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Natural and orthogonal model for estimating gene–gene interactions applied to cutaneous melanoma

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Abstract

Epistasis, or gene–gene interaction, results from joint effects of genes on a trait; thus, the same alleles of one gene may display different genetic effects in different genetic backgrounds. In this study, we generalized the coding technique of a natural and orthogonal interaction (NOIA) model for association studies along with gene–gene interactions for dichotomous traits and human complex diseases. The NOIA model which has non-correlated estimators for genetic effects is important for estimating influence from multiple loci. We conducted simulations and data analyses to evaluate the performance of the NOIA model. Both simulation and real data analyses revealed that the NOIA statistical model had higher power for detecting main genetic effects and usually had higher power for some interaction effects than the usual model. Although associated genes have been identified for predisposing people to melanoma risk: HERC2 at 15q13.1, MC1R at 16q24.3 and CDKN2A at 9p21.3, no gene–gene interaction study has been fully explored for melanoma. By applying the NOIA statistical model to a genome-wide melanoma dataset, we confirmed the previously identified significantly associated genes and found potential regions at chromosomes 5 and 4 that may interact with the HERC2 and MC1R genes, respectively. Our study not only generalized the orthogonal NOIA model but also provided useful insights for understanding the influence of interactions on melanoma risk.

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Acknowledgments

The preparation of this manuscript was supported by Cancer Prevention and Research Institute of Texas RP100443, National Institutes of Health Grants U19CA148127 and R01CA134682. We also acknowledge the support for Feifei Xiao by National Institutes of Health Grant, R01DA016750, from Dr. Heping Zhang, Yale University School of Public Health.

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Authors and Affiliations

  1. Department of Biostatistics, Yale University School of Public Health, New Haven, CT, USA

    Feifei Xiao

  2. Biostatistics/Epidemiology/Research Design Core, Center for Clinical and Translational Sciences, The University of Texas Health Science Center at Houston, Houston, TX, USA

    Jianzhong Ma

  3. Department of Bioinformatics and Computational Biology, The University of Texas M.D. Anderson Cancer Center, Houston, TX, USA

    Guoshuai Cai

  4. Department of Surgical Oncology, The University of Texas M.D. Anderson Cancer Center, Houston, TX, USA

    Shenying Fang & Jeffrey E. Lee

  5. Department of Epidemiology, The University of Texas M.D. Anderson Cancer Center, Houston, TX, USA

    Qingyi Wei

  6. Department of Community and Family Medicine, Geisel School of Medicine, Dartmouth College, 46 Centerra Parkway, Suite 330, Lebanon, NH, 03766, USA

    Christopher I. Amos

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  1. Feifei Xiao
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  2. Jianzhong Ma
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  3. Guoshuai Cai
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  7. Christopher I. Amos
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Correspondence to Christopher I. Amos.

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F. Xiao and J. Ma contributed equally.

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Supplementary material 1 (DOCX 31 kb)

439_2013_1392_MOESM2_ESM.tif

Figure S1. Density distribution of the estimates of the parameters from a simulated data analysis in Fig. 1, with a quantitative trait influenced by two loci and positive interaction coefficients. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms (TIFF 10 kb)

439_2013_1392_MOESM3_ESM.tif

Figure S2. Density distribution of the estimates of the parameters from a simulated data analysis in Fig. 2, with a quantitative trait influenced by two loci and negative interaction coefficients. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms (TIFF 10 kb)

439_2013_1392_MOESM4_ESM.tif

Figure S3. Density distribution of the estimates of the parameters from a simulated data analysis in Fig. 3, with a quantitative trait influenced by two loci and no interactions. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms (TIFF 10 kb)

439_2013_1392_MOESM5_ESM.tif

Figure S4. Power under different critical values of the \(P\) values obtained using the Wald test for the case–control simulation dataset under scenario 2 when negative interaction effects present. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The upper panel is for the additive effects and dominant effects of locus \(A\) and locus \(B\), respectively. The bottom panel is for the interaction effect between locus \(A\) and locus \(B\). The simulating values of the genetic effects were \({\vec{{E}}}_{\text{F}}^{\text{T}} =[{ - 2.00, 0.50, 0.30, 0.40, 0.37, - 0.15, - 0.08, - 0.10, - 0.04} ]\) Corresponding values of the statistical genetic effects were \({\vec{{E}}}_{\text{S}}^{\text{T}} =[{ - 1.29, 0.46, 0.24, 0.39, 0.29, - 0.23, - 0.10, - 0.12, - 0.04 } ]\) (TIFF 12 kb)

439_2013_1392_MOESM6_ESM.tif

Figure S5. Power under different critical values of the \(P\) values obtained using the Wald test for the case–control simulation dataset under scenario 3 when no interaction effects present. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms. The upper panel is for the additive effects and dominant effects of locus \(A\) and locus \(B\), respectively. The bottom panel is for the interaction effect between locus \(A\) and locus \(B\). The simulating values of the genetic effects were \({\vec{{E}}}_{\text{F}}^{\text{T}} =[{ - 2.0, 0.5, 0.3, 0.4, 0.37, 0.0, 0.0, 0.0, 0.0} ]\). Corresponding values of the statistical genetic effects were \({\vec{{E}}}_{\text{S}}^{\text{T}} =[{ - 1.18, 0.62, 0.30, 0.55, 0.37, 0.0, 0.0, 0.0, 0.0} ]\) (TIFF 12 kb)

439_2013_1392_MOESM7_ESM.tif

Figure S6. Density distribution of the estimates of the parameters from a simulated data analysis in Fig. 4, with a case–control trait influenced by two loci and positive interaction coefficients. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms (TIFF 9 kb)

439_2013_1392_MOESM8_ESM.tif

Figure S7. Density distribution of the estimates of the parameters from a simulated data analysis in Figure S4, with a case–control trait influenced by two loci and negative interaction coefficients. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms (TIFF 10 kb)

439_2013_1392_MOESM9_ESM.tif

Figure S8. Density distribution of the estimates of the parameters from a simulated data analysis in Figure S5, with a case–control trait influenced by two loci and no interactions. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The arrows show the true simulated genetic effect terms (TIFF 9 kb)

439_2013_1392_MOESM10_ESM.tif

Figure S9 Power under different critical values of the \(P\) values obtained using the Wald test for the quantitative simulation data influence by two loci and positive interaction coefficients. The minor allele frequency was 0.49. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The upper panel is for the additive effects and dominant effects of locus \(A\) and locus \(B\), respectively. The bottom panel is for the interaction effect between locus \(A\) and locus \(B\). The simulating values of the genetic effects were \({\vec{{E}}}_{\text{F}}^{\text{T}} =[{100.00, 1.50, 0.40, 1.10, 0.50, 0.80, 0.23, 0.32, 0.12} ]\). Corresponding values of the statistical genetic effects were \({\vec{{E}}}_{\text{S}}^{\text{T}} =[{104.16, 2.46, 0.69, 2.02, 0.88, 0.8, 0.23, 0.32, 0.12} ]\) (TIFF 12 kb)

439_2013_1392_MOESM11_ESM.tif

Figure S10. Power under different critical values of the \(P\) values obtained using the Wald test for the quantitative simulation data influence by two loci with no interaction effects. The minor allele frequency was 0.49. For each graph, Greek symbols and solid lines correspond to the NOIA method, and the broken line corresponds to the functional method. The upper panel is for the additive effects and dominant effects of locus \(A\) and locus \(B\), respectively. The bottom panel is for the interaction effect between locus \(A\) and locus \(B\). The simulating values of the genetic effects were \({\vec{{E}}}_{\text{F}}^{\text{T}} =[{100.00, 1.50, 0.40, 1.10, 0.50, 0.0, 0.0, 0.0, 0.0} ]\). Corresponding values of the statistical genetic effects were \({\vec{{E}}}_{\text{S}}^{\text{T}} =[{103.05, 1.50, 0.40, 1.10, 0.50, 0.0, 0.0, 0.0, 0.0} ]\) (TIFF 12 kb)

439_2013_1392_MOESM12_ESM.tif

Figure S11. Q–Q plot for P values of genotyped SNPs obtained from NOIA statistical model without dominance component testing on additive effect estimation. \(\lambda = 1.011\) (TIFF 108 kb)

439_2013_1392_MOESM13_ESM.tif

Figure S12. Q–Q plot for P values of genotyped SNPs obtained from NOIA statistical model with dominance component detection on additive effect estimation. \(\lambda = 1.014\). SNPs with genotype frequency of minor homozygote less than 0.005 were filtered (TIFF 108 kb)

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Xiao, F., Ma, J., Cai, G. et al. Natural and orthogonal model for estimating gene–gene interactions applied to cutaneous melanoma. Hum Genet 133, 559–574 (2014). https://doi.org/10.1007/s00439-013-1392-2

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