Abstract
There is tremendous scientific and medical interest in the use of biomarkers to better facilitate medical decision making. In this article, we present a simple framework for assessing the predictive ability of a biomarker. The methodology requires use of techniques from a subfield of survival analysis termed semi-competing risks; results are presented to make the article self-contained. As we show in the article, one natural interpretation of semi-competing risks model is in terms of modifying the classical risk set approach to survival analysis that is more germane to medical decision making. A crucial parameter for evaluating biomarkers is the predictive hazard ratio, which is different from the usual hazard ratio from Cox regression models for right-censored data. This quantity will be defined; its estimation, inference, and adjustment for covariates will be discussed. Aspects of causal inference related to these procedures will also be described. The methodology is illustrated with an evaluation of serum albumin in terms of predicting death in patients with primary biliary cirrhosis.
Similar content being viewed by others
References
Baker SG, Kramer BS, Srivastava S (2002) Markers for early detection of cancer: statistical guidelines for nested case control studies. BMC Med Res Methodol 2:4
Biomarkers Working Group (2001) Biomarkers and surrogate endpoints: preferred definitions and conceptual framework. Clin Pharmacol Ther 69:89–95
Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151
Day R, Bryant J, Lefkopolou M (1997) Adaptation of bivariate frailty models for prediction, with application to biological markers as prognostic indicators. Biometrika 84:45–56
Efron B, Tibshirani R (1986) Bootstrap method for standard errors, confidence intervals and other measures of statistical accuracy. Stat Sci 1:54–77
Fine JP, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88:907–919
Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New York
Gail M (1981) Evaluating serial cancer marker studies in patients at risk of recurrent disease. Biometrics 37:67–78
Gail MH, Pfeiffer RM (2005) On criteria for evaluating models of absolute risk. Biostatistics 6:227–239
Ghosh D (2006) Semiparametric inferences for association with semi-competing risks data. Stat Med 25:2059–2070
Ghosh D (2009) On assessing surrogacy in a single-trial setting using a semi-competing risks paradigm. Biometrics 65:521–529
Ghosh D, Taylor JM, Sargent DJ (2012) Meta-analysis for surrogacy: accelerated failure time modelling and semi-competing risks (with discussion). Biometrics 68:226–247
Harrell FE, Lee KL, Mark DB (1996) Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Stat Med 15:361–387
Heagerty PJ, Lumley T, Pepe MS (2000) Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 56:337–344
Heagerty PJ, Zheng Y (2005) Survival model predictive accuracy and ROC curves. Biometrics 61:92–105
Jin Z, Ying Z, Wei LJ (2001) A simple resampling method by perturbing the minimand. Biometrika 88:381–390
Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974
Murtaugh PA, Dickson ER, Van Dam GM, Malinchoc M, Grambsch PM, Langworthy AL, Gips CH (1994) Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits. Hepatology 20:126–134
Oakes D (1982) A model for association in bivariate survival data. J R Stat Soc B 44:414–422
Oakes D (1986) Semiparametric inference in a model for association in bivariate survival data. Biometrika 73:353–361
Pepe MS, Etzioni R, Feng Z, Potter JD, Thompson ML, Thornquist M, Winget M, Yasui Y (2001) Phases of biomarker development for early detection of cancer. J Natl Cancer Inst 93:1054–1061
Pepe MS, Janes H, Longton G, Leisenring W, Newcomb P (2006) Limitations of the odds ratio in gauging the performance of a diagnostic, prognostic, or screening marker. Am J Epidemiol 159:882–890
Saha P, Heagerty PJ (2010) Time-dependent predictive accuracy in the presence of competing risks. Biometrics 66:999–1011
Zheng Y, Cai T, Jin Y, Feng Z (2012) Evaluating prognostic accuracy of biomarkers under competing risks. Biometrics 68:388–396
Acknowledgments
This research was supported by NIH R01-CA129102. The author thanks the Associate Editor and one referee, whose comments substantially improved the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ghosh, D. A Modified Risk Set Approach to Biomarker Evaluation Studies. Stat Biosci 8, 395–406 (2016). https://doi.org/10.1007/s12561-016-9166-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12561-016-9166-8