To control false positives in gene-gene interaction analysis: two novel conditional entropy-based approaches

Optimized permutation testing for information theoretic measures of multi-gene interactions

Background

Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large.

Results

In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 10³ for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples.

Conclusions

The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts.

Modified entropy-based procedure detects gene-gene-interactions in unconventional genetic models

BACKGROUND

Since it is assumed that genetic interactions play an important role in understanding the mechanisms of complex diseases, different statistical approaches have been suggested in recent years for this task. One interesting approach is the entropy-based IGENT method by Kwon et al. that promises an efficient detection of main effects and interaction effects simultaneously. However, a modification is required if the aim is to only detect interaction effects.

METHODS

Based on the IGENT method, we present a modification that leads to a conditional mutual information based approach under the condition of linkage equilibrium. The modified estimator is investigated in a comprehensive simulation based on five genetic interaction models and applied to real data from the genome-wide association study by the North American Rheumatoid Arthritis Consortium (NARAC).

RESULTS

The presented modification of IGENT controls the type I error in all simulated constellations. Furthermore, it provides high power for detecting pure interactions specifically on unconventional genetic models both in simulation and real data.

CONCLUSIONS

The proposed method uses the IGENT software, which is free available, simple and fast, and detects pure interactions on unconventional genetic models. Our results demonstrate that this modification is an attractive complement to established analysis methods.

Transferring entropy to the realm of GxG interactions

Genome-wide association studies are moving to genome-wide interaction studies, as the genetic background of many diseases appears to be more complex than previously supposed. Thus, many statistical approaches have been proposed to detect gene-gene (GxG) interactions, among them numerous information theory-based methods, inspired by the concept of entropy. These are suggested as particularly powerful and, because of their nonlinearity, as better able to capture nonlinear relationships between genetic variants and/or variables. However, the introduced entropy-based estimators differ to a surprising extent in their construction and even with respect to the basic definition of interactions. Also, not every entropy-based measure for interaction is accompanied by a proper statistical test. To shed light on this, a systematic review of the literature is presented answering the following questions: (1) How are GxG interactions defined within the framework of information theory? (2) Which entropy-based test statistics are available? (3) Which underlying distribution do the test statistics follow? (4) What are the given strengths and limitations of these test statistics?