In association studies, the combined effects of single nucleotide polymorphism (SNP)-SNP interactions and the problem of imbalanced data between cases and controls are frequently ignored. In the present study, we used an improved multifactor dimensionality reduction (MDR) approach namely MDR-ER to detect the high order SNP-SNP interaction in an imbalanced breast cancer data set containing seven SNPs of chemokine CXCL12/CXCR4 pathway genes. Most individual SNPs were not significantly associated with breast cancer. After MDR-ER analysis, six significant SNP-SNP interaction models with seven genes (highest cross-validation consistency, 10; classification error rates, 41.3–21.0; and prediction error rates, 47.4–55.3) were identified. CD4 and VEGFA genes were associated in a 2-loci interaction model (classification error rate, 41.3; prediction error rate, 47.5; odds ratio (OR), 2.069; 95% bootstrap CI, 1.40–2.90; P=1.71E-04) and it also appeared in all the best 2-7-loci models. When the loci number increased, the classification error rates and P-values decreased. The powers in 2-7-loci in all models were >0.9. The minimum classification error rate of the MDR-ER-generated model was shown with the 7-loci interaction model (classification error rate, 21.0; OR=15.282; 95% bootstrap CI, 9.54–23.87; P=4.03E-31). In the epistasis network analysis, the overall effect with breast cancer susceptibility was identified and the SNP order of impact on breast cancer was identified as follows: CD4 = VEGFA > KITLG > CXCL12 > CCR7 = MMP2 > CXCR4. In conclusion, the MDR-ER can effectively and correctly identify the best SNP-SNP interaction models in an imbalanced data set for breast cancer cases.
breast cancersingle nucleotide polymorphismgene-gene interactionsimbalanced data setmultifactor dimensionality reductionIntroduction
Breast cancer is the most commonly occurring malignant disease in women. The effective identification and screening of biomarkers for breast cancer prediction may reduce the occurrence of breast cancer (1). Single nucleotide polymorphisms (SNPs), the most abundant variants of the human genome (2), have become significant biomarkers for personalized medicine and the recognition of disease/cancer susceptibility (3–5).
Chemokines play a vital role in carcinogenesis (6,7). The representative chemokines are the chemokine ligand CXCL12 also known as stromal cell-derived factor-1 (SDF-1) and its receptor CXC chemokine receptor 4 (CXCR4) which are two main cross-talking factors in tumor microenvironments such as breast carcinogenesis (8). Moreover, the evidence of possible crosstalk between CXCL12, vascular endothelial growth factor (VEGF) (9), matrix metalloproteinase 2 (MMP2) (10), soluble KIT ligands (KITLG) (11), CXCR4, T-cell antigen T4/LEU3 (CD4) (12), and CC-chemokine receptor 7 (CCR7) (13) are supported by the prediction of protein-protein interaction software (STRING 9) (14) and previously discussed (15). Therefore, the relationship between SNPs for these CXCL12/CXCR4-related genes warrants investigation.
Although many disease/cancer-associated SNPs have been reported, the impact of more rare or non-significant SNPs is underestimated and this may partly contribute to 'missing heritability' (16). Lack of a detailed inspection of gene-gene (SNP-SNP) interactions is one of the most common reasons of 'missing heritability' effects (17). For example, several SNPs were reported to be unassociated with diseases and cancers without considering the SNP-SNP interaction (18–20). Recently, the analyses of gene-gene interactions in association studies have been developed in terms of SNP-SNP interactions (21–30). Alternatively, a multifactor dimensionality reduction (MDR) is a data mining technique to provide a non-linear model associated with disease (31). It introduces a strategy with data reduction to identify both high- and low-disease risk associated multiple SNP genotype combinations for SNP-SNP interactions. Biologically meaningful results can be detected without a big sample population because MDR uses a k-fold cross-validation (CV). The CV can be regarded as a replication data set technique. The advantage of CV over the repeated random sub-sampling is that all samples are used for training and each sample is used only once for validation. Moreover, MDR has been successfully applied to identify SNP-SNP interactions in various diseases, e.g., atrial fibrillation (32) and coronary artery disease (33). However, MDR cannot quantitatively evaluate the disease susceptibility of genotype combinations (34). Recently, improved MDR methods such as MDR-ER (35) and weighted risk score-based MDR (34) were developed to solve this problem. Moreover, MDR-ER introduces two functions to improve the classification step and an evaluation of error rate in MDR, and it can be applied to the data set of imbalanced numbers of cases and controls.
In our previous investigation (15), we focused on the determination of SNP genotypes of seven SNPs of CXCL12-related genes in terms of PCR-restriction fragment length polymorphism (RFLP) analysis for cases and controls. The SNP barcode method was used to investigate the association of potentially combined SNP genotypes of CXCL12-related genes. A significant number of genotype combinations of the selected SNPs were reported to be protective against breast cancer and a low risk population of breast cancer patients with these specific combinations was identified. However, their possible SNP-SNP interactions were less investigated (15). This would be important especially for the understanding of a multifactorial interaction in the risk assessment of breast cancer.
In this study, we used the MDR-ER strategy to identify the best breast cancer-associated model for seven SNPs in SNP-SNP interaction of CXCL12/CXCR4-related genes, including CXCL12 (rs1801157, G801A), CXCR4 (rs2228014, I142I), VEGF (rs3025039, C936T, 3′-untranslated region), KITLG (rs10506957, intron 1), MMP2 (rs2287074), CD4 (rs12812942, intron 3), and CCR7 (rs3136685, intron 1) which have been reported in several non-MDR disease association studies (15,36–38). The results show that MDR-ER may effectively identify the significant SNP-SNP interaction models of breast cancer susceptibility for imbalanced data sets.
Materials and methodsMDR
MDR is a model-free and non-parametric method for the detection of complex disease/cancer-associated gene-gene (SNP-SNP) interactions (31). The principle of MDR is accomplished by classification to reduce more attributes (loci) into a single attribute (locus). Thus, high-order SNP-SNP interactions can be detected statistically where the data space is transformed into a two-way contingency table.
The MDR procedure is illustrated in Fig. 1. N SNPs are considered in a case-control data set, and M is the maximum order of SNP-SNP interactions we want to explore, i.e., M≤N. Let m be the number of order SNP-SNP interactions (m≤M). The procedures to perform the MDR for detecting the best m-way SNP-SNP interaction model are explained in two parts as follows:
1. Run k-fold (usually k=10) cross-validation (CV) to detect the best m-way interaction (SNP-SNP interaction) model. For each CV fold, steps 1–7 are repeated successively:
Step 1. Select a ith part data set for the test data set and the remaining as the training data set.
Step 2. The pool of all SNPs consists of a set of m SNPs.
Step 3. m SNPs and their possible multifactor cells are presented in m-dimensional space (label 3, Fig. 1):
Equation 1 shows the possible multifactor cells in the m-dimensional space:
L={l1,l2,l3,…,lm}The value of m is dependent on the number of considerable factors. Subsequently, a set of m genetic and/or environmental factors is chosen.
Step 4. Each multifactor cell is labelled as high-risk when the case/control ratio is higher than or equal to the threshold T (T=1), otherwise the cell is labelled as a low-risk.
The total number of cases and controls are respectively counted in the multifactor cell, and the case/control ratio is calculated by Equation 2.
where
where P is the case data set; N, the control data set; P*, the number of case groups in a training set; N*, the number of control groups in a training set; L, a vector of variable combinations. The function u() determines a score of '1' if all elements l in L match the cases or controls; otherwise given a score of '0'.
The high/low risk in each multifactor cell is determined. Each multifactor cell is labelled as 'H' or 'L' symbol. Label 'H' indicates that ratio in the multifactor cell meets or exceeds a threshold (high-risk group); otherwise, the label is 'L' (low-risk group). The threshold is equal to the one in a balanced data set.
Step 5. Repeat steps 2–5 until all possible sets of m SNPs are evaluated.
Step 6. Evaluate all possible combinations of m SNPs, build
(Nm) contingency tables, and correspondingly get
(Nm) training error rates. The model with the minimum training error rate (classification error rate) is selected in each CV, and the prediction error rate of the model is evaluated using the independent test data set.
Step 4 reduces the possible combinations in n-loci into a two-way contingency table [true positive (TP), false positive (FP), true negative (TN), and false negative (FN)]. TP is the total number of labeled 'H' in the case data. FP is the total number of labeled 'H' in the control data. FN is the total number of labeled 'L' in the case data. TN is the total number of labeled 'L' in the control data. Thus, statistical analysis can be used to evaluate the n-loci effect. Equation 3 is used to evaluate model classification error rate and prediction error rate.
where C is the possible combination of m SNPs.
Step 7. Repeat steps 1–7 until k=10.
Collect CV to create cross-validation consistency (CVC) and select the highest frequency with CVC as the best SNP-SNP interaction models. The classification error rate of the best model is calculated as the averaged classification error rates in those CVC included k models, and the prediction error rate is calculated as the averaged prediction error rates in those CVC included k models.
After classification error rate evaluates all the possible SNP-SNP interaction models, the model with minimum error rate is regarded as the best SNP-SNP interaction model of training data at ith-fold CV. This best SNP-SNP interaction model is then evaluated by testing the data for evaluating the prediction error rate. Thus, the aforementioned steps 1–7 are repeated in each fold CV. The best SNP-SNP interaction model with a minimum classification error rate is chosen at each CV, and the ten best SNP-SNP interaction models of ten-fold CV are classified by the same model. The number of best models in a classified group are counted and named CVC. Finally, a nSNP-SNP interaction model of CVC with highest occurrence frequency results is regarded as the best model. If the equal frequency of CVC occurs in two or more models, then the model found first is the best SNP-SNP interaction model. The classification error rate of the final selected best model is calculated from averaged k classification error rates of models included in highest frequency with CVC.
Improved MDR for an imbalanced data set (MDR-ER)
MDR-ER was proposed previously (35). MDR-ER introduced the percentage concept to improve Equations 2 and 3 for imbalanced data. Equation 2 of MDR is modified as Equation 4 which evaluates the ratio of the percentages of cases and controls.
where
where P is the case data set; N, the control data set; P*, the number of case groups in a training set; N*, the number of control groups in a training set; L, a vector of variable combinations.
The function u() determines a score of '1' if all elements l in L match the cases or controls; otherwise it is given a score of '0'. As in the classification of MDR, label 'H' is the ratio in the multifactor cell meeting or exceeding a threshold (=1); otherwise the label is 'L'.
MDR-ER modifies the classification/prediction error rate function of MDR (Equation 3). Equation 5 is the adjusted classification/prediction error rate function based on the arithmetic mean of sensitivity and specificity. The adjusted classification/prediction error rate is algebraically identical to the error rate if the case and the control data sets are imbalanced.
where TP is the total number of labeled 'H' in the case data; FP, the total number of labeled 'H' in the control data; FN, the total number of labeled 'L' in the case data; TN, the total number of labeled 'L' in the control data.
Statistical analyses
Statistical analyses were evaluated by the two-way contingency table and its TP, FP, TN, and FN values were respective averages of TP, FP, TN, and FN in that CVC included the best SNP-SNP interaction models in the training models. The disease risks of SNPs were evaluated by SPSS version 19.0 (SPSS, Inc., Chicago, IL, USA), including the odds ratio (OR) or the bootstrap OR and its 95% confidence interval (CI). P-values were used to define significant differences between the cases and the controls. The Power and Sample Size Calculations (PS) tool (39) was used to evaluate the power with statistical analysis. The Power can determine the null hypothesis (OR=1) with Type I error probability α (=0.05), i.e., the probability of rejecting the OR=1.
ResultsData set
A breast cancer data set containing breast cancer patients (n=220) and normal controls (n=334) was obtained from our previous study (15). The genotype information is available at http://bioinfo.kmu.edu.tw/brca-7SNP_all_BPSO.xls. Seven SNPs of CXCL12-related genes were included, such as CD4 (rs12812942), CCR7 (rs3136685), CXCR4 (rs2228014), CXCL12 (rs1801157), VEGFA (rs3025039), MMP2 (rs2287074), and KITLG (rs10506957). However, the data mining strategy-based SNP-SNP interaction was not addressed. In the present study, we applied the MDR-ER to detect the best SNP-SNP interaction model with a significant difference between breast cancer (cases) and normal (controls) groups.
Single SNP analysis
Table I shows the OR, bootstrap OR and its 95% CI of each single SNP in the breast cancer association. The distribution of genotypes for most SNPs showed no significant difference between the case and the control groups.
SNP-SNP interaction analysis - the determination of the best model in CVC
Although many 2-loci models exist, only the significant 2-loci SNP-SNP interaction models are provided in Table II. The best model in CVC was defined by the model which has the minimum classification error rate. Among 2-loci SNP-SNP interaction models, the minimum classification error of the best 2-loci model (CD4 + VEGFA) in CVC is 0.413. Fig. 2 shows the details of the 2-loci interaction (CD4 + VEGFA) based on a MDR-ER method in a breast cancer study. The percentages of genotypes for the CD4 and the VEGFA genes in the cases and the controls are shown (Fig. 2A). Cells with a SNP combination of higher risk of breast cancer are marked with a gray background, i.e., the percentages of the cases were higher than those of the controls. Fig. 2B provides the ratios of each 2-loci SNP-SNP interaction. SNP combinations of breast cancer risk (OR>1) are identified (marked in gray colors). Fig. 2C shows that genotype effects (CC, CT, and TT) of the VEGFA gene were not additive to the genotypes (AA, AT, and TT) of the CD4 gene - it indicates an interaction between these two genes. Similarly, all the best models in CVC in terms of 3-7-loci SNP-SNP interaction models were selected (see details in Table III). In the 4-loci SNP-SNP interaction, the interactions (CD4 + CCR7 + VEGFA + KITLG), (CD4 + VEGFA + MMP2 + KITLG), and (CD4 + CXCL12 + VEGFA + KITLG) had an equal frequency in CVC, indicating that they have the same importance in breast cancer. Table III shows the first identified model, i.e., CD4 + CXCL12 + VEGFA + KITLG.
SNP-SNP interaction analysis - error rates
Table III shows the best 2-7-loci SNP-SNP interaction models using MDR-ER analysis. When the loci number was increased, the best SNP-SNP interaction training models showed higher consistency of breast cancer and lower classification error rates (ranging from 41.3 to 21.0). The prediction error rates of the best SNP-SNP interaction training models in 2-7-loci are the region between 47.4 and 55.3. The 7-loci model shows a minimum classification error rate of 21.0% and the 3-loci model shows a minimum prediction error rate of 47.4, which are observed by chance in randomized data based on the null hypothesis of no association. In addition, the frequency differences between the case and the control groups of the best MDR-ER-generated 2-7-loci models were significant (P<0.01). The 2-7-loci models suggest that all SNPs of CD4, CCR7, CXCR4, CXCL12, VEGFA, MMP2, and KITLG genes are associated with breast cancer.
SNP-SNP interaction analysis - OR, P-value, and power analysis
In Table III, the OR values in the 2-7-loci models were increased from 2.069 to 15.282 and the 95% CI was 1.44–24.14. The bootstrapping in 1,000 samples with the adjustments of 95% CI of OR (95% bootstrap CI) values were adjusted from 1.40 to 23.87 for the 2-7-loci models. The P-values of the 2-7-loci models decreased from 1.71E-04 to 4.03E-31. The P-values were decreased and 95% bootstrap CI values were increased when the loci numbers increased, indicating that the risk for breast cancer was increased by a combined effect of SNPs. In the example of the 7-loci SNP-SNP interaction model, the power analysis in the case data set showed that the probability of exposure among controls was 0.231 (77/334, 77 is FP). The powers in the 2-7-loci, ranging from 0.978 to 1.000, showed that occurrence probability in all models was >0.9. These findings suggest that all these seven SNPs are highly associated with breast cancer.
Fig. 3 shows an SNP-SNP interaction network of a 7-loci SNP-SNP interaction model associated with breast cancer susceptibility. The epistasis networks were constructed by integrating 13 significant 2-loci SNP-SNP interaction models (Table II) where the non-significant interactions are not shown. The susceptibility to breast cancer can be explained by showing the details of a two-factor interaction based on the MDR-ER method in the example of CD4 + VEGFA (Fig. 2) as well as other two-factor interactions (data not shown). In Fig. 3, genes (SNPs) involved in one or more significant interactions are represented as nodes, and the pairs of genes (SNPs) with significant interactions are connected by lines. Each line is labeled with the corresponding OR value and the thickness of the lines represent the stronger OR values. Thus, Fig. 3 can clearly illustrate how combined effects are associated with SNP (genes) to generate the overall effect.
Discussion
Many breast cancer studies have reported several breast cancer-associated genes, including CD4 (15), CCR7 (13,15), CXCR4 (15), CXCL12 (36,40), VEGF (41), and MMP2 (10). In the individual SNP analysis (Table I), only the SNP of the VEGFA gene was found to be breast cancer-associated but it was still not significant after Bonferroni's correction. In general, these rare and non-significant SNPs are commonly ignored and we propose that they may partly solve the problem of missing heritability. However, epistasis of rare SNPs is not the only way to address missing heritability of common complex traits. Without the help of computation, rare SNPs could hardly explain missing heritability in asthma (42). To improve the sensitivity of association, these hitherto non-significant SNPs were further combined and the possible combined effects associated with breast cancer were examined in this study. Likewise, some SNPs may have additive SNP-SNP interactions or non-additive effects for genomic monitoring and prediction of complex traits (43).
Based on imbalanced cases and controls, the MDR-ER algorithm explored six multiple SNP loci with significant associations with breast cancer in terms of the 2-7-loci with OR values (Table III). If the true OR of the best model for breast cancer in exposed subjects relative to unexposed subjects is 15.282 (OR value of 7-loci SNP-SNP interaction model), we can reject the null hypothesis that OR=1 with the probability (power) 1.000. The type I error probability associated with the test of this null hypothesis was 0.05. Furthermore, the OR values in the 2-7-loci showed a gradual increase, suggesting that all genes (SNPs) in the 2-7-loci were additive and highly associated with breast cancer.
The key evaluations in MDR-ER represent a classification error rate and prediction error rate which aim to correctly evaluate the proportion of an incorrect prediction. The incorrect prediction error in MDR-ER is a measurement for internal validation that avoids finding an association by chance in the test sample. When the error rate is <50%, the associations by chance are significantly reduced. Thus, in Table III, the 4-, 6- and 7-loci results (prediction error rates >50%) cannot be considered as the predictive models. While the 2-, 3- and 5-loci results showed prediction error rates ~47%, and the 3-loci had the lowest prediction error rate. Therefore, these MDR-ER generated SNP-SNP interaction models are very effective for classification of the disease risk, and suggest that SNP combination of CD4, VEGFA, and KITLG genes provide the best predictive models. Moreover, a SNP combination of CD4 and VEGFA genes is included in all the best 2-7 loci models, suggesting that it is really driving the associations in breast cancer.
For example in Fig. 3, CXCL12 was only significantly associated with CXCR4 and KITLG (OR=1.520 and 1.506, respectively) but it had an overall effect by integrating KITLG with CD4, CCR7, VEGFA, and MMP2. All lines in Fig. 3 were found to connect to KITLG, indicating that all SNPs from all the listed genes were joined together with the SNP of KITLG which is the main connector of this network. The breast cancer associated effect of KITLG has been less mentioned previously, however, the importance of KITLG was detectable using a MDR-ER algorithm-based SNP-SNP interaction.
According to the performance of OR values, the CD4 and VEGFA (2.069) were the best models in the 2-loci and CD4 and KITLG (2.000) were subsequently integrated with this best 2-loci model, where the difference was very small (0.069). They showed a strong interaction in breast cancer, but CD4 and VEGFA were more highly associated with breast cancer than KITLG. Thus, an order of SNPs with breast cancer association can be suggested as follows: CD4 = VEGFA > KITLG > CXCL12 > CCR7 = MMP2 > CXCR4. This combined effect order can detect the overall effect of the impact of a gene (SNP) on breast cancer. Therefore, we suggest that CD4, VEGFA, KITLG, CXCL12, CCR7, MMP2, and CXCR4 genes have an overall effect with breast cancer susceptibility.
In the 2-loci SNP-SNP interaction model, the comparison between MDR and MDR-ER faced with the imbalanced data set are shown in Fig. 4. When using MDR, the large number of the group (either the cases or the controls) of the imbalanced data set can affect the high- or low-risk classification and the evaluation for classification error rate compared to that of MDR-ER. Using MDR analysis in the present study (220 cases and 334 controls), the number of low-risk groups was greater than the high-risk groups in 100 selected models (Fig. 4A). MDR-based classification error rates were 0.37–0.4 and TPs were always higher than TNs (Fig. 4C). However, the averages of sensitivity and specificity in the 100 models were 0.07 and 0.96, respectively. This result suggests that this low classification error rate and high OR value using MDR are generated by its high TN but low TP values implying a low sensitivity for disease detection.
In contrast, MDR-ER showed balanced frequencies between the numbers of high- and low-risk groups in each model (Fig. 4B). Its TN values were not always higher than its TP values and classification error rates were also improved in MDR-ER (Fig. 4D). The averages of sensitivity and specificity in the 100 models using MDR-ER were 0.589–0.511, respectively.
MDR-ER is designed to combine two improved functions to measure the low- and high-risk groups and it evaluates the classification error to select the best model. Thus, MDR-ER allows for gene-gene interaction detection studies on imbalanced data sets without the balanced study population technologies. Moreover, MDR-ER holds the original MDR characteristics, including a non-parametric method and assumes no particular genetic model. Therefore, it can provide strong detecting ability to imbalanced data sets for analyzing the possible gene-gene and gene-environment interactions. When imbalanced data sets are used, MDR-ER has several advantages which are as follows: i) MDR-ER improves the classification function to effectively classify cells into low- and high-risk groups; thus the number of TPs can be increased; ii) the final best model has a low error rate and a high sensitivity for disease prediction; iii) MDR-ER only adjusts and improves two formulas and therefore the number of procedures and parameters are not increased; and iv) MDR-ER is based on the quantitative value of the ratios representing better classifications results.
The MDR and MDR-ER can be limited by the overall running time due to the rapidly growing total number of SNP combinations when the number of SNPs, order, and sample size are increased. Substantial time requirements may limit the multiple tests in finding more complex interactions between genes related to diseases.
In conclusion, we demonstrated that MDR-ER can effectively and correctly identify the best SNP-SNP interaction models in an imbalanced data set. The joint effect of SNP-SNP interactions of chemokine CXCL12/CXCR4 pathway genes in breast cancer susceptibility was also identified. MDR-ER has potential to apply to many other associated studies with imbalanced data sets.
Acknowledgments
This study was supported by funds of the Ministry of Science and Technology, Taiwan (MOST 102-2221-E-151-024-MY3 and MOST 104-2320-B-037-013-MY3), the National Sun Yat-sen University-KMU Joint Research Project (no. NSYSU-KMU 105-p022), and the Health and Welfare Surcharge of Tobacco Products, the Ministry of Health and Welfare, Taiwan, Republic of China (MOHW105-TDU-B-212-134005). We also thank Dr Hans-Uwe Dahms for his help with the English editing.
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MDR flowchart.
The best 2-loci interactions are analyzed by MDR-ER. The SNP-SNP interaction between CD4 and VEGFA genes was used as an example. (A) The joint distribution of the genotypes of the CD4 and VEGFA genes. High- and low-risks are expressed under the grey and white backgrounds, respectively. The left bar (black color) in a cell represents the frequency of counting cases and the right bar (white color) represents the frequency of counting controls. (B) The ratio between the cases and the controls in each cell. The gray and white bars represent the high- and low-risks, respectively. (C) The deviation with pattern of the odds ratio from two-way interaction models. The reference for the odds ratio is the combination of the major genotypes of these two genes.
SNP-SNP interaction network. The epistasis networks of 7-loci models for SNP-SNP interaction were found to be associated with breast cancer. Significant SNP-SNP interactions (P<0.05) in these multi-foci models are connected by lines, and the strength of interaction is labeled with OR values. The thicker and thinner lines represent the higher and lower interactions, respectively.
Comparison difference between MDR and MDR-ER in the imbalanced data set using the 2-loci SNP-SNP interaction. (A and B) The numbers of high- and low-risk groups in the algorithm implementation, respectively. The distribution differences between the numbers of high- and low-risk groups are shown. (C and D) The frequencies of TP and TN, and the classification error rate in algorithm implementation, respectively. The left and right scales of the vertical axis show the log10 value for the total numbers of TP and TN, and the classification error rate, respectively. The top solid line in (C) indicates the adjusted error rate based on Equation 5. The horizontal axis indicates the 100 models of the 2-loci SNP-SNP interaction. All models are sorted by the classification error rate and selected by systematic sampling.
The performance of eight individual SNPs for the case and the control groups.
Locus
Genotypes
Cases (n=220) n (%)
Controls (n=334) n (%)
Odds ratioa
Bootstrap odds ratiob
Bootstrap 95% CIc
CD4 gene rs12812942
AA
128 (58.2)
174 (52.1)
AT
76 (34.5)
141 (42.2)
0.733
0.746
(0.521, 1.064)
TT
16 (7.3)
19 (5.7)
1.145
1.228
(0.540, 2.361)
CCR7 gene rs3136685
GG
77 (35.0)
107 (32.0)
GA
114 (51.8)
180 (53.9)
0.880
0.897
(0.590, 1.293)
AA
29 (13.2)
47 (14.1)
0.857
0.887
(0.474, 1.464)
CXCR4 gene rs2228014
CC
151 (68.6)
254 (76.0)
CT
63 (28.6)
73 (21.9)
1.452
1.451
(0.863, 2.137)
TT
6 (2.7)
7 (2.1)
1.442
1.790
(0.369, 5.641)
CXCL12 gene rs1801157
GG
106 (48.2)
175 (52.4)
GA
98 (44.5)
136 (40.7)
1.190
1.209
(0.818, 1.669)
AA
16 (7.3)
23 (6.9)
1.148
1.198
(0.534, 2.216)
VEGFA gene rs3025039
CC
155 (70.5)
211 (63.2)
CT
59 (26.8)
117 (35.0)
0.686
0.680
(0.438, 0.976)
TT
6 (2.7)
6 (1.8)
1.361
1.626
(0.340, 4.889)
MMP2 gene rs2287074
GG
113 (51.4)
164 (49.1)
GA
93 (42.3)
139 (41.6)
0.971
0.976
(0.677, 1.392)
AA
14 (6.4)
31 (9.3)
0.655
0.676
(0.293, 1.278)
KITLG gene rs10506957
TT
133 (60.5)
182 (54.5)
TC
69 (31.4)
133 (39.8)
0.710
0.721
(0.475, 1.037)
CC
18 (8.2)
19 (5.7)
1.296
1.390
(0.608, 2.645)
Data from our previous results (15).
Bootstrap odds ratio: odds ratio is adjusted by deviation which is calculated by bootstrap results based on 1,000 bootstrap samples.
Bootstrap results are based on 1,000 bootstrap samples.
2-Loci SNP-SNP interactions among seven SNPs assessed by MDR-ERa.
2-Loci
Odds ratio (95% CI)
Bootstrap 95% CI
P-value
Error rate
CD4 + CCR7
1.519 (1.04, 2.23)
(1.04, 2.25)
0.032
0.454
CD4 + CXCR4
1.549 (1.06, 2.26)
(1.07, 2.27)
0.022
0.449
CD4 + VEGFA
2.069 (1.44, 2.98)
(1.40, 2.90)
1.71E-04
0.413
CD4 + KITLG
2.000 (1.28, 3.14)
(1.24, 3.24)
0.002
0.441
CCR7 + VEGFA
1.537 (1.06, 2.24)
(1.06, 2.27)
0.025
0.450
CCR7 + KITLG
1.491 (1.04, 2.14)
(1.04, 2.25)
0.027
0.452
CXCR4 + CXCL12
1.520 (1.05, 2.21)
(1.05, 2.17)
0.005
0.451
CXCR4 + VEGFA
1.714 (1.14, 2.57)
(1.03, 2.54)
0.009
0.448
CXCR4 + KITLG
1.781 (1.19, 2.67)
(1.19, 2.74)
0.005
0.440
CXCL12 + KITLG
1.506 (1.05, 2.17)
(1.04, 2.18)
0.027
0.449
VEGFA + MMP2
1.537 (1.05, 2.24)
(1.07, 2.23)
0.026
0.450
VEGFA + KITLG
1.732 (1.21, 2.49)
(1.19, 2.44)
0.003
0.432
MMP2 + KITLG
1.808 (1.25, 2.62)
(1.28, 2.67)
0.002
0.430
All 2-loci SNP-SNP interactions with significant testing accuracy were identified by the MDR-ER method. The minimum error rate is marked in bold type.
Analysis results of the best 2- to 7-loci SNP-SNP interaction models using MDR-ER.