ベキ正規分布に基づくROC曲線の構成
医学分野では,適切に疾病の有無を予測するための臨床検査値の探索が重要な要件の一つである.このとき,有用な統計的方法の一つが受信者動作特性(ROC:Receiver Operating Characteristic)曲線である.そこでは,解釈の簡便さ,あるいはその後の統計的推測の観点から,正規分布に基づくROC曲線が広く用いられている.ただし,このような検査値が正規分布に従う現象は稀である.このとき,検査値の正規性を満たすために,検査値にベキ変換を施し,そのうえで正規分布に基づく方法が適用されている.しかしながら,この変換に基づく方法では,ROC曲線の推定から曲線の解釈までの一貫性を保持できない...
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| Published in | 計算機統計学 Vol. 23; no. 1; pp. 1 - 23 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | Japanese |
| Published |
日本計算機統計学会
2010
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| Online Access | Get full text |
| ISSN | 0914-8930 2189-9789 |
| DOI | 10.20551/jscswabun.23.1_1 |
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| Abstract | 医学分野では,適切に疾病の有無を予測するための臨床検査値の探索が重要な要件の一つである.このとき,有用な統計的方法の一つが受信者動作特性(ROC:Receiver Operating Characteristic)曲線である.そこでは,解釈の簡便さ,あるいはその後の統計的推測の観点から,正規分布に基づくROC曲線が広く用いられている.ただし,このような検査値が正規分布に従う現象は稀である.このとき,検査値の正規性を満たすために,検査値にベキ変換を施し,そのうえで正規分布に基づく方法が適用されている.しかしながら,この変換に基づく方法では,ROC曲線の推定から曲線の解釈までの一貫性を保持できない.本論文では,包括的な接近法として,検査値の潜在基礎分布にベキ正規分布を想定したベキ正規ROC曲線を提案した.そのうえで,疾病の有無を識別する最適カットオフ値を選定した.さらに,ベキ正規ROC曲線の性能を,事例および若干の数値検証により評価した.その結果,ベキ正規ROC曲線は,2群が異なる形状を示す場合にも適合結果が良好であった. |
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| AbstractList | 医学分野では,適切に疾病の有無を予測するための臨床検査値の探索が重要な要件の一つである.このとき,有用な統計的方法の一つが受信者動作特性(ROC:Receiver Operating Characteristic)曲線である.そこでは,解釈の簡便さ,あるいはその後の統計的推測の観点から,正規分布に基づくROC曲線が広く用いられている.ただし,このような検査値が正規分布に従う現象は稀である.このとき,検査値の正規性を満たすために,検査値にベキ変換を施し,そのうえで正規分布に基づく方法が適用されている.しかしながら,この変換に基づく方法では,ROC曲線の推定から曲線の解釈までの一貫性を保持できない.本論文では,包括的な接近法として,検査値の潜在基礎分布にベキ正規分布を想定したベキ正規ROC曲線を提案した.そのうえで,疾病の有無を識別する最適カットオフ値を選定した.さらに,ベキ正規ROC曲線の性能を,事例および若干の数値検証により評価した.その結果,ベキ正規ROC曲線は,2群が異なる形状を示す場合にも適合結果が良好であった. |
| Author | 下川, 敏雄 後藤, 昌司 |
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| References | 8) LUSTED L. B. Logical analysis in Roentgen diagnosis. Radiology. (1960) vol.74, p.178-193. 10) LUSTED L. B. Decision-making studies in patient management. New England Journal of Medicine. (1971) vol.284, p.416-424. 21) ZHOU X. H. Statistical Methods in Diagnostic Medicine. Wiley. (2002 5) GOTO M. Some properties of power-normal distribution. Bulletin of the Biometric Soc.. (1980) vol.1, p.28-54. 28) 後藤, 昌司. ほか. ベキ正規分布のパラメータの推定 : 推定量の漸近挙動について. 計算機統計学. 日本計算機統計学会. (1991) vol.4, no.1, p.45-60. 29) 下川, 敏雄. ほか. データ適応型判別解析とその診断. 計算機統計学. 日本計算機統計学会. (2005) vol.17, no.2, p.87-108. 24) METZ C. E. ROC methodology in radiologic imaging. Invest Radiol. (1986) vol.21, p.720-733. doi:10.1097/00004424-198609000-00009 22) ZOU K. H. Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests. Statistics in Medicine. (1997) vol.16, p.21-43. 11) MOLODIANOVITCH K. Comparing the area under two correlated ROC curve : parametric and non-parametric approaches. Biometrical Journal. (2006) vol.48, no.3, p.745-757. 3) GODDARD M. J. Receiver operating characteristic (ROC) curves and non-normal data : an empirical study. Statistics in Medicine. (1990) vol.9, p.325-337. 16) PATTON D. D. A utility-based model for comparing the cost-effectiveness of diagnostic studies. Invest. Radiol.. (1989) vol.46, p.653-660. 19) WIEAND S. A family of nonparametric statistics for comparing diagnostic markers with paired of unpaired data. Biometrika. (1989) vol.76, p.585-592. 12) OBUCHOWSKI N. A. Sample size determination for diagnostic accuracy studies involving binormal ROC curve indicies. Statistics in Medicine. (1997) vol.16, p.1529-1542. 26) PEPE M. S. A regression modelling framework for receiver operating characteristic curve in medical diagnostic testing. Biometrika. (1997) vol.84, p.595-608. doi:10.1093/biomet/84.3.595 27) PETERSON W. W. The theory of signal detectability. IRE Transactions. (1954) vol.PGIT-4, p.171-212. doi:10.1109/TIT.1954.1057460 23) GOTO M. Power-normal distribution and its applications. Reports of Statistical Research and Application, Japanese Union for Scientist and Engineers. (1983) vol.30, no.3, p.8-28. 4) GOTO M. Some linear models for power transformed data. The 10th International Biometric Conference, August, 6-10, 1979. (1979 6) HUANG Y. A parametric ROC model based approach for evaluating the predictiveness of continuous markers in case-control study. University of Washington. (2007 7) HSIAO J. K. Diagnosing diagnoses : Receiver operating characteristic methods and psychiatry. Arch Gen Psychiantry. (1989) vol.46, p.664-667. 1) BOX G. E. P. An analysis of transformations. J. Roy. Statist. Soc., B. (1964) vol.26, p.211-252. 14) PEPE M. S. An interpretation for the ROC curve and inference using GLM procedures. Biometrics. (2000) vol.56, p.352-359. 25) METS CE. Some practical issues of experimental design and data analysis in radiological ROC studies. Invest Radiol. (1989) vol.24, p.234-245. doi:10.1097/00004424-198903000-00012 30) 濱崎 俊光. ほか. ベキ変換の変換尺度の不変化調整. 計算機統計学. 日本計算機統計学会. (1997) vol.9, no.1, p.37-53. 2) EGAN J. P. Signal Detection Theory and ROC Analysis. Academic Press. (1975 17) SOMOZA E. "Biological markers" andy psychiatric diagnosis : risk-benefit balancing using ROC analysis. Biological Psychiatry.. (1991) vol.29, p.811-826. 9) LUSTED L. B. Introduction to Medical Decision Making. Thomas. (1968 13) PEPE M. S. Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics. (1998) vol.54, p.124-135. 18) WALD A. Statistical Decision Functions. Wiley. (1950 15) PEPE M. S. The statistical Evaluation of Medical Tests for Classification and Prediction. Oxford Press. (2003 20) ZAREMBKA P. Transformation of variables in economics. Frontiers in Econometrics. Academic Press. (1974) p.81-104. |
| References_xml | – reference: 1) BOX G. E. P. An analysis of transformations. J. Roy. Statist. Soc., B. (1964) vol.26, p.211-252. – reference: 9) LUSTED L. B. Introduction to Medical Decision Making. Thomas. (1968) – reference: 17) SOMOZA E. "Biological markers" andy psychiatric diagnosis : risk-benefit balancing using ROC analysis. Biological Psychiatry.. (1991) vol.29, p.811-826. – reference: 18) WALD A. Statistical Decision Functions. Wiley. (1950) – reference: 13) PEPE M. S. Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics. (1998) vol.54, p.124-135. – reference: 22) ZOU K. H. Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests. Statistics in Medicine. (1997) vol.16, p.21-43. – reference: 21) ZHOU X. H. Statistical Methods in Diagnostic Medicine. Wiley. (2002) – reference: 27) PETERSON W. W. The theory of signal detectability. IRE Transactions. (1954) vol.PGIT-4, p.171-212. doi:10.1109/TIT.1954.1057460 – reference: 7) HSIAO J. K. Diagnosing diagnoses : Receiver operating characteristic methods and psychiatry. Arch Gen Psychiantry. (1989) vol.46, p.664-667. – reference: 3) GODDARD M. J. Receiver operating characteristic (ROC) curves and non-normal data : an empirical study. Statistics in Medicine. (1990) vol.9, p.325-337. – reference: 20) ZAREMBKA P. Transformation of variables in economics. Frontiers in Econometrics. Academic Press. (1974) p.81-104. – reference: 12) OBUCHOWSKI N. A. Sample size determination for diagnostic accuracy studies involving binormal ROC curve indicies. Statistics in Medicine. (1997) vol.16, p.1529-1542. – reference: 11) MOLODIANOVITCH K. Comparing the area under two correlated ROC curve : parametric and non-parametric approaches. Biometrical Journal. (2006) vol.48, no.3, p.745-757. – reference: 5) GOTO M. Some properties of power-normal distribution. Bulletin of the Biometric Soc.. (1980) vol.1, p.28-54. – reference: 14) PEPE M. S. An interpretation for the ROC curve and inference using GLM procedures. Biometrics. (2000) vol.56, p.352-359. – reference: 28) 後藤, 昌司. ほか. ベキ正規分布のパラメータの推定 : 推定量の漸近挙動について. 計算機統計学. 日本計算機統計学会. (1991) vol.4, no.1, p.45-60. – reference: 6) HUANG Y. A parametric ROC model based approach for evaluating the predictiveness of continuous markers in case-control study. University of Washington. (2007) – reference: 30) 濱崎 俊光. ほか. ベキ変換の変換尺度の不変化調整. 計算機統計学. 日本計算機統計学会. (1997) vol.9, no.1, p.37-53. – reference: 16) PATTON D. D. A utility-based model for comparing the cost-effectiveness of diagnostic studies. Invest. Radiol.. (1989) vol.46, p.653-660. – reference: 24) METZ C. E. ROC methodology in radiologic imaging. Invest Radiol. (1986) vol.21, p.720-733. doi:10.1097/00004424-198609000-00009 – reference: 29) 下川, 敏雄. ほか. データ適応型判別解析とその診断. 計算機統計学. 日本計算機統計学会. (2005) vol.17, no.2, p.87-108. – reference: 15) PEPE M. S. The statistical Evaluation of Medical Tests for Classification and Prediction. Oxford Press. (2003) – reference: 19) WIEAND S. A family of nonparametric statistics for comparing diagnostic markers with paired of unpaired data. Biometrika. (1989) vol.76, p.585-592. – reference: 8) LUSTED L. B. Logical analysis in Roentgen diagnosis. Radiology. (1960) vol.74, p.178-193. – reference: 23) GOTO M. Power-normal distribution and its applications. Reports of Statistical Research and Application, Japanese Union for Scientist and Engineers. (1983) vol.30, no.3, p.8-28. – reference: 26) PEPE M. S. A regression modelling framework for receiver operating characteristic curve in medical diagnostic testing. Biometrika. (1997) vol.84, p.595-608. doi:10.1093/biomet/84.3.595 – reference: 2) EGAN J. P. Signal Detection Theory and ROC Analysis. Academic Press. (1975) – reference: 25) METS CE. Some practical issues of experimental design and data analysis in radiological ROC studies. Invest Radiol. (1989) vol.24, p.234-245. doi:10.1097/00004424-198903000-00012 – reference: 10) LUSTED L. B. Decision-making studies in patient management. New England Journal of Medicine. (1971) vol.284, p.416-424. – reference: 4) GOTO M. Some linear models for power transformed data. The 10th International Biometric Conference, August, 6-10, 1979. (1979) |
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