Two-stage receiver operating-characteristic curve estimator for cohort studies.

asymptotic distributions receiver-operating characteristic (ROC) curve time-dependent ROC curve two-stage estimator

Journal

The international journal of biostatistics
ISSN: 1557-4679
Titre abrégé: Int J Biostat
Pays: Germany
ID NLM: 101313850

Informations de publication

Date de publication:
21 08 2020
Historique:
received: 27 08 2019
accepted: 25 05 2020
pubmed: 31 8 2020
medline: 15 12 2021
entrez: 31 8 2020
Statut: epublish

Résumé

The receiver operating-characteristic (ROC) curve is a graphical statistical tool routinely used for studying the classification accuracy in both, diagnostic and prognosis problems. Given the different nature of these situations, ROC curve estimation has been separately considered for binary (diagnostic) and time-to-event (prognosis) outcomes, even for data coming from the same study design. In this work, the authors propose a two-stage ROC curve estimator which allows to link both contexts through a general prediction model (first-stage) and the empirical cumulative estimator of the distribution function (second-stage) of the considered test (marker) on the total population. The so-called two-stage Mixed-Subject (sMS) approach proves its behavior on both, large-samples (theoretically) and finite-samples (via Monte Carlo simulations). Besides, a useful asymptotic distribution for the concomitant area under the curve is also computed. Results show the ability of the proposed estimator to fit non-standard situations by considering flexible predictive models. Two real-world examples, one with binary and one with time-dependent outcomes, help us to a better understanding of the proposed methodology on usual practical circumstances. The R code used for the practical implementation of the proposed methodology and its documentation is provided as supplementary material.

Identifiants

pubmed: 32862149
doi: 10.1515/ijb-2019-0097
pii: /j/ijb.ahead-of-print/ijb-2019-0097/ijb-2019-0097.xml
doi:

Types de publication

Journal Article Research Support, Non-U.S. Gov't

Langues

eng

Sous-ensembles de citation

IM

Pagination

117-137

Informations de copyright

© 2020 Walter de Gruyter GmbH, Berlin/Boston.

Références

Green, DM, Swets, JA. Signal detection theory and psychophysics. New York, NY: Wiley; 1966.
Zhou, X-H, Obuchowski, NA, McClish, DK. Statistical methods in diagnostic medicine. New York, NY: Wiley Blackwell; 2002.
Krzanowski, WJ, Hand, DJ. ROC curves for continuous data, volume 111 of Monographs on Statistics and Applied Probability. Boca Raton, FL:CRC Press; 2009.
Pepe, MS. The statistical evaluation of medical tests for classification and prediction. Oxford: Oxford University Press; 2004.
Gneiting, T, Vogel, P. Receiver Operating Characteristic (ROC) curves; 2018. arXiv e-prints, art. arXiv:1809.04808, September.
Pérez-Fernández, S, Martínez-Camblor, P, Filzmoser, P, nsROC, NC. An R package for non-standard ROC curve analysis. R J 2018;10:55–77. https://doi.org/10.32614/RJ-2018-043.
Fluss, R, Faraggi, D, Reiser, B. Estimation of the Youden index and its associated cutoff point. Biometrical J 2005;47:458–72. https://doi.org/10.1002/bimj.200410135.
Demidenko, E. The p-Value you can’t buy. Am Statist 2016;70:33–8. https://doi.org/10.1080/00031305.2015.1069760.
Gonçalves, L, Oliveira, MR, Subtil, A, de Zea Bermudez, P. ROC curve estimation: An overview. Revstat Stat J 2014;12:1–20.
Heagerty, PJ, Lumley, T, Pepe, MS. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 2000;56:337–44. https://doi.org/10.1111/j.0006-341x.2000.00337.x.
Martínez-Camblor, P, Bayón, GF, Pérez-Fernández, S. Cumulative/dynamic ROC curve estimation. J Stat Comput Simul 2016;86:3582–94. https://doi.org/10.1080/00949655.2016.1175442.
Li, L, Greene, T, Hu, B. A simple method to estimate the time-dependent receiver operating characteristic curve and the area under the curve with right censored data. Stat Methods Med Res 2018;27:2264–78. https://doi.org/10.1177/0962280216680239.
Song, X, Zhou, X-H. A semiparametric approach for the covariate specific ROC curve with survival outcome. Stat Sin 2008;18:947–65.
Liu, D, Cai, T, Zheng, Y. Evaluating the predictive value of biomarkers with stratified case-cohort design. Biometrics 2012;68:1219–27. https://doi.org/10.1111/j.1541-0420.2012.01787.x.
Chambless, LE, Diao, G. Estimation of time-dependent area under the ROC curve for long-term risk prediction. Stat Med 2006;25:3474–86. https://doi.org/10.1002/sim.2299.
Blanche, P, Dartigues, J-F, Jacqmin-Gadda, H. Review and comparison of roc curve estimators for a time-dependent outcome with marker-dependent censoring. Biometrical J 2013;55:687–704. https://doi.org/10.1002/bimj.201200045.
Harrell, FE. Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Springer Series in Statistics. Cham, Switzerland: Springer International Publishing;2015.
Hsieh, F, Turnbull, W. B. Nonparametric and semiparametric estimation of the receiver operating characteristic curve. Ann Statist 1996;24:25–40. https://doi.org/10.1214/aos/1033066197.
Spanos, A, Harrell, FE, Durack, DT. Differential diagnosis of acute meningitis: an analysis of the predictive value of initial observations. J Am Med Assoc 1989;262:2700–7. https://doi.org/10.1001/jama.1989.03430190084036.
Durrleman, S, Simon, R. Flexible regression models with cubic splines. Stat Med 1989;8:551–61. https://doi.org/10.1002/sim.4780080504.
Fleming, TR, Harrington, DP. Counting processes and survival analysis. Hoboken, New Jersey: John Wiley & Sons; 1991.
Dickson, ER, Grambsch, PM, Fleming, TR, Fisher, LD, Langworthy, A. Prognosis in primary biliary cirrhosis: model for decision making. Hepatology 1989;10:1–7. https://doi.org/10.1002/hep.1840100102.
Heagerty, PJ, Zheng, Y. Survival model predictive accuracy and ROC curves. Biometrics 2005;61:92–105. https://doi.org/10.1111/j.0006-341x.2005.030814.x.
Cox, DR. Regression models and life-tables. J R Stat Soc Ser B 1972;34:187–220. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x.
Hurvich, CM, Simonoff, JS, Tsai, C-L. Smoothing parameter selection in nonparametric regression using an improved akaike information criterion. J R Stat Soc Ser B 1998;60:271–93. https://doi.org/10.1111/1467-9868.00125.
Stone, CJ, Hansen, MH, Kooperberg, C, Truong, YK. Polynomial splines and their tensor products in extended linear modeling. Ann Stat 1997;25:1371–425. https://doi.org/10.1214/aos/1031594728.
Zhou, S, Shen, X, Wolfe, DA. Local asymptotics for regression splines and confidence regions. Ann Stat 1998;26:1760–82. https://doi.org/10.1214/aos/1024691356.
Falk, M, Wisheckel, F. Asymptotic independence of bivariate order statistics. Stat Probabil Lett 2017;125:91–8.
Goldstein, B, Giroir, B, Randolph, A. International pediatric sepsis consensus conference: definitions for sepsis and organ dysfunction in pediatrics. Pediatr Crit Care Med 2005;6:2–8. https://doi.org/10.1097/01.pcc.0000149131.72248.e6.
Martínez-Camblor, P, Pardo-Fernández, JC. Parametric estimates for the receiver operating characteristic curve generalization for non-monotone relationships. Stat Methods Med Res 2019;28:2032–48. https://doi.org/10.1177/0962280217747009.
Efron, B, Tibshirani, RJ. An introduction to the Bootstrap. Number 57 in monographs on statistics and applied probability. Boca Raton, FL, USA: Chapman & Hall/CRC; 1993.
Martínez-Camblor, P, Pérez-Fernández, S, Díaz-Coto, S. Improving the biomarker diagnostic capacity via functional transformations. J Appl Stat 2019;46:1550–66. https://doi.org/10.1080/02664763.2018.1554628.
van der Vaart, AW. Asymptotic statistics. Cambridge series in statistical and probabilistic mathematics. Cambridge, England: Cambridge University Press; 1998.
Mansuy, R, Yor, M. Aspects of Brownian Motion. Universitext. New York: Springer Berlin Heidelberg; 2008.
Heagerty, PJ, Saha-Chaudhuri, P. survivalROC: time-dependent ROC curve estimation from censored survival data. R package version 1.0.3; 2013.

Auteurs

Susana Díaz-Coto (S)

Department of Statistics, University of Oviedo, Oviedo, Spain.

Norberto Octavio Corral-Blanco (NO)

Department of Statistics, University of Oviedo, Oviedo, Spain.

Pablo Martínez-Camblor (P)

Biomedical Data Science Department, Geisel school of Medicine at Dartmouth, Hanover, NH, USA.

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