Improved branch and bound algorithm for detecting SNP-SNP interactions in breast cancer

M E T H O D O L O G Y

Open Access

Improved branch and bound algorithm for

detecting SNP-SNP interactions in breast cancer

Li-Yeh Chuang

, Hsueh-Wei Chang

, Ming-Cheng Lin

and Cheng-Hong Yang

Abstract

Background: Single nucleotide polymorphisms (SNPs) in genes derived from distinct pathways are associated with a breast cancer risk. Identifying possible SNP-SNP interactions in genome-wide case–control studies is an important task when investigating genetic factors that influence common complex traits; the effects of SNP-SNP interaction need to be characterized. Furthermore, observations of the complex interplay (interactions) between SNPs for high-dimensional combinations are still computationally and methodologically challenging. An improved branch and bound algorithm with feature selection (IBBFS) is introduced to identify SNP combinations with a maximal difference of allele frequencies between the case and control groups in breast cancer, i.e., the high/low risk combinations of SNPs.

Results: A total of 220 real case and 334 real control breast cancer data are used to test IBBFS and identify significant SNP combinations. We used the odds ratio (OR) as a quantitative measure to estimate the associated cancer risk of multiple SNP combinations to identify the complex biological relationships underlying the

progression of breast cancer, i.e., the most likely SNP combinations. Experimental results show the estimated odds ratio of the best SNP combination with genotypes is significantly smaller than 1 (between 0.165 and 0.657) for specific SNP combinations of the tested SNPs in the low risk groups. In the high risk groups, predicted SNP combinations with genotypes are significantly greater than 1 (between 2.384 and 6.167) for specific SNP combinations of the tested SNPs.

Conclusions: This study proposes an effective high-speed method to analyze SNP-SNP interactions in breast cancer association studies. A number of important SNPs are found to be significant for the high/low risk group. They can thus be considered a potential predictor for breast cancer association.

Background

At present, identifying SNP-SNP interactions in genome-wide case–control studies is computationally and methodo-logically challenging [1]. To better understand the complex disease characteristics in case–control studies, we extended previous research of a breast cancer study and simul-taneously explored single nucleotide polymorphism (SNP) combinations in low and high risk groups [2]. In complex diseases and cancers, joint genetic effects (epistasis) across the whole genome need to be considered. In a recent study, Phillips identifies three types of epistasis: compositional epistasis, statistical epistasis and functional epistasis [3]. Compositional epistasis blocks the effect of one allele by

another at a different locus, statistical epistasis constitutes a statistical deviation from the additive effects of two loci on the phenotype, and functional epistasis addresses molecular interactions [3,4].

Many methods have been developed to detect epistasis on the basis of a statistical definition to explore gene-gene interactions or SNP-SNP interactions (epistasis) in complex diseases; these include logic regression [5,6], Multifactor-Dimensionality Reduction (MDR) [7], Poly-morphism Interaction Analysis (PIA) [8], Bayesian model selection [9], SNPruler [10], random jungle [11], genetic algorithms [12] and other methods [13-16]. The challenges posed by traditional parametric statistical methods (e.g., logistic regression models) have been detailed in Hahn [6]. The MDR method is inspired by the combinatorial partitioning method, in which a data-reduction method effectively reduces the genotype

* Correspondence:chyang@cc.kuas.edu.tw

5

Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 80778, Taiwan Full list of author information is available at the end of the article

JOURNAL OF

CLINICAL BIOINFORMATICS

© 2013 Chuang et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Chuanget al. Journal of Clinical Bioinformatics 2013, 3:4 http://www.jclinbioinformatics.com/content/3/1/4

predictors from n dimensions to one dimension. However, the computational load can be excessive when dealing with more than 10 polymorphisms [17]. PIA uses a case-based exclusion for missing SNP data, i.e., only those subjects for which all SNPs are identified (in a particular combination) are used in the analysis. SNPruler is a statis-tical method for identifying SNP combinations; it uses the Chi-square test to design the bound in the original Branch and Bound algorithm. Unlike our study, which focuses on the difference between cases and controls, SNPruler fo-cuses on the ratio between cases and controls. Although these methods are widely used, they can still be improved upon. As a test data set increases in size, the run time increases exponentially with the order of interaction. However, few studies address SNP-SNP interactions for multiple SNPs. Hence, when a data set is sufficiently large, selecting an appropriate method becomes important.

This study proposes a method based on statistical epistasis and an improved branch and bound algorithm combined with feature selection (IBBFS) to explore combinations of SNP-SNP interactions in a breast can-cer association study. The proposed method can reduce the search time and accurately determine the difference between cases and controls in low and high risk groups. Finally, we use the odds ratio (OR) as a quantitative measure to assess combinations of SNPs in the case– control studies. The odds ratio is a commonly-used

statistic that expresses the strength of association be-tween exposure and disease [18-20]. Experimental results show that the IBBFS method can determine risk factors in breast cancers.

Results

Identification of best SNP-SNP interaction combinations with maximal difference between cases and controls

The IBBFS method was used to find the best combin-ation of SNPs in the high and low risk groups, with the best combinations of two-SNP interaction results shown in Table 1. We sorted the combinations of the two-SNP results and selected the top three maximum difference combinations in the low and high risk groups. In Table 1, the six specific SNP combinations with their corresponding genotypes (i.e., the SNPs (4, 7) with genotype (2–3) [CXCL12 (rs1801157)-AG]-[KITLG (rs10506957)-CC]) showed a maximal difference value of 7 between the 4 samples in the control data and the 11 samples in the high risk case data groups. The SNPs (3, 4) with genotype (1–1), [CXCR4 (rs2228014)-CC]-[CXCL12 (rs1801157)-GG], showed a maximal difference value of 68 between the 137 samples in the control data and the 69 samples in low risk case data groups. SNPs (4, 7) with genotype (2–3) and SNPs (3, 4) with genotype (1–1) are statistically significant because their p-value is smaller than 0.05. We then extended the best results of the

two-Table 1 Estimated best combinations of two SNPs on the occurrence of breast cancer

Combined SNP number (specific SNPs)

SNP Genotypes Control number / Case number CC SN SP Average Odds Ratio (95%CI) p-value

High-risk Two SNPs Other 330/209

SNPs (4, 7) 2-3 4/11 0.616 0.050 0.988 0.551 4.342 (1.259-16.394) 0.013 (Diff. = 7) Two SNPs Other 327/209 SNPs (4, 6) 3-2 7/11 0.610 0.050 0.979 0.546 2.459 (0.867-7.143) 0.084 (Diff. = 4) Two SNPs Other 289/172 SNPs (3, 5) 2-1 45/48 0.608 0.218 0.865 0.564 1.792 (1.118-2.875) 0.014 (Diff. = 3)

Low-risk Two SNPs Other 197/151

SNPs (3, 4) 1-1 137/69 0.480 0.314 0.589 0.461 0.657 (0.452-0.955) 0.025 (Diff. = 68) Two SNPs Other 226/174 SNPs (3, 7) 1-2 108/46 0.491 0.209 0.676 0.459 0.553 (0.364-0.839) 0.004 (Diff. = 62) Two SNPs Other 223/168 SNPs (1, 3) 2-1 111/52 0.496 0.236 0.668 0.467 0.622 (0.415-0.931) 0.017 (Diff. = 59) NOTE

-Other: The reference group, indicating the union of all other possible two to seven SNP combinations; N.E: Not estimable; CC: Correct; SN: Sensitivity; SP: Specificity.

Chuanget al. Journal of Clinical Bioinformatics 2013, 3:4 Page 2 of 10

SNP combinations to three SNPs. In this way all combinations are extended until the maximum number of SNPs was reached.

Finally, we used IBBFS to find the best-performing combinations of three or more SNPs, with results shown in Tables 2 and 3. Table 2 shows the maximum difference combinations (two to seven SNPs) for the high risk category. These respective combinations are SNPs (4, 7) with genotypes (2–3) and an OR of 4.342, SNPs (3, 5, 6) with genotypes (2-1-1) and an OR of 2.384, SNPs (3, 4, 5, 6) with genotypes (2-1-1-1) and an OR of 3.024, and SNPs (1, 3, 4, 5, 6) with genotypes (1-2-1-1-1) and an OR of 3.133. These two-to-five SNP combinations are statistically significant with a p-value smaller than 0.05. However, for combinations of six SNPs and combinations of seven SNPs, the p-value is greater than 0.05. In Table 3, the results for SNPs (3, 4) with genotypes (1–1), SNPs (1, 3, 5) with genotypes (2-1-1), SNPs (1, 2, 3, 4) with genotypes (2-2-1-1), and SNPs (1, 2, 3, 4, 5) with genotypes (2-2-1-1-1) all have a p-value smaller than 0.05. For all other combinations of SNPs the p-value was greater than 0.05. These experi-mental results prove that the proposed IBBFS method can handle combinations of multiple SNPs and deter-mine the best combination of two to seven SNPs, both the in low and high risk categories.

Analysis of combinations of SNP (4, 7) and combinations of SNP (3, 4) in breast cancer

First, we analyzed the high risk combination of SNP (4, 7) in breast cancer. Information related to the SNP (4, 7) com-bination and the OR results are shown in Table 4, while Figure 1 displays a bar graph illustrating the OR value. Two SNPs are shown in a 3 × 3 table that represents nine state combinations. IBBFS shows that SNP (4, 7) with genotype (2–3) with a maximal OR value of 4.342 (p-value < 0.05) has a maximal difference of 7 between the case and control groups. We observe that, for other combinations of SNP (4, 7) with genotype (1–2), the OR value is at a minimum and the p-values are statistically significant (p-value < 0.05). Hence, only two combinations of SNP (4, 7) in the 3 × 3 table are statistically significant (p-value < 0.05).

Secondly, we analyzed the low risk combinations of SNP (3, 4), with the related information and OR results shown in Table 5. The bar graphs in Figure 2 illustrate the OR value. When the combination of SNP (3, 4) with genotype (1–1) is chosen, the minimum OR value is 0.657 (p-value < 0.05). Here, the maximum difference also is SNP (3, 4) with genotype (1–1), with a difference of 68 between cases and controls. When considering combinations of more SNPs, the frequently occurring combinations of two SNPs in the following combinations are important.

Table 2 Estimated best combinations of SNPs on the occurrence of breast cancer in the high risk group

Combined SNP number (specific SNPs) SNP Genotypes Control number / Case number

CC SN SP Average Odds Ratio (CI) p-value

Two SNPs Other 330/209 SNPs (4, 7) 2-3 4/11 0.615 0.050 0.988 0.551 4.342 (1.259-16.934) 0.013 (Diff. = 7) Three SNPs Other 314/191 SNPs (3, 5, 6) 2-1-1 20/29 0.619 0.132 0.940 0.564 2.384 (1.263-4.518) 0.005 (Diff. = 9) Four SNPs Other 325/203 SNPs (3, 4, 5, 6) 2-1-1-1 9/17 0.617 0.077 0.973 0.556 3.024 (1.246-7.491) 0.008 (Diff. = 8) Five SNPs Other 329/210 SNPs (1, 3, 4, 5, 6) 1-2-1-1-1 5/10 0.612 0.045 0.985 0.547 3.133 (0.969-10.680) 0.031 (Diff. = 5) Six SNPs Other 332/214 SNPs (1, 2, 3, 5, 6, 7) 1-2-2-1-1-2 0/4 0.610 0.018 1.000 N.E (Diff. = 4) Seven SNPs Other 333/216 SNPs (1, 2, 3, 4, 5, 6, 7) 2-2-2-1-1-1-1 1/4 0.608 0.014 0.997 0.540 6.167 (0.648-145.871) 0.084 (Diff. = 3) NOTE

-Other: The reference group, indicating the union of all other possible two to seven SNP combinations; N.E: Not estimable; CC: Correct; SN: Sensitivity; SP: Specificity.

Chuanget al. Journal of Clinical Bioinformatics 2013, 3:4 Page 3 of 10

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doi:10.1186/2043-9113-3-4

Cite this article as: Chuang et al.: Improved branch and bound algorithm for detecting SNP-SNP interactions in breast cancer. Journal of Clinical Bioinformatics 2013 3:4.

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