Estimated effect (odds ratio and 95% CI) from individual SNPs of 23 steroid hormone metabolisms and signalling-related genes on the occurrence of breast cancer in patients.

a<p>Data collected from literature <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037018#pone.0037018-Pharoah1" target="_blank">[14]</a>.</p>b<p>Data highlighted in bold text are statistically significant results.</p>c<p>All the [Ch/position], i.e., [Chromosome no./Chromosome position], information is based on “Assembly GRCh37”.</p>d<p>The contig information is shown in SNP no. (contig accession no.) as follows: SNP 1–2 (NT_011519.10); SNPs 3 (NT_010194.17); SNPs 4–15 (NT_025741.15); SNPs 16–19 (NT_033899.8); SNPs 20–22 (NT_010718.16); SNPs 23 (NT_167197.1).</p>e<p>Values with <i>p</i> value<0.05 are highlighted in bold fonts.</p

Pseudo-code for randomly generated data.

<p>Pseudo-code for randomly generated data.</p

Boxplots displaying the extremes, the upper and lower quartiles, and the median of the maximum difference between cases and controls for (A) the IPSO algorithm and (B) the PSO algorithm on three to ten combined SNPs over 20 runs.

<p>The boundary of the box closest to zero indicates the 25th percentile, a line within the box marks the median, and the boundary of the box farthest from zero indicates the 75th percentile. Error bars above and below the boxes indicate the 90th and 10th percentiles, respectively. The triangle symbols indicate the 95th and 5th percentiles.</p

The best estimated protective SNP combinations on the occurrence of breast cancer as determined by IPSO.

*<p>The SNP combinations on the occurrence of breast cancer are significantly different (<i>p value</i><0.05). Sen.; Sensitivity; Spe., specificity; PPV, positive predictive value; NPV, negative predictive value. The meanings of the SNP and genotype numbers are provided in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037018#pone-0037018-t003" target="_blank">Table 3</a>. For example, barcode SNPs (4-19)-genotype (1-1) is [rs3020314-CC]-[rs500760-AA]; SNPs (4, 19, 23) with genotype 1-1-2; [rs3020314-CC]-[rs500760-AA]-[rs2017591-TC].</p

Population initialization using conservation of the best 5 results.

<p>Population initialization using conservation of the best 5 results.</p

IPSO pseudo-code.

<p>IPSO pseudo-code.</p

The maximum difference between cases and controls for PSO and IPSO on the best barcodes containing two to ten SNPs.

<p>The maximum difference between cases and controls for PSO and IPSO on the best barcodes containing two to ten SNPs.</p

MDR-ER: Balancing Functions for Adjusting the Ratio in Risk Classes and Classification Errors for Imbalanced Cases and Controls Using Multifactor-Dimensionality Reduction

<div><p>Background</p><p>Determining the complex relationship between diseases, polymorphisms in human genes and environmental factors is challenging. Multifactor dimensionality reduction (MDR) has proven capable of effectively detecting statistical patterns of epistasis. However, MDR has its weakness in accurately assigning multi-locus genotypes to either high-risk and low-risk groups, and does generally not provide accurate error rates when the case and control data sets are imbalanced. Consequently, results for classification error rates and odds ratios (<i>OR</i>) may provide surprising values in that the true positive (TP) value is often small.</p><p>Methodology/Principal Findings</p><p>To address this problem, we introduce a classifier function based on the ratio between the percentage of cases in case data and the percentage of controls in control data to improve MDR (MDR-ER) for multi-locus genotypes to be classified correctly into high-risk and low-risk groups. In this study, a real data set with different ratios of cases to controls (1∶4) was obtained from the mitochondrial D-loop of chronic dialysis patients in order to test MDR-ER. The TP and TN values were collected from all tests to analyze to what degree MDR-ER performed better than MDR.</p><p>Conclusions/Significance</p><p>Results showed that MDR-ER can be successfully used to detect the complex associations in imbalanced data sets.</p></div

Frequency analysis of TP, TN, classification error, and numbers of high-risk and low-risk groups in 2-locus genotypes.

<p>Frequency analysis of TP, TN, classification error, and numbers of high-risk and low-risk groups in 2-locus genotypes.</p

MDR pseudo-code.

<p>MDR pseudo-code.</p