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Abstract

Prognostic biomarkers for survival outcomes are widely used in clinical research and practice. Such biomarkers are often evaluated using a C-index as well as quantities based on time-dependent receiver operating characteristic curves. Existing methods for their evaluation generally assume that censoring is uninformative in the sense that the censoring time is independent of the failure time with or without conditioning on the biomarker under evaluation. With focus on the C-index and the area under a particular receiver operating characteristic curve, we describe and compare three estimation methods that account for informative censoring based on observed baseline covariates. Two of them are straightforward extensions of existing plug-in and inverse probability weighting methods for uninformative censoring. By appealing to semiparametric theory, we also develop a doubly robust, locally efficient method that is more robust than the plug-in and inverse probability weighting methods and typically more efficient than the inverse probability weighting method. The methods are evaluated and compared in a simulation study, and applied to real data from studies of breast cancer and heart failure.

Keywords

Area under receiver operating characteristic curve C-index double robustness semiparametric theory time-dependent area under receiver operating characteristic curve time to event

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References

Harrell

Califf

Pryor

et al. Evaluating the yield of medical tests. J Am Med Assoc 1982; 247: 2543–2546.

Gonen

Heller

. Concordance probability and discriminatory power in proportional hazards regression. Biometrika 2005; 92: 965–970.

Heagerty

Zheng

. Survival model predictive accuracy and ROC curves. Biometrics 2005; 61: 92–105.

Uno

Cai

Pencina

et al. On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Stat Med 2011; 30: 1105–1117.

Heagerty

Lumley

Pepe

. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 2000; 56: 337–344.

Zhou

Obuchowski

McClish

. Statistical methods in diagnostic medicine. New York: Wiley, 2002.

Pepe

. The statistical evaluation of medical tests for classification and prediction. New York: Oxford University Press, 2003.

Zou

Liu

Bandos

et al. Statistical evaluation of diagnostic performance: topics in ROC analysis. Boca Raton, FL: Chapman & Hall/CRC, 2011.

Chambless

Diao

. Estimation of time-dependent area under the ROC curve for long-term risk prediction. Stat Med 2006; 25: 3474–3486.

10.

Hung

Chiang

. Estimation methods for time-dependent AUC models with survival data. Can J Stat 2010; 38: 8–26.

11.

Chiang

Hung

. Non-parametric estimation for time-dependent AUC. J Stat Plan Infe 2011; 140: 1162–1174.

12.

Song

Zhou

. Nonparametric ROC based evaluation for survival outcomes. Stat Med 2012; 31: 2660–2675.

13.

Dustin

Fuqua

SAW

. ESR1 mutations in breast cancer. Cancer 2019; 125: 3714–3728.

14.

Ejlertsen

Aldridge

Nielsen

et al. for the Danish Breast Cancer Cooperative Group, the BIG 1-98 Collaborative Group, and the International Breast Cancer Study Group. Prognostic and predictive role of ESR1 status for postmenopausal patients with endocrine-responsive early breast cancer in the Danish cohort of the BIG 1-98 trial. Ann Oncol 2012; 23: 1138–1144.

15.

Sheng

Guo

. Prognostic role of methylated GSTP1, p16, ESR1 and PITX2 in patients with breast cancer: a systematic meta-analysis under the guideline of PRISMA. Medicine 2017; 96: e7476.

16.

Zhang

Hong

et al. Clinical value of circulating ESR1 mutations for patients with metastatic breast cancer: a meta-analysis. Cancer Manag Res 2018; 10: 2573–2580.

17.

Vitale

Ruigrok-Ritstier

Timmermans

et al. The prognostic and predictive value of ESR1 fusion gene transcripts in primary breast cancer. BMC Cancer 2022; 22, 165.

18.

van de Vijver

van ’T Veer

et al. A gene-expression signature as a predictor of survival in breast cancer. New Engl J Med 2002; 347: 1999–2009.

19.

Cox

. Regression models and life tables. J R Stat Soc, Ser B (Stat Methodol) 1972; 34: 187–200.

20.

Bickel

Klaassen

CAJ

Ritov

et al. Efficient and adaptive estimation for semiparametric models. Baltimore, MD: Johns Hopkins University Press, 1993.

21.

Tsiatis

. Semiparametric theory and missing data. New York: Springer, 2006.

22.

Ahmad

Munir

Bhatti

et al. Survival analysis of heart failure patients: a case study. PLoS ONE 2017; 12: e0181001SEP.

23.

Chernozhukov

Chetverikov

Demirer

et al. Double machine learning for treatment and structural parameters. Technical report, cemmap working paper, Centre for Microdata Methods and Practice, 2016.

24.

Benkeser

Carone

van der Laan

et al. Doubly robust nonparametric inference on the average treatment effect. Biometrika 2017; 104: 863–880.

25.

Zhang

Liu

. Estimating the population average treatment effect in observational studies with choice-based sampling. Int J Biostat 2019; 15. DOI: 10.1515/ijb-2018-0093.

26.

Cappiello

Zhang

Shen

et al. Adjusting for population differences using machine learning methods. J R Stat Soc, Ser C (Appl Stat) 2021; 70: 750–769.

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Evaluating prognostic biomarkers for survival outcomes subject to informative censoring

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