption of additive relationships between risk loci is common but is likely to be an oversimplification of the underlying biology for Alzheimer’s disease and other complex diseases [11, 12, 14]. In fact, there may be underlying gene-gene interactions not examined in the Verhaaren et al. study or others that improve Alzheimer’s disease status prediction performance.

Ebbert et al. [13] evaluated the possible interactions between the AlzGene.org variants and their effects on Alzheimer’s disease in several large, independent data sets. Briefly, Ebbert et al. genotyped each locus in 2,419 subjects from the Cache County Study on Memory Health and Aging to verify results by Verhaaren et al. and explore statistical epistasis among the loci to determine if any interactions are informative to the model in the presence of the main (individual) allele effects. Two interactions were significant in the model: an interaction between CD33 and MS4A4E (; SF 5.31, 95% CI 1.79–15.77) and between CLU and MS4A4E (; SF 3.81, 95% CI 1.28–11.32).

5. Future Directions

Many researchers are focusing their efforts on epistasis and the community is beginning to discover epistatic interactions that play a role in Alzheimer’s disease, but based on odds ratios none of the as-yet discovered interactions appear to play a significant role in Alzheimer’s disease etiology. Each of the top candidate genes individually has a consistent and strong signal across numerous data sets, making it a reasonable hypothesis that there are interactions between them. It is not reasonable, however, to assume that the most critical interactions are only between loci with main effects. As such, researchers must approach epistasis in Alzheimer’s disease with even larger data sets using exhaustive, genome-wide approaches as demonstrated by the exciting study by Gusareva et al. [66].

The International Genomics of Alzheimer’s Project (IGAP) has a data set of over 74,000 cases and controls [4]—a massive data set by today’s standards. Given the success by Gusareva et al., a similar agnostic (hypothesis-free) approach in such a large data set would likely result in more stable interactions associated with Alzheimer’s disease case-control status, thus leading to potentially useful approaches for both diagnostics and therapeutics. IGAP also discovered several more alleles with main effects in a recent study (Table 1) [4]. Rerunning our analysis across the top loci including IGAP’s newly discovered loci may uncover new interactions.

Ultimately, however, we must bridge the gap between statistical and biological epistasis. Biological experiments demonstrating tangible effects on known or novel Alzheimer’s disease pathology will be essential to understanding the underlying etiology. These gene-gene interactions may involve physical interactions between proteins, or they may be indirect where they affect a downstream product.

6. Conclusions

Epistasis plays a central role in most phenotypes and may play a significant role in Alzheimer’s disease. To understand Alzheimer’s disease etiology, researchers must utilize both statistical and biological epistasis studies to identify critical interactions and to characterize their functional roles. Some studies have already demonstrated that epistasis plays a role in Alzheimer’s disease, but the findings are insufficient to develop effective therapies. By focusing on epistasis and bridging the gap between the statistical and biological knowledge base, researchers will contribute invaluable information for revealing the disease’s etiology and developing effective treatments.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

P. G. Ridge, M. T. W. Ebbert, and J. S. K. Kauwe, “Genetics of alzheimer's disease,” BioMed Research International, vol. 2013, Article ID 254954, 13 pages, 2013.

A. C. Naj, G. Jun, G. W. Beecham et al., “Common variants at MS4A4/MS4A6E, CD2AP, CD33 and EPHA1 are associated with late-onset Alzheimer's disease,” Nature Genetics, vol. 43, no. 5, pp. 436–441, 2011.

P. Hollingworth, D. Harold, R. Sims et al., “Common variants at ABCA7, MS4A6A/MS4A4E, EPHA1, CD33 and CD2AP are associated with Alzheimer's disease,” Nature Genetics, vol. 43, no. 5, pp. 429–435, 2011.

J. Williams and P. Amouyel, “Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease,” Nature Genetics, vol. 45, no. 12, pp. 1452–1458, 2013.

C. Cruchaga, C. M. Karch, S. C. Jin et al., “Rare coding variants in the phospholipase D3 gene confer risk for Alzheimer's disease,” Nature, vol. 505, pp. 550–554, 2014.

R. Guerreiro, A. Wojtas, J. Bras et al., “TREM2 variants in Alzheimer's disease,” The New England Journal of Medicine, vol. 368, no. 2, pp. 117–127, 2013.

T. Jonsson, H. Stefansson, S. Steinberg et al., “Variant of TREM2 associated with the risk of Alzheimer's disease,” The New England Journal of Medicine, vol. 368, pp. 107–116, 2013.

T. Jonsson, J. K. Atwal, S. Steinberg et al., “A mutation in APP protects against Alzheimer's disease and age-related cognitive decline,” Nature, vol. 488, no. 7409, pp. 96–99, 2012.

P. G. Ridge, S. Mukherjee, P. K. Crane, and J. S. K. Kauwe, “Alzheimer's disease: analyzing the missing heritability,” PLoS ONE, vol. 8, no. 11, Article ID e79771, 2013.

O. Combarros, C. M. van Duijn, N. Hammond et al., “Replication by the Epistasis Project of the interaction between the genes for IL-6 and IL-10 in the risk of Alzheimer's disease,” Journal of Neuroinflammation, vol. 6, article 22, 2009.

J. M. Bullock, C. Medway, M. Cortina-Borja et al., “Discovery by the Epistasis Project of an epistatic interaction between the GSTM3 gene and the HHEX/IDE/KIF11 locus in the risk of Alzheimer's disease,” Neurobiology of Aging, vol. 34, no. 4, pp. 1309.e1–1309.e7, 2013.

O. Combarros, M. Cortina-Borja, A. D. Smith, and D. J. Lehmann, “Epistasis in sporadic Alzheimer's disease,” Neurobiology of Aging, vol. 30, no. 9, pp. 1333–1349, 2009.

M. T. W. Ebbert, P. G. Ridge, A. R. Wilson et al., “Population-based analysis of Alzheimer's disease risk alleles implicates genetic interactions,” Biological Psychiatry, vol. 75, no. 9, pp. 732–737, 2014.

J. H. Moore and S. M. Williams, “Traversing the conceptual divide between biological and statistical epistasis: systems biology and a more modern synthesis,” BioEssays, vol. 27, no. 6, pp. 637–646, 2005.

A. S. Andrew, H. H. Nelson, K. T. Kelsey et al., “Concordance of multiple analytical approaches demonstrates a complex relationship between DNA repair gene SNPs, smoking and bladder cancer susceptibility,” Carcinogenesis, vol. 27, no. 5, pp. 1030–1037, 2006.

L. Briollais, Y. Wang, I. Rajendram et al., “Methodological issues in detecting gene-gene interactions in breast cancer susceptibility: a population-based study in Ontario,” BMC Medicine, vol. 5, article 22, 2007.

M. Chen, A. M. Kamat, M. Huang et al., “High-order interactions among genetic polymorphisms in nucleotide excision repair pathway genes and smoking in modulating bladder cancer risk,” Carcinogenesis, vol. 28, no. 10, pp. 2160–2165, 2007.

C. T. Tsai, J. J. Hwang, M. D. Ritchie et al., “Renin-angiotensin system gene polymorphisms and coronary artery disease in a large angiographic cohort: detection of high order gene-gene interaction,” Atherosclerosis, vol. 195, no. 1, pp. 172–180, 2007.

I. H. S. Chan, T. F. Leung, N. L. S. Tang et al., “Gene-gene interactions for asthma and plasma total IgE concentration in Chinese children,” Journal of Allergy and Clinical Immunology, vol. 117, no. 1, pp. 127–133, 2006.

J.-Y. Lee, J.-C. Kwon, and J.-J. Kim, “Multifactor dimensionality reduction (MDR) analysis to detect single nucleotide polymorphisms associated with a carcass trait in a Hanwoo population,” Asian-Australasian Journal of Animal Sciences, vol. 21, no. 6, pp. 784–788, 2008.

M. D. Ritchie, D. W. Haas, A. A. Motsinger et al., “Drug transporter and metabolizing enzyme gene variants and nonnucleoside reverse-transcriptase inhibitor hepatotoxicity,” Clinical Infectious Diseases, vol. 43, no. 6, pp. 779–782, 2006.

H.-W. Park, E.-S. Shin, J.-E. Lee et al., “Multilocus analysis of atopy in Korean children using multifactor-dimensionality reduction,” Thorax, vol. 62, no. 3, pp. 265–269, 2007.

M. Manuguerra, G. Matullo, F. Veglia et al., “Multi-factor dimensionality reduction applied to a large prospective investigation on gene-gene and gene-environment interactions,” Carcinogenesis, vol. 28, no. 2, pp. 414–422, 2007.

A. Julià, J. Moore, L. Miquel et al., “Identification of a two-loci epistatic interaction associated with susceptibility to rheumatoid arthritis through reverse engineering and multifactor dimensionality reduction,” Genomics, vol. 90, no. 1, pp. 6–13, 2007.

T. L. Edwards, K. Lewis, D. R. Velez, S. Dudek, and M. D. Ritchie, “Exploring the performance of multifactor dimensionality reduction in large scale SNP studies and in the presence of genetic heterogeneity among epistatic disease models,” Human Heredity, vol. 67, no. 3, pp. 183–192, 2009.

M. D. Ritchie, L. W. Hahn, N. Roodi et al., “Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer,” American Journal of Human Genetics, vol. 69, no. 1, pp. 138–147, 2001.

Y. M. Cho, M. D. Ritchie, J. H. Moore et al., “Multifactor-dimensionality reduction shows a two-locus interaction associated with Type 2 diabetes mellitus,” Diabetologia, vol. 47, no. 3, pp. 549–554, 2004.

M. D. Ritchie, L. W. Hahn, and J. H. Moore, “Power of multifactor dimensionality reduction for detecting gene-gene interactions in the presence of genotyping error, missing data, phenocopy, and genetic heterogeneity,” Genetic Epidemiology, vol. 24, no. 2, pp. 150–157, 2003.

L. W. Hahn, M. D. Ritchie, and J. H. Moore, “Multifactor dimensionality reduction software for detecting gene-gene and gene-environment interactions,” Bioinformatics, vol. 19, no. 3, pp. 376–382, 2003.

C. S. Coffey, P. R. Hebert, M. D. Ritchie et al., “An application of conditional logistic regression and multifactor dimensionality reduction for detecting gene-gene interactions on risk of myocardial infarction: the importance of model validation,” BMC Bioinformatics, vol. 5, article 49, 2004.

S. Y. Lee, Y. Chung, R. C. Elston, Y. Kim, and T. Park, “Log-linear model-based multifactor dimensionality reduction method to detect gene-gene interactions,” Bioinformatics, vol. 23, no. 19, pp. 2589–2595, 2007.

E. Rodríguez-Rodríguez, I. Mateo, J. Infante et al., “Interaction between HMGCR and ABCA1 cholesterol-related genes modulates Alzheimer's disease risk,” Brain Research, vol. 1280, pp. 166–171, 2009.

K. J. H. Robson, D. J. Lehmann, V. L. C. Wimhurst et al., “Synergy between the C2 allele of transferrin and the C282Y allele of the haemochromatosis gene (HFE) as risk factors for developing Alzheimer's disease,” Journal of Medical Genetics, vol. 41, no. 4, pp. 261–265, 2004.

J. S. K. Kauwe, S. Bertelsen, K. Mayo et al., “Suggestive synergy between genetic variants in TF and HFE as risk factors for Alzheimer's disease,” The American Journal of Medical Genetics, Part B: Neuropsychiatric Genetics, vol. 153, no. 4, pp. 955–959, 2010.

A. Muendlein, C. H. Saely, T. Marte et al., “Synergistic effects of the apolipoprotein E ε3/ε2/ε4, the cholesteryl ester transfer protein TaqIB, and the apolipoprotein C3—482 C > T polymorphisms on their association with coronary artery disease,” Atherosclerosis, vol. 199, no. 1, pp. 179–186, 2008.

L. Polito, P. G. Kehoe, A. Davin et al., “The SIRT2 polymorphism rs10410544 and risk of Alzheimer's disease in two Caucasian case-control cohorts,” Alzheimer's and Dementia, vol. 9, no. 4, pp. 392–399, 2013.

M. Hiltunen, A. Mannermaa, S. Helisalmi et al., “Butyrylcholinesterase K variant and apolipoprotein E4 genes do not act in synergy in Finnish late-onset Alzheimer's disease patients,” Neuroscience Letters, vol. 250, no. 1, pp. 69–71, 1998.

F. Licastro, M. Chiappelli, L. M. E. Grimaldi et al., “A new promoter polymorphism in the alpha-1-antichymotrypsin gene is a disease modifier of Alzheimer's disease,” Neurobiology of Aging, vol. 26, no. 4, pp. 449–453, 2005.

C. Talbot, H. Houlden, N. Craddock et al., “Polymorphism in AACT gene may lower age of onset of Alzheimer's disease,” NeuroReport, vol. 7, no. 2, pp. 534–536, 1996.

O. Combarros, M. García-Román, A. Fontalba et al., “Interaction of the H63D mutation in the hemochromatosis gene with the apolipoprotein E epsilon 4 allele modulates age at onset of Alzheimer's disease,” Dementia and Geriatric Cognitive Disorders, vol. 15, no. 3, pp. 151–154, 2003.

K. Kamino, K. Nagasaka, M. Imagawa et al., “Deficiency in mitochondrial aldehyde dehydrogenase increases the risk for late-onset Alzheimer's disease in the Japanese population,” Biochemical and Biophysical Research Communications, vol. 273, no. 1, pp. 192–196, 2000.

J.-M. Kim, R. Stewart, I.-S. Shin, J.-S. Jung, and J.-S. Yoon, “Assessment of association between mitochondrial aldehyde dehydrogenase polymorphism and Alzheimer's disease in an older Korean population,” Neurobiology of Aging, vol. 25, no. 3, pp. 295–301, 2004.

G. Kang, W. Yue, J. Zhang, Y. Cui, Y. Zuo, and D. Zhang, “An entropy-based approach for testing genetic epistasis underlying complex diseases,” Journal of Theoretical Biology, vol. 250, no. 2, pp. 362–374, 2008.

X. Wan, C. Yang, Q. Yang et al., “BOOST: a fast approach to detecting gene-gene interactions in genome-wide case-control studies,” American Journal of Human Genetics, vol. 87, no. 3, pp. 325–340, 2010.

H. He, W. S. Oetting, M. J. Brott, and S. Basu, “Pair-wise multifactor dimensionality reduction method to detect gene-gene interactions in a case-control study,” Human Heredity, vol. 69, no. 1, pp. 60–70, 2010.

M. Y. Park and T. Hastie, “Penalized logistic regression for detecting gene interactions,” Biostatistics, vol. 9, no. 1, pp. 30–50, 2008.

S. K. Musani, D. Shriner, N. Liu et al., “Detection of gene x gene interactions in genome-wide association studies of human population data,” Human Heredity, vol. 63, no. 2, pp. 67–84, 2007.

D. R. Velez, B. C. White, A. A. Motsinger et al., “A balanced accuracy function for epistasis modeling in imbalanced datasets using multifactor dimensionality reduction,” Genetic Epidemiology, vol. 31, no. 4, pp. 306–315, 2007.

J. H. Moore, “Computational analysis of gene-gene interactions using multifactor dimensionality reduction,” Expert Review of Molecular Diagnostics, vol. 4, no. 6, pp. 795–803, 2004.

T. Cattaert, M. L. Calle, S. M. Dudek et al., “Model-based multifactor dimensionality reduction for detecting epistasis in case-control data in the presence of noise,” Annals of Human Genetics, vol. 75, no. 1, pp. 78–89, 2011.

J. Namkung, R. C. Elston, J.-M. Yang, and T. Park, “Identification of gene-gene interactions in the presence of missing data using the multifactor dimensionality reduction method,” Genetic Epidemiology, vol. 33, no. 7, pp. 646–656, 2009.

J. H. Moore, J. C. Gilbert, C.-T. Tsai et al., “A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility,” Journal of Theoretical Biology, vol. 241, no. 2, pp. 252–261, 2006.

G. P. Page, V. George, R. C. Go, P. Z. Page, and D. B. Allison, ““Are we there yet?”: deciding when one has demonstrated specific genetic causation in complex diseases and quantitative traits,” American Journal of Human Genetics, vol. 73, no. 4, pp. 711–719, 2003.

C. G. Howard and P. Bock, “Using a hierarchical approach to avoid over-fitting in early vision,” in Proceedings of the 12th IAPR International Conference on Pattern Recognition, Volume 1—Conference A: Computer Vision amp; Image Processing, pp. 826–829, 1994.

P. Gorroochurn, S. E. Hodge, G. A. Heiman, M. Durner, and D. A. Greenberg, “Non-replication of association studies: ‘Pseudo-failures’ to replicate?” Genetics in Medicine, vol. 9, no. 6, pp. 325–331, 2007.

M. J. Wade, “Epistasis, complex traits, and mapping genes,” Genetica, vol. 112-113, pp. 59–69, 2001.

J. R. Connor, S. L. Menzies, S. M. St. Martin, and E. J. Mufson, “A histochemical study of iron, transferrin, and ferritin in Alzheimer's diseased brains,” Journal of Neuroscience Research, vol. 31, no. 1, pp. 75–83, 1992.

D. A. Loeffler, J. R. Connor, P. L. Juneau et al., “Transferrin and iron in normal, Alzheimer's disease, and Parkinson's disease brain regions,” Journal of Neurochemistry, vol. 65, no. 2, pp. 710–724, 1995.

M. A. Smith, P. L. R. Harris, L. M. Sayre, and G. Perry, “Iron accumulation in Alzheimer disease is a source of redox-generated free radicals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 94, no. 18, pp. 9866–9868, 1997.

J. N. Feder, D. M. Penny, A. Irrinki et al., “The hemochromatosis gene product complexes with the transferrin receptor and lowers its affinity for ligand binding,” Proceedings of the National Academy of Sciences of the United States of America, vol. 95, no. 4, pp. 1472–1477, 1998.

A. Townsend and H. Drakesmith, “Role of HFE in iron metabolism, hereditary haemochromatosis, anaemia of chronic disease, and secondary iron overload,” The Lancet, vol. 359, no. 9308, pp. 786–790, 2002.

S. Giunta, R. Galeazzi, M. B. Valli, E. H. Corder, and L. Galeazzi, “Transferrin neutralization of amyloid beta 25-35 cytotoxicity,” Clinica Chimica Acta, vol. 350, no. 1-2, pp. 129–136, 2004.

D. J. Lehmann, J. Williams, J. Mcbroom, and A. D. Smith, “Using meta-analysis to explain the diversity of results in genetic studies of late-onset Alzheimer's disease and to identify high-risk subgroups,” Neuroscience, vol. 108, no. 4, pp. 541–554, 2001.

J. Infante, C. Sanz, J. L. Fernández-Luna, J. Llorca, J. Berciano, and O. Combarros, “Gene-gene interaction between interleukin-6 and interleukin-10 reduces AD risk,” Neurology, vol. 63, no. 6, pp. 1135–1136, 2004.

E. J. Remarque, E. L. E. M. Bollen, A. W. E. Weverling-Rijnsburger, J. C. Laterveer, G. J. Blauw, and R. G. J. Westendorp, “Patients with Alzheimer's disease display a pro-inflammatory phenotype,” Experimental Gerontology, vol. 36, no. 1, pp. 171–176, 2001.

E. S. Gusareva, M. M. Carrasquillo, C. Bellenguez et al., “Genome-wide association interaction analysis for Alzheimer's disease,” Neurobiology of Aging, vol. 35, no. 11, pp. 2436–2443, 2014.

R. C. Dickson, “Thematic review series: sphingolipids. New insights into sphingolipid metabolism and function in budding yeast,” Journal of Lipid Research, vol. 49, no. 5, pp. 909–921, 2008.

D. Berchtold, M. Piccolis, N. Chiaruttini et al., “Plasma membrane stress induces relocalization of Slm proteins and activation of TORC2 to promote sphingolipid synthesis,” Nature Cell Biology, vol. 14, no. 5, pp. 542–547, 2012.

A. Pierce, N. Podlutskaya, J. J. Halloran et al., “Over-expression of heat shock factor 1 phenocopies the effect of chronic inhibition of TOR by rapamycin and is sufficient to ameliorate Alzheimer's-like deficits in mice modeling the disease,” Journal of Neurochemistry, vol. 124, no. 6, pp. 880–893, 2013.

B. F. J. Verhaaren, M. W. Vernooij, P. J. Koudstaal et al., “Alzheimer's disease genes and cognition in the nondemented general population,” Biological Psychiatry, vol. 73, no. 5, pp. 429–434, 2013.