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Wang J, Jiang X, Ning J. Evaluating dynamic and predictive discrimination for recurrent event models: use of a time-dependent C-index. Biostatistics 2023:kxad031. [PMID: 37952117 DOI: 10.1093/biostatistics/kxad031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 10/21/2023] [Accepted: 10/25/2023] [Indexed: 11/14/2023] Open
Abstract
Interest in analyzing recurrent event data has increased over the past few decades. One essential aspect of a risk prediction model for recurrent event data is to accurately distinguish individuals with different risks of developing a recurrent event. Although the concordance index (C-index) effectively evaluates the overall discriminative ability of a regression model for recurrent event data, a local measure is also desirable to capture dynamic performance of the regression model over time. Therefore, in this study, we propose a time-dependent C-index measure for inferring the model's discriminative ability locally. We formulated the C-index as a function of time using a flexible parametric model and constructed a concordance-based likelihood for estimation and inference. We adapted a perturbation-resampling procedure for variance estimation. Extensive simulations were conducted to investigate the proposed time-dependent C-index's finite-sample performance and estimation procedure. We applied the time-dependent C-index to three regression models of a study of re-hospitalization in patients with colorectal cancer to evaluate the models' discriminative capability.
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Affiliation(s)
- Jian Wang
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, 7007 Bertner Ave, 1MC12.3557, Houston, TX 77030, United States
| | - Xinyang Jiang
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, 7007 Bertner Ave, 1MC12.3557, Houston, TX 77030, United States
| | - Jing Ning
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, 7007 Bertner Ave, 1MC12.3557, Houston, TX 77030, United States
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van Geloven N, Giardiello D, Bonneville EF, Teece L, Ramspek CL, van Smeden M, Snell KIE, van Calster B, Pohar-Perme M, Riley RD, Putter H, Steyerberg E. Validation of prediction models in the presence of competing risks: a guide through modern methods. BMJ 2022; 377:e069249. [PMID: 35609902 DOI: 10.1136/bmj-2021-069249] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Nan van Geloven
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, Netherlands
| | - Daniele Giardiello
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, Netherlands
- Netherlands Cancer Institute, Amsterdam, Netherlands
| | - Edouard F Bonneville
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, Netherlands
| | - Lucy Teece
- Centre for Prognosis Research, Research Institute for Primary Care and Health Sciences, Keele University, Keele, UK
| | - Chava L Ramspek
- Department of Clinical Epidemiology, Leiden University Medical Centre, Leiden, Netherlands
| | - Maarten van Smeden
- Department of Epidemiology, University Medical Centre Utrecht, Utrecht, Netherlands
| | - Kym I E Snell
- Centre for Prognosis Research, Research Institute for Primary Care and Health Sciences, Keele University, Keele, UK
| | - Ben van Calster
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, Netherlands
- Department of Development and Regeneration, KU Leuven, Leuven, Belgium
| | - Maja Pohar-Perme
- Department of Biostatistics and Medical Informatics, University of Ljubljana, Ljubljana, Slovenia
| | - Richard D Riley
- Centre for Prognosis Research, Research Institute for Primary Care and Health Sciences, Keele University, Keele, UK
| | - Hein Putter
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, Netherlands
| | - Ewout Steyerberg
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, Netherlands
- Department of Public Health, Erasmus MC-University Medical Centre, Rotterdam, Netherlands
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