Araştırma Makalesi
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ROC Curves in Survival Analysis and an Application

Yıl 2024, , 490 - 503, 23.12.2024

Şeyma Sertkaya Duru Karasoy

https://doi.org/10.19113/sdufenbed.1528404

Öz

The survival data includes survival times and status indicating whether the event occurred. Receiver Operating Characteristic (ROC) curves used in the analysis of survival data determine how well they discriminate between those who experience the event and those who do not, allowing to choose the correct cut-off value. Since time is involved in survival analysis and the status may change, classical ROC curves do not give accurate results. For this reason, new methods have been developed by researching time-dependent ROC curves and ROC curve estimates denoted by ROC(t) have been proposed. Among the ROC curve estimator methods used for survival analysis in this paper, cumulative sensitivity and dynamic specificity (CD), incident sensitivity and dynamic specificity (ID), incident sensitivity and static selectivity (IS) and finally the naive estimator is introduced. To demonstrate the applicability of these estimators, an application was made on real data, cervical cancer. For the data, CD1 and CD2 gave similar results. Additionally, CD5 and CD6 also gave similar results. While ID1 had the lowest classification performance, CD4 showed good classification performance from the 10th month.

Anahtar Kelimeler

ROC nearest neighbor estimator ROC Kaplan-Meier ROC survival Survival analysis Time dependent ROC curves

Kaynakça

  • [1] Kaplan, E. L. and Meier, P. 1958. Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53, 457-481.
  • [2] Heagerty, P. J., Lumley, T, Pepe, M. S. 2000. Time-Dependent ROC Curves for Censored Survival Data and A Diagnostic Marker. Biometrics, 56(2), 337–344.
  • [3] Amico, M., Keilegom, V. I. and Han, B. 2021. Assessing Cure Status Prediction from Survival Data Using Receiver Operating Characteristic Curves. Biometrika, 108(3), 727–740.
  • [4] Pepe, M. S. 2003. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press, USA.
  • [5] Kamarudin, N. K., Cox, T. and Kolamunnage-Dona, R. 2017. Time-Dependent ROC Curve Analysis in Medical Research: Current Methods and Applications. BMC Medical Research Methodology, 17(53), 2-19.
  • [6] Dey, R., Hanley, J.A. and Saha-Chaudhuri, P., 2023. Inference for Covariate-Adjusted Time-Dependent Prognostic Accuracy Measures, Statictic in Medicine, 42, 4082-4110.
  • [7] Ying, A., 2024. Proximal Survival Analysis to Handle Dependent Right Censoring, Journal of the Royal Statistical Society Series B: Statistical Methodology, 00, 1-21.
  • [8] Swets, J. A. and Pickett, R. M. 1982. Evaluation of Diagnostic Systems: Methods from Signal Detection Theory. Academic Press, New York.
  • [9] Hanley, J. A. 1989. Receiver Operating Characteristic (ROC) Methodology: The State of The Art. Critical Reviews in Diagnostic Imaging, 29, 307-335.
  • [10] Begg, C. G. 1991. Advances in Statistical Methodology for Diagnostic Medicine in The 1980's. Statistics in Medicine, 10, 1887-1895.
  • [11] Zweig, M. H. and Campbell, G. 1993. Receiver-Operator Characteristic Plots: A Fundamental Evaluation Tool in Clinical Medicine. Clinical Chemistry, 39(4), 561-577.
  • [12] Pepe, M., Leisenring, W., and Rutter, C. 2000. Evaluating Diagnostic Tests in Public Health. Handbook of Biostatistics, 18, 397-422.
  • [13] Beyene, K.M. and Ghouch, A. E., 2022, Time-Dependent ROC Curve Estimation for Interval-Censored Data, Biometrical Journal, 64, 1056-1074.
  • [14] Zhou, K. H., Hall, W. J., and Shapiro, D. E. 1997. Smooth Nonparametric Receiver Operating Characteristic (ROC) Curves for Continuous Diagnostic Tests. Statistics in Medicine, 16, 2143-2156.
  • [15] Metz, C. E., Herman, B. A., and Shen, J. 1998. Maximum Likelihood Estimation of Receiver Operating Characteristic (ROC) Curves from Continuously Distributed Data. Statistics in Medicine 17, 1033-1053.
  • [16] Touraine, C., Winter, A., Castan, F., Azria, D. and Gourgou, S., 2023. Time-Dependent ROC Curve Analysis for Assessing the Capability of Radiation-Induced CD8 T-Lymphocyte Apoptosis to Predict Late Toxicities after Adjuvant Radiotherapy of Breast Cancer Patients, 15, 4676.
  • [17] Etzioni, R., Pepe, M., Longton, G., Hu, C. and Goodman, G. 1999. Incorporating The Time Dimension in Receiver Operating Characteristic Curves: A Case Study of Prostate Cancer. Medical Decision Making, 19(3), 242–251.
  • [18] Slate, E. H. and Turnbull, B. W. 2000. Statistical Models for Longitudinal Biomarkers of Disease Onset. Statistics in Medicine, 19, 617–637.
  • [19] Heagerty, P. J. and Zheng, Y. 2005. Survival Model Predictive Accuracy and ROC Curves. Biometrics, 61(1), 92–105.
  • [20] Song, X. and Zhou, X. H. 2008. A Semiparametric Approach for The Covariate Specific ROC Curve with Survival Outcome. Statistica Sinica, 18(3), 947-965.
  • [21] Anonim. https://www.researchgate.net/figure/Three-examples-of-ROC-curves-Two-threshold-levels-labeled-A-and-B-are-identified-on_fig2_347797026 (Erişim tarihi: 05.05.2024).
  • [22] Heagerty, P. J. and Zheng, Y. 2004. Semiparametric Estimation of Time-Dependent ROC Curves for Longitudinal Marker Data. Biostatistics, 5(4), 615–632.
  • [23] Gönen, M. and Heller, G. 2005. Concordance Probability and Discriminatory Power in Proportional Hazards Regression. Biometrika, 92, 965–970.
  • [24] Zhang, Y. and Shao, Y. 2018. Concordance Measure and Discriminatory Accuracy in Transformation Cure Models. Biostatistics, 19, 14–26.
  • [25] Beyene, K. M., El Ghouch, A. and Oulhaj, A. 2019. On The Validity of Time-Dependent AUC Estimation in The Presence of A Cure Fraction. Biometrical Journal, 61, 1430–1447.
  • [26] Kim, Y. J. 2022. Review for Time-Dependent ROC Analysis Under Diverse Survival Models. The Korean Journal of Applied Statistics, 35(1), 35–47.
  • [27] Akritas, M. G., 1994. Nearest Neighbor Estimation of a Bivariate Distribution under Random Censoring. The Annals of Statistic, 22(3), 1299–1327.
  • [28] Blanche, P, Dartigues, J. F. and Jacqmin-Gadda, H. 2013. Review and Comparison of ROC Curve Estimators for A Time-Dependent Outcome with Marker-Dependent Censoring. Biometrical Journal, 55(5), 687–704.
  • [29] Chambless, L. E. and Diao, G. 2006. Estimation of Time-Dependent Area Under The ROC Curve for Long-Term Risk Prediction. Statistic in Medicine, 25(20), 3474–3486.
  • [30] Viallon, V. and Latouche, A. 2011. Discrimination Measures for Survival Outcomes: Connection Between The AUC and The Predictiveness Curve. Biometrical Journal, 53(2), 217–236.
  • [31] Uno, H., Cai, T. X., Tian, L. and Wei, L. J. 2007. Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models. Journal of the American Statistical Association, 102(478), 527–537.
  • [32] Hung, H. and Chiang, C. 2010a. Optimal Composite Markers for Time-Dependent Receiver Operating Characteristic Curves with Censored Survival Data. Scandinavian Journal of Statistics, 37, 664–679.
  • [33] Hung, H. and Chiang, C. 2010b. Estimation Methods for Time-Dependent AUC Models with Survival Data. Canadian Journal of Statistics, 38, 8–26.
  • [34] Lambert, J. and Chevret, S. 2014. Summary Measure of Discrimination in Survival Models Based on Cumulative/Dynamic Time-Dependent ROC Curves. Statistical Methods in Medical Research, 25(5), 2088- 2102.
  • [35] Royston, P. and Parmar, M. K. 2011. The Use of Restricted Mean Survival Time to Estimate The Treatment Effect in Randomized Clinical Trials When The Proportional Hazards Assumption is in Doubt. Statistic in Medicine, 30(19), 2409–2421.
  • [36] Cox, D. R. 1972. Regression Models and Life Tables. Journal of the Royal Statistical Society Series B, 34(2), 187–220.
  • [37] Aalen, O. O. 1989. A Linear Regression Model for the Analysis of Life Times. Statistic in Medicine, 8(8), 907–925.
  • [38] Xu, R. and O'Quigley, J. 2000. Proportional Hazards Estimate of The Conditional Survival Function. Journal of the Royal Statistical Society Series B (Statistical Methodology), 62(4), 667–680.
  • [39] Saha-Chaudhuri, P. and Heagerty, P. J. 2013. Nonparametric Estimation of A Time-Dependent Predictive Accuracy Curve. Biostatistics, 14(1), 42–59.
  • [40] Shen, W., Ning, J. and Yuan, Y. 2015. A Direct Method to Evaluate The Time‐Dependent Predictive Accuracy for Biomarkers. Biometrics, 71(2), 439–449.
  • [41] Royston, P. and Altman, D. G. 1994. Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling. Journal of the Royal Statistical Society Series C (Applied Statistics), 43(3), 429-467.
  • [42] Cai, T., Pepe, M. S., Lumley, T., Zheng, Y. and Jenny, N. J. 2006. The Sensitivity and Specificity of Markers for Event Times. Biostatistics, 7(2), 182–197.
  • [43] Heagerty, P. J. and Zheng, Y. 2007. Prospective Accuracy for Longitudinal Markers. Biometrics, 63(2), 332–341.
  • [44] Çiftçi, E. 2023. Çok durumlu modellerde geçiş olasılıklarının tahmini. Hacettepe üniversitesi, Fen Bilimleri Enstitüsü, Doktora Tezi, 164s, Ankara.
  • [45] Sertkaya, Ş. 2024. Yaşam çözümlemesinde alıcı işlem karakteristiği eğrileri. Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 70s, Ankara.
  • [46] Blanche, P. Package ‘timeROC’, https://cran.r-project.org/web/packages/timeROC/timeROC.pdf (Erişim tarihi: 20.05.2024).
  • [47] Heagerty, P. J. and Saha-Chaudhuri P. Package ‘risksetROC’, https://cran.r-project.org/web/packages/risksetROC/risksetROC.pdf (Erişim tarihi: 20.05.2024a).
  • [48] Heagerty, P. J. and Saha-Chaudhuri, P., Package ‘survivalROC’, https://cran.r-project.org/web/packages/survivalROC/survivalROC.pdf (Erişim tarihi: 20.05.2024b).
  • [49] Potapov. S., Adler. W. and Schmid. M., survAUC: Estimators of Prediction Accuracy, https://cran.r-project.org/web/packages/survAUC/survAUC.pdf (Erişim tarihi: 20.05.2024).
  • [50] Scheike, T., Timereg Package, https://cran.r-project.org/web/packages/timereg/timereg.pdf (Erişim tarihi: 20.05.2024).
  • [51] Therneau, T. M. and Lumley, T., Package ‘survival’, https://cran.r-project.org/web/packages/survival/survival.pdf (Erişim tarihi: 20.05.2024).
  • [52] Lu Y., Wang L., Liu P., Yang P. and You M. 2012. Gene-Expression Signature Predicts Postoperative Recurrence in Stage I Non-Small Cell Lung Cancer Patients. PLos One, 7(1).
  • [53] Yue Y., Cui X., Bose S., Audeh W., Zhang X. and Fraass B. 2015. Stratifying Triple-Negative Breast Cancer Prognosis Using 18 F-FDG-PET/CT Imaging. Breast Cancer Res Treat., 153(3):607–16.
  • [54] Yue Y., Astvatsaturyan K., Cui X., Zhang X., Fraass B. and Bose S. 2016. Stratification of Prognosis of Triple-Negative Breast Cancer Patients Using Combinatorial Biomarkers. PLos One. 11(3).
  • [55] Sayın, C.E. and Ünal, İ. 2022. Time-Dependent Receiver Operating Characteristic Analysis and Applications in The Field of Medicine. Black Sea Journal Health Science, 5(3), 411-416.

Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama

Yıl 2024, , 490 - 503, 23.12.2024

Şeyma Sertkaya Duru Karasoy

https://doi.org/10.19113/sdufenbed.1528404

Öz

Yaşam verisi, yaşam sürelerini ve olayın gerçekleşip gerçekleşmediğini gösteren durumu içerir. Yaşam verilerinin analizinde kullanılan alıcı işlem karakteristiği (ROC) eğrileri olayı yaşayanlar ile yaşamayanlar arasında ne kadar iyi ayrım yaptığını belirleyip doğru eşik değerini seçmeyi sağlar. Yaşam çözümlemesinde süre söz konusu olduğu için durum değişebileceğinden klasik ROC eğrileri doğru sonuçlar vermez. Bu nedenle zamana bağlı ROC eğrileri üzerinde araştırmalar yapılarak yeni yöntemler geliştirilmiş ve ROC(t) ile gösterilen ROC eğrisi tahminleri önerilmiştir. Bu makalede yaşam çözümlemesi için kullanılan ROC eğrisi tahmin edicileri yöntemlerinden kümülatif duyarlılık ve dinamik seçicilik (CD), olay duyarlılığı ve dinamik seçicilik (ID), olay duyarlılığı ve statik seçicilik (IS) ve son olarak naive tahmin edicisi tanıtılmıştır. Bu tahmin edicilerin uygulanabilirliğini göstermek için gerçek veri olan serviks kanseri verisi üzerinde uygulama yapılmıştır. Bu veri için CD1 ile CD2 benzer sonuçlar vermiştir. Ayrıca CD5 ile CD6 da benzer sonuçlar vermiştir. ID1 en düşük sınıflandırma performansına sahipken CD4, 10. aydan itibaren iyi bir sınıflandırma performansı göstermiştir.

Anahtar Kelimeler

ROC en yakın komşu tahmin edicisi ROC Kaplan-Meier ROC yaşam Yaşam çözümlemesi Zamana bağlı ROC eğrileri

Kaynakça

  • [1] Kaplan, E. L. and Meier, P. 1958. Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53, 457-481.
  • [2] Heagerty, P. J., Lumley, T, Pepe, M. S. 2000. Time-Dependent ROC Curves for Censored Survival Data and A Diagnostic Marker. Biometrics, 56(2), 337–344.
  • [3] Amico, M., Keilegom, V. I. and Han, B. 2021. Assessing Cure Status Prediction from Survival Data Using Receiver Operating Characteristic Curves. Biometrika, 108(3), 727–740.
  • [4] Pepe, M. S. 2003. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press, USA.
  • [5] Kamarudin, N. K., Cox, T. and Kolamunnage-Dona, R. 2017. Time-Dependent ROC Curve Analysis in Medical Research: Current Methods and Applications. BMC Medical Research Methodology, 17(53), 2-19.
  • [6] Dey, R., Hanley, J.A. and Saha-Chaudhuri, P., 2023. Inference for Covariate-Adjusted Time-Dependent Prognostic Accuracy Measures, Statictic in Medicine, 42, 4082-4110.
  • [7] Ying, A., 2024. Proximal Survival Analysis to Handle Dependent Right Censoring, Journal of the Royal Statistical Society Series B: Statistical Methodology, 00, 1-21.
  • [8] Swets, J. A. and Pickett, R. M. 1982. Evaluation of Diagnostic Systems: Methods from Signal Detection Theory. Academic Press, New York.
  • [9] Hanley, J. A. 1989. Receiver Operating Characteristic (ROC) Methodology: The State of The Art. Critical Reviews in Diagnostic Imaging, 29, 307-335.
  • [10] Begg, C. G. 1991. Advances in Statistical Methodology for Diagnostic Medicine in The 1980's. Statistics in Medicine, 10, 1887-1895.
  • [11] Zweig, M. H. and Campbell, G. 1993. Receiver-Operator Characteristic Plots: A Fundamental Evaluation Tool in Clinical Medicine. Clinical Chemistry, 39(4), 561-577.
  • [12] Pepe, M., Leisenring, W., and Rutter, C. 2000. Evaluating Diagnostic Tests in Public Health. Handbook of Biostatistics, 18, 397-422.
  • [13] Beyene, K.M. and Ghouch, A. E., 2022, Time-Dependent ROC Curve Estimation for Interval-Censored Data, Biometrical Journal, 64, 1056-1074.
  • [14] Zhou, K. H., Hall, W. J., and Shapiro, D. E. 1997. Smooth Nonparametric Receiver Operating Characteristic (ROC) Curves for Continuous Diagnostic Tests. Statistics in Medicine, 16, 2143-2156.
  • [15] Metz, C. E., Herman, B. A., and Shen, J. 1998. Maximum Likelihood Estimation of Receiver Operating Characteristic (ROC) Curves from Continuously Distributed Data. Statistics in Medicine 17, 1033-1053.
  • [16] Touraine, C., Winter, A., Castan, F., Azria, D. and Gourgou, S., 2023. Time-Dependent ROC Curve Analysis for Assessing the Capability of Radiation-Induced CD8 T-Lymphocyte Apoptosis to Predict Late Toxicities after Adjuvant Radiotherapy of Breast Cancer Patients, 15, 4676.
  • [17] Etzioni, R., Pepe, M., Longton, G., Hu, C. and Goodman, G. 1999. Incorporating The Time Dimension in Receiver Operating Characteristic Curves: A Case Study of Prostate Cancer. Medical Decision Making, 19(3), 242–251.
  • [18] Slate, E. H. and Turnbull, B. W. 2000. Statistical Models for Longitudinal Biomarkers of Disease Onset. Statistics in Medicine, 19, 617–637.
  • [19] Heagerty, P. J. and Zheng, Y. 2005. Survival Model Predictive Accuracy and ROC Curves. Biometrics, 61(1), 92–105.
  • [20] Song, X. and Zhou, X. H. 2008. A Semiparametric Approach for The Covariate Specific ROC Curve with Survival Outcome. Statistica Sinica, 18(3), 947-965.
  • [21] Anonim. https://www.researchgate.net/figure/Three-examples-of-ROC-curves-Two-threshold-levels-labeled-A-and-B-are-identified-on_fig2_347797026 (Erişim tarihi: 05.05.2024).
  • [22] Heagerty, P. J. and Zheng, Y. 2004. Semiparametric Estimation of Time-Dependent ROC Curves for Longitudinal Marker Data. Biostatistics, 5(4), 615–632.
  • [23] Gönen, M. and Heller, G. 2005. Concordance Probability and Discriminatory Power in Proportional Hazards Regression. Biometrika, 92, 965–970.
  • [24] Zhang, Y. and Shao, Y. 2018. Concordance Measure and Discriminatory Accuracy in Transformation Cure Models. Biostatistics, 19, 14–26.
  • [25] Beyene, K. M., El Ghouch, A. and Oulhaj, A. 2019. On The Validity of Time-Dependent AUC Estimation in The Presence of A Cure Fraction. Biometrical Journal, 61, 1430–1447.
  • [26] Kim, Y. J. 2022. Review for Time-Dependent ROC Analysis Under Diverse Survival Models. The Korean Journal of Applied Statistics, 35(1), 35–47.
  • [27] Akritas, M. G., 1994. Nearest Neighbor Estimation of a Bivariate Distribution under Random Censoring. The Annals of Statistic, 22(3), 1299–1327.
  • [28] Blanche, P, Dartigues, J. F. and Jacqmin-Gadda, H. 2013. Review and Comparison of ROC Curve Estimators for A Time-Dependent Outcome with Marker-Dependent Censoring. Biometrical Journal, 55(5), 687–704.
  • [29] Chambless, L. E. and Diao, G. 2006. Estimation of Time-Dependent Area Under The ROC Curve for Long-Term Risk Prediction. Statistic in Medicine, 25(20), 3474–3486.
  • [30] Viallon, V. and Latouche, A. 2011. Discrimination Measures for Survival Outcomes: Connection Between The AUC and The Predictiveness Curve. Biometrical Journal, 53(2), 217–236.
  • [31] Uno, H., Cai, T. X., Tian, L. and Wei, L. J. 2007. Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models. Journal of the American Statistical Association, 102(478), 527–537.
  • [32] Hung, H. and Chiang, C. 2010a. Optimal Composite Markers for Time-Dependent Receiver Operating Characteristic Curves with Censored Survival Data. Scandinavian Journal of Statistics, 37, 664–679.
  • [33] Hung, H. and Chiang, C. 2010b. Estimation Methods for Time-Dependent AUC Models with Survival Data. Canadian Journal of Statistics, 38, 8–26.
  • [34] Lambert, J. and Chevret, S. 2014. Summary Measure of Discrimination in Survival Models Based on Cumulative/Dynamic Time-Dependent ROC Curves. Statistical Methods in Medical Research, 25(5), 2088- 2102.
  • [35] Royston, P. and Parmar, M. K. 2011. The Use of Restricted Mean Survival Time to Estimate The Treatment Effect in Randomized Clinical Trials When The Proportional Hazards Assumption is in Doubt. Statistic in Medicine, 30(19), 2409–2421.
  • [36] Cox, D. R. 1972. Regression Models and Life Tables. Journal of the Royal Statistical Society Series B, 34(2), 187–220.
  • [37] Aalen, O. O. 1989. A Linear Regression Model for the Analysis of Life Times. Statistic in Medicine, 8(8), 907–925.
  • [38] Xu, R. and O'Quigley, J. 2000. Proportional Hazards Estimate of The Conditional Survival Function. Journal of the Royal Statistical Society Series B (Statistical Methodology), 62(4), 667–680.
  • [39] Saha-Chaudhuri, P. and Heagerty, P. J. 2013. Nonparametric Estimation of A Time-Dependent Predictive Accuracy Curve. Biostatistics, 14(1), 42–59.
  • [40] Shen, W., Ning, J. and Yuan, Y. 2015. A Direct Method to Evaluate The Time‐Dependent Predictive Accuracy for Biomarkers. Biometrics, 71(2), 439–449.
  • [41] Royston, P. and Altman, D. G. 1994. Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling. Journal of the Royal Statistical Society Series C (Applied Statistics), 43(3), 429-467.
  • [42] Cai, T., Pepe, M. S., Lumley, T., Zheng, Y. and Jenny, N. J. 2006. The Sensitivity and Specificity of Markers for Event Times. Biostatistics, 7(2), 182–197.
  • [43] Heagerty, P. J. and Zheng, Y. 2007. Prospective Accuracy for Longitudinal Markers. Biometrics, 63(2), 332–341.
  • [44] Çiftçi, E. 2023. Çok durumlu modellerde geçiş olasılıklarının tahmini. Hacettepe üniversitesi, Fen Bilimleri Enstitüsü, Doktora Tezi, 164s, Ankara.
  • [45] Sertkaya, Ş. 2024. Yaşam çözümlemesinde alıcı işlem karakteristiği eğrileri. Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 70s, Ankara.
  • [46] Blanche, P. Package ‘timeROC’, https://cran.r-project.org/web/packages/timeROC/timeROC.pdf (Erişim tarihi: 20.05.2024).
  • [47] Heagerty, P. J. and Saha-Chaudhuri P. Package ‘risksetROC’, https://cran.r-project.org/web/packages/risksetROC/risksetROC.pdf (Erişim tarihi: 20.05.2024a).
  • [48] Heagerty, P. J. and Saha-Chaudhuri, P., Package ‘survivalROC’, https://cran.r-project.org/web/packages/survivalROC/survivalROC.pdf (Erişim tarihi: 20.05.2024b).
  • [49] Potapov. S., Adler. W. and Schmid. M., survAUC: Estimators of Prediction Accuracy, https://cran.r-project.org/web/packages/survAUC/survAUC.pdf (Erişim tarihi: 20.05.2024).
  • [50] Scheike, T., Timereg Package, https://cran.r-project.org/web/packages/timereg/timereg.pdf (Erişim tarihi: 20.05.2024).
  • [51] Therneau, T. M. and Lumley, T., Package ‘survival’, https://cran.r-project.org/web/packages/survival/survival.pdf (Erişim tarihi: 20.05.2024).
  • [52] Lu Y., Wang L., Liu P., Yang P. and You M. 2012. Gene-Expression Signature Predicts Postoperative Recurrence in Stage I Non-Small Cell Lung Cancer Patients. PLos One, 7(1).
  • [53] Yue Y., Cui X., Bose S., Audeh W., Zhang X. and Fraass B. 2015. Stratifying Triple-Negative Breast Cancer Prognosis Using 18 F-FDG-PET/CT Imaging. Breast Cancer Res Treat., 153(3):607–16.
  • [54] Yue Y., Astvatsaturyan K., Cui X., Zhang X., Fraass B. and Bose S. 2016. Stratification of Prognosis of Triple-Negative Breast Cancer Patients Using Combinatorial Biomarkers. PLos One. 11(3).
  • [55] Sayın, C.E. and Ünal, İ. 2022. Time-Dependent Receiver Operating Characteristic Analysis and Applications in The Field of Medicine. Black Sea Journal Health Science, 5(3), 411-416.
Toplam 55 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Biyoistatistik, Uygulamalı İstatistik
Bölüm Makaleler
Yazarlar

Şeyma Sertkaya Bu kişi benim 0009-0004-0804-8970

Duru Karasoy 0000-0002-2258-4479

Yayımlanma Tarihi 23 Aralık 2024
Gönderilme Tarihi 5 Ağustos 2024
Kabul Tarihi 25 Ekim 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Sertkaya, Ş., & Karasoy, D. (2024). Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28(3), 490-503. https://doi.org/10.19113/sdufenbed.1528404
AMA Sertkaya Ş, Karasoy D. Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. Aralık 2024;28(3):490-503. doi:10.19113/sdufenbed.1528404
Chicago Sertkaya, Şeyma, ve Duru Karasoy. “Yaşam Çözümlemesinde ROC Eğrileri Ve Bir Uygulama”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28, sy. 3 (Aralık 2024): 490-503. https://doi.org/10.19113/sdufenbed.1528404.
EndNote Sertkaya Ş, Karasoy D (01 Aralık 2024) Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28 3 490–503.
IEEE Ş. Sertkaya ve D. Karasoy, “Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 28, sy. 3, ss. 490–503, 2024, doi: 10.19113/sdufenbed.1528404.
ISNAD Sertkaya, Şeyma - Karasoy, Duru. “Yaşam Çözümlemesinde ROC Eğrileri Ve Bir Uygulama”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28/3 (Aralık 2024), 490-503. https://doi.org/10.19113/sdufenbed.1528404.
JAMA Sertkaya Ş, Karasoy D. Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2024;28:490–503.
MLA Sertkaya, Şeyma ve Duru Karasoy. “Yaşam Çözümlemesinde ROC Eğrileri Ve Bir Uygulama”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 28, sy. 3, 2024, ss. 490-03, doi:10.19113/sdufenbed.1528404.
Vancouver Sertkaya Ş, Karasoy D. Yaşam Çözümlemesinde ROC Eğrileri ve Bir Uygulama. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2024;28(3):490-503.

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