Objective: Time-dependent reciever operating characteristics (ROC) curves are statistical methods which can be used when the specified outcome is an event which can take place at any time after the diagnostic test has been measured and may be right censored. This work presents an approach for making inference related to the performance of prognostic biomarker which can be measured from smaller number of patients, by borrowing information from the other biomarker(s) which can be measured from larger number of patients for right censored survival data. Material and Methods: Simulation studies were performed to see the performance of the proposed modification. We evaluated estimators related to the time dependent ROC function and the area under the curve (AUC) in terms of efficiency and unbiasedness to see whether proposed modification provides benefit over the original method. Results: It is observed that proposed approach yielded smaller bias, mean square error and standard deviation values for most scenarios in the simulation studies. Conclusion: The proposed approach, which combines information from different samples with different biomarkers may be useful to make inference related to the biomarker of interest which is measured from sample with a smaller size.
Keywords: Biomarker; censored data; time dependent ROC curves
Amaç: Zamana bağlı ROC eğrileri sonuç, tanı testinin ölçülmesinden sonra herhangi bir zamanda gerçekleşebilen ve sağdan sansürlü olay olarak tanımlandığında kullanılabilen istatistiksel yöntemlerdir. Bu çalışma, sağdan sansürlü sağkalım verileri için daha fazla sayıda hastadan ölçülebilen diğer biyobelirteçlerden bilgi alınarak az sayıda hasta için ölçülebilen prognostik biyobelirtecin performansı ile ilişkili çıkarım yapan bir yaklaşım sunmaktadır. Gereç ve Yöntemler: Önerilen modifikasyonun performansını görmek için simülasyon çalışmaları yapılmıştır. Önerilen yöntemin orijinal yönteme üstünlük sağlayıp sağlamadığını görmek için etkinlik ve yansızlık açısından eğri altında kalan alanla (AUC) ve zamana bağlı ROC fonksiyonuyla ilişkili tahmin ediciler değerlendirilmiştir. Bulgular: Önerilen yaklaşımın simülasyon çalışmalarındaki birçok senaryo için daha küçük yanlılık, hata kareler ortalaması ve standart sapma değerleri verdiği görülmüştür. Sonuç: Farklı biyobelirteçler ile farklı örneklemlerden elde edilen bilgiyi birleştiren önerilen yaklaşım, örneklemden daha küçük olan ilgilenilen biyobelirteçle ilgili çıkarım yapmak için yararlı olabilir.
Anahtar Kelimeler: Biyobelirteç; sansürlü veri; zamana bağlı ROC eğrileri
- Metzker ML. Sequencing technologies-the next generation. Nat Rev Genet. 2010;11(1):31-46. [Crossref] [PubMed]
- O'Connor L, Glynn B. Recent advances in the development of nucleic acid diagnostics. Expert Rev Med Devices. 2010;7(4):529-39. [Crossref] [PubMed]
- Hu ZZ, Huang H, Wu CH, Jung M, Dritschilo A, Riegel AT, et al. Omics-based molecular target and biomarker identification. Methods Mol Biol. 2011;719:547- 71. [Crossref] [PubMed] [PMC]
- Committee on the Review of Omics-Based Tests for Predicting Patient Outcomes in Clinical Trials; Board on Health Care Services; Board on Health Sciences Policy; Institute of Medicine. Evolution of translational omics: lessons learned and the path forward. National Academies Press, Washington (DC); 2012.
- Janvilisri T, Suzuki H, Scaria J, Chen JW, Charoensawan V. High-throughput screening for biomarker disvcovery. Dis Markers. 2015;2015:108064. [Crossref] [PubMed] [PMC]
- Fitó M, Melander O, Martínez JA, Toledo E, Carpéné C, Corella D. Advances in integrating traditional and omic biomarkers when analyzing the effects of the mediterranean diet intervention in cardiovascular prevention. Int J Mol Sci. 2016;17(9):1469. [Crossref] [PubMed] [PMC]
- Ombrone D, Giocaliere E, Forni G, Malvagia S, la Marca G. Expanded newborn screening by mass spectrometry: new tests, future perspectives. Mass Spectrom Rev. 2016;35(1):71-84. [Crossref] [PubMed]
- Dodd L, Pepe MS. Partial AUC estimation and regression. Biometrics. 2003;59(3):614-23. [Crossref] [PubMed]
- Green DM, Sweets JA. Signal Detection Theory and Psychopath. New York: John & Wiley; 1996.
- Obuchowski NA. Sample size tables for receiver operating characteristic studies. AJR Am J Roentgenol. 2000;175(3):603-8. [Crossref] [PubMed]
- Pepe MS. The Statistical Evaluation of Medical Tests for Classification and Prediction. 1st ed. New York: Oxford University Press; 2003. p.302.
- Zhou XH, Obuchowski NA, McClish DK. Statistical Methods in Diagnostic Medicine. 2nd ed. New York: John Wiley & Sons; 2011. p.592. [Crossref]
- Schisterman EF, Albert PS. The biomarker revolution. Stat Med. 2012;31(22):2513-5. [Crossref] [PubMed] [PMC]
- Dorfman R. The detection of defective members of large populations. Ann Math Statist. 1943;14(4):436-40. [Crossref]
- Faraggi D, Reiser B, Schisterman EF. ROC curve analysis for biomarkers based on pooled assessments. Stat Med. 2003;22(15):2515-27. [Crossref] [PubMed]
- Vexler A, Schisterman EF, Liu A. Estimation of ROC curves based on stably distributed biomarkers subject to measurement error and pooling mixtures. Stat Med. 2008;27(2):280-96. [Crossref] [PubMed] [PMC]
- Schisterman EF, Vexler A, Mumford SL, Perkins NJ. Hybrid pooled-unpooled design for cost efficient measurement of biomarkers. Stat Med. 2010;29(5):597- 613.
- Zhang Z, Lui A, Lyles R, Mukherjee B. Logistic regression analysis of biomarker data subject to pooling and dichotomization. Stat Med. 2012;31(22):2473-84. [Crossref] [PubMed]
- Stein C. Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proceeding of the 3rd Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press; 1956. p.197-206.
- Cox DR. Combination of data. Encyclopedia of Statistical Sciences. John Wiley; 1981. p.45-52.
- James W, Stein C. Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. California: University of California Press; 1961. p.361-79.
- Hu F, Zidek JV. The weighted likelihood. Can J Stat. 2002;30(3):347-71. [Crossref]
- Wang X, Van Eeden C, Zidek JV. Asymptotic properties of maximum weighted likelihood estimators. J Stat Plan Inference. 2004;119:37-54. [Crossref]
- Wang X, Zidek JV. Selecting likelihood weights by cross-validation. Ann Statist. 2005;33(2):463-501. [Crossref]
- Plante JF. Nonparametric adaptive likelihood weights. Can J Stat. 2008;36:443-61. [Crossref]
- Plante JF. About an adaptively weighted Kaplan-Meier estimate. Lifetime Data Anal. 2009;15(3):295-315. [Crossref] [PubMed]
- Heagerty PJ, Zheng Y. Survival model predictive accuracy and ROC curves. Biometrics. 2005;61(1):92-105. [Crossref] [PubMed]
- Heagerty PJ, Lumley T, Pepe MS. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics. 2000;56(2):337-44. [Crossref] [PubMed]
- Cai T, Pepe MS, Zheng Y, Lumley T, Jenny NS. The sensitivity and specificity of markers for event times. Biostatistics. 2006;7(2):182-97. [Crossref] [PubMed]
- Pepe MS, Zheng Y, Jin Y, Huang Y, Parikh CR, Levy WC. Evaluating the ROC performance of markers for future events. Lifetime Data Anal. 2008;14(1):86- 113. [Crossref] [PubMed]
- Etzioni R, Pepe M, Longton G, Hu C, Goodman G. Incorporating the time dimension in receiver operating characteristic curves: a case study of prostate cancer. Med Decis Making. 1999;19(3):242-51. [Crossref] [PubMed]
- Slate EH, Turnbull BW. Statistical models for longitudinal biomarkers of disease onset. Stat Med. 2000;19(4):617-37. [Crossref]
- Akritas MG. Nearest neighbor estimation of a bivariate distribution under random censoring. Ann Statist. 1994;22(3):1299-327. [Crossref]
- Chambless LE, Diao G. Estimation of time-dependent area under the ROC curve for long-term risk prediction. Stat Med. 2006;25(20):3474-86. [Crossref] [PubMed]
- Song X, Zhou X. A semiparametric approach for the covariate-specific ROC curve with survival outcome. Stat Sin. 2008;18:947-65.
- Uno H, Cai T, Tian L, Wei L. Evaluating prediction rules for t-year survivors with censored regression models. J Am Stat Assoc. 2007;102(478):527-37. [Crossref]
- Hung H, Chiang CT. Optimal composite markers for time-dependent receiver operating characteristic curves with censored survival data. Scand J Stat. 2010;37(4):664-79. [Crossref]
- Wolf P, Schmidt G, Ulma K. The use of ROC for defining the validity of the prognostic index incensored data. Stat Probabil Lett. 2011;81(7):783-91. [Crossref]
- Blanche P, Dartigues JF, Jacqmin-Gadda H. Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring. Biom J. 2013;55(5):687-704. [Crossref] [PubMed]
- Li L, Greene T, Hu B. A simple method to estimate the time-dependent ROC curve and the area under the curve with right censored data. Stat Methods Med Res. 2016;27(8):2264-78. [Crossref] [PubMed]
- Martínez-Camblor P, Bayón GF, Pérez-Fernández S. Cumulative/dynamic ROC curve estimation. J Stat Comput Sim. 2016;86:3582-94. [Crossref]
- Martínez-Camblor P, Pardo-Fernández JC. Smooth time-dependent receiver operating characteristic curve estimators. Stat Methods Med Res. 2017;27:651-74. [Crossref] [PubMed]
- Plante JF. 'MAMSE' package on the CRAN. Version: 0.2-1. Title: MAMSE: Calculation of Minimum Averaged Mean Squared Error (MAMSE) Weights; 2017.
- Li L, Wu C. 'tdROC' package on the CRAN. Version 1.0. Title: Nonparametric Estimation of Time-Dependent ROC Curve from Right Censored Survival Data; 2016.
- R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria; 2018.
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