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Detecting gene–gene interactions that underlie human diseases

Key Points

  • Interactions between genetic loci might reduce the power to detect genetic effects in genetic association studies, if these interactions are not allowed for.

  • Statistical interaction corresponds to a departure from the additive effects of two or more variables in a linear model describing the relationship between an outcome and predictor variables.

  • A variety of methods can be used to test for statistical interaction between predictor variables that encode the genotype and an outcome variable corresponding to the disease phenotype.

  • Logistic regression is one method that can be used either to test for interaction, or to test for association while allowing for interaction.

  • Given genome-wide data, an exhaustive search is feasible for investigating two-way interactions (that is, all pairwise combinations of loci) but not for investigation of higher-order interactions.

  • Filtering approaches allow one to reduce the number of loci considered and thus the number of interaction tests performed.

  • Data-mining or machine-learning methods, such as random forests and Multifactor Dimensionality Reduction (MDR), can allow one to search through the space of possible interactions.

  • Bayesian model selection approaches offer an alternative approach for searching through the space of possible interactions.

  • The biological interpretation of statistical interactions is complex. The degree to which statistical interaction implies interaction or synergism in a causal sense might be extremely limited.

Abstract

Following the identification of several disease-associated polymorphisms by genome-wide association (GWA) analysis, interest is now focusing on the detection of effects that, owing to their interaction with other genetic or environmental factors, might not be identified by using standard single-locus tests. In addition to increasing the power to detect associations, it is hoped that detecting interactions between loci will allow us to elucidate the biological and biochemical pathways that underpin disease. Here I provide a critical survey of the methods and related software packages currently used to detect the interactions between genetic loci that contribute to human genetic disease. I also discuss the difficulties in determining the biological relevance of statistical interactions.

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Figure 1: Semi-exhaustive search of pairwise interactions between 89,294 SNPs.
Figure 2: Random Jungle analysis of 89,294 SNPs.
Figure 3: Multifactor Dimensionality Reduction (MDR) and Tuned ReliefF (TuRF) analysis of 6,113 SNPs.
Figure 4: Bayesian Epistasis Association Mapping (BEAM) analysis of 47,727 SNPs.

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Acknowledgements

Support for this work was provided by the Wellcome Trust (Grant reference 074524). I thank J. Barrett for assistance with interpretation of the WTCCC Crohn's results, and the WTCCC for making their data freely available. I also thank J. Moore for useful discussions of data-mining methods in general and MDR in particular, and K. Keen for pointing out the origins of the term epistasis.

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Supplementary information

Supplementary Box S1

Different models of interaction (PDF 253 kb)

Supplementary Box S2

Effects – interacting, independent or otherwise (PDF 294 kb)

Supplementary Table 1

Top pairwise interactions as detected from a--fast-epistasis analysis of the WTCCC Crohn's disease and control data using PLINK (PDF 164 kb)

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The process of extracting hidden patterns and potentially useful information from large amounts of data.

Machine learning

The ability of a program to learn from experience, that is, to modify its execution on the basis of newly acquired information. A major focus of machine-learning research is to automatically produce models (rules and patterns) from data.

Bayesian model selection

A statistical approach for selecting models by incorporating both prior distributions for parameters of the models and the observed experimental data.

Maximum likelihood

A statistical approach that is used to make inferences about the combination of parameter values that gives the greatest probability of obtaining the observed data.

Saturated

A term for a statistical model that is as full as possible (saturated) with parameters. Such a model is sometimes useful as it serves as a benchmark to quantify how well a simpler model (one with fewer parameters) fits the data.

Penetrance

The probability of displaying a particular phenotype (for example, succumbing to a disease) given that one has a specific genotype.

Marginal effects

The average effects (for example, penetrances) of a single variable, averaged over the possible values taken by other variables. These could be calculated for one locus of a two-locus system as the average of the two-locus penetrances, averaged over the three possible genotypes at the other locus.

Logistic regression model

A statistical model that is used when the outcome is binary. It relates the log odds of the probability of an event to a linear combination of the predictor variables.

Multinomial regression

A statistical approach, similar to logistic regression, which is used when the outcome takes one of several possible categorical values.

Confounding

A phenomenon whereby the measure of association between two variables is distorted because other variables, associated with both variables of interest, are not controlled for in the calculation.

Empirical Bayes procedure

A hierarchical model in which the hyperparameter is not a random variable but is estimated by another (often classical) method.

Information theory

A branch of applied mathematics involving the quantification of information.

Entropy

A key measure used in information theory that quantifies the uncertainty associated with a random variable. For example, a variable indicating the outcome from a toss of a coin will have less entropy than a variable indicating the outcome from a roll of a die (two versus six equally likely outcomes).

Permutation

This method is often used in hypothesis testing. An empirical distribution of a test statistic is obtained by permuting the original sample many times and recalculating the value of the test statistic in each permuted data set. Each permuted sample is considered to be a sample of the population under the null hypothesis.

Multiple testing

An analysis in which multiple independent hypotheses are tested. If a large number of tests are performed, the significance level (p value) of any particular test must be interpreted in light of this fact, as the overall combined probability of making a type I error will increase.

Bonferroni correction

The simplest correction of individual p values for multiple hypothesis testing can be calculated using pcorrected = 1 – (1 – puncorrected)n, in which n is the number of hypotheses tested. This formula assumes that the hypotheses are all independent, and simplifies to pcorrected = npuncorrected when npuncorrected <<1.

Q–Q plot

A quantile–quantile plot is a diagnostic plot that can be used to compare the distribution of observed test statistics with the distribution expected under the null hypothesis. Those tests that lie significantly above the line of equality between observed and expected quantiles are considered significant in the context of the number of tests performed.

High-dimensional data

Data that contain information on a large number of variables, albeit possibly measured in a small number of subjects or replicates.

Cross-validation

This approach involves partitioning a data set into smaller subsamples, performing an analysis in one subsample and using the other subsample to measure or validate how well the analysis has performed. To reduce variability, multiple rounds of cross-validation are often performed using different partitions of the data and the validation results are averaged over the rounds.

Overfitting

The phenomenon in which a complex model might provide a good fit to the current data set but is overfitted to the random quirks present in that particular data set and therefore cannot be generalized to future data sets in the way that a simpler model might be.

Bootstrap samples

These are data sets obtained by taking a random sample of the original data, usually with replacement. One then applies the same analysis as was applied to the real data. This is repeated many times, allowing one to assess the variability in results incurred owing to random sampling.

Frequentist

A statistical approach for testing hypotheses by assessing the strength of evidence for the hypothesis provided by the data.

Burn-in period

In Markov chain Monte Carlo analysis, a period at the start of the computation in which the values taken by the parameters are ignored when constructing the posterior distribution.

Compositional epistasis

The blocking of one allelic effect by an allele at another locus.

Statistical epistasis

The average effect of substitution of alleles at combinations of loci, with respect to the average genetic background of the population.

Functional epistasis

The molecular interactions that proteins and other genetic elements have with one another.

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Cordell, H. Detecting gene–gene interactions that underlie human diseases. Nat Rev Genet 10, 392–404 (2009). https://doi.org/10.1038/nrg2579

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