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Open Access Methodology article

Application of permanents of square matrices for DNA identification in multiple-fatality cases

Maiko Narahara1, Keiji Tamaki2 and Ryo Yamada1*

Author Affiliations

1 Unit of Statistical Genetics, Center for Genomic Medicine, Graduate School of Medicine, Kyoto University, 53 Shogoin Kawahara-cho, Sakyo-Ku, Kyoto, Japan

2 Department of Forensic Medicine and Molecular Pathology, Graduate School of Medicine, Kyoto University, Yoshida-Konoe-Cho, Sakyo-Ku, Kyoto, Japan

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BMC Genetics 2013, 14:72  doi:10.1186/1471-2156-14-72

Published: 21 August 2013

Additional files

Additional file 1:

Distributions of conditional probabilities of permanent method and posterior odds of LR method. Distributions of identical pairs and non-identical pairs are shown in red and blue, respectively. Probabilities obtained with the permanent method are shown as odds. Values are obtained from 20 uniform datasets of family types 2, 3, 5, 6, 7, 8, or 9. Family types are defined in Table 1.

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Additional file 2:

ROC curves of pooled results obtained from 20 datasets for each family type. ROC curves of test results for family types 2, 3, 5, 6, 7, 8, and 9 are shown. Discriminant performance was compared between the permanent method (solid line) and the LR method (dashed line). AUC (95% confidence interval (CI)) and P values of the DeLong test are shown. Family types are defined in Table 1.

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Additional file 3:

Supplementary tables (Table S1 – S6). Table S1. Results of the ROC analysis for each dataset for the uniform-pedigree analysis. Table S2. Counts of family types that were randomly sampled for the mixed-pedigree analysis. Table S3. Results of the ROC analysis for each dataset for the mixed-pedigree analysis. Table S4. Counts of family types in the complete part and additional parts that were randomly sampled for the analysis of the incomplete datasets. Table S5. Results of the ROC analysis for each dataset for the analysis of the incomplete datasets. Table S6. Acceptance numbers corresponding to values of δ and ϵ.

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Additional file 4:

Conditional probabilities obtained with permanent method for assumed exact results and worst-scenario results. Conditional probabilities obtained from worst-effect approximation errors are plotted against those obtained from assumed exact computation of permanent for mixed datasets (shown in a log10 scale).

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