Dimensionality reduction approach for many-objective epistasis analysis

In epistasis analysis, single-nucleotide polymorphism-single-nucleotide polymorphism interactions (SSIs) among genes may, alongside other environmental factors, influence the risk of multifactorial diseases. To identify SSI between cases and controls (i.e. binary traits), the score for model quality is affected by different objective functions (i.e. measurements) because of potential disease model preferences and disease complexities. Our previous study proposed a multiobjective approach-based multifactor dimensionality reduction (MOMDR), with the results indicating that two objective functions could enhance SSI identification with weak marginal effects. However, SSI identification using MOMDR remains a challenge because the optimal measure combination of objective functions has yet to be investigated. This study extended MOMDR to the many-objective version (i.e. many-objective MDR, MaODR) by integrating various disease probability measures based on a two-way contingency table to improve the identification of SSI between cases and controls. We introduced an objective function selection approach to determine the optimal measure combination in MaODR among 10 well-known measures. In total, 6 disease models with and 40 disease models without marginal effects were used to evaluate the general algorithms, namely those based on multifactor dimensionality reduction, MOMDR and MaODR. Our results revealed that the MaODR-based three objective function model, correct classification rate, likelihood ratio and normalized mutual information (MaODR-CLN) exhibited the higher 6.47% detection success rates (Accuracy) than MOMDR and higher 17.23% detection success rates than MDR through the application of an objective function selection approach. In a Wellcome Trust Case Control Consortium, MaODR-CLN successfully identified the significant SSIs (P < 0.001) associated with coronary artery disease. We performed a systematic analysis to identify the optimal measure combination in MaODR among 10 objective functions. Our combination detected SSIs-based binary traits with weak marginal effects and thus reduced spurious variables in the score model. MOAI is freely available at https://sites.google.com/view/maodr/home.