Lifetime Data Analysis

, Volume 20, Issue 2, pp 234–251

Calibrated predictions for multivariate competing risks models

  • Malka Gorfine
  • Li Hsu
  • David M. Zucker
  • Giovanni Parmigiani

DOI: 10.1007/s10985-013-9260-x

Cite this article as:
Gorfine, M., Hsu, L., Zucker, D.M. et al. Lifetime Data Anal (2014) 20: 234. doi:10.1007/s10985-013-9260-x


Prediction models for time-to-event data play a prominent role in assessing the individual risk of a disease, such as cancer. Accurate disease prediction models provide an efficient tool for identifying individuals at high risk, and provide the groundwork for estimating the population burden and cost of disease and for developing patient care guidelines. We focus on risk prediction of a disease in which family history is an important risk factor that reflects inherited genetic susceptibility, shared environment, and common behavior patterns. In this work family history is accommodated using frailty models, with the main novel feature being allowing for competing risks, such as other diseases or mortality. We show through a simulation study that naively treating competing risks as independent right censoring events results in non-calibrated predictions, with the expected number of events overestimated. Discrimination performance is not affected by ignoring competing risks. Our proposed prediction methodologies correctly account for competing events, are very well calibrated, and easy to implement.


Risk prediction Competing risks Frailty model  Multivariate survival model Calibration ROC analysis 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Malka Gorfine
    • 1
  • Li Hsu
    • 2
  • David M. Zucker
    • 3
  • Giovanni Parmigiani
    • 4
    • 5
  1. 1.Faculty of Industrial Engineering and ManagementTechnion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Division of Public Health SciencesFred Hutchinson Cancer Research CenterSeattleUSA
  3. 3.Department of StatisticsHebrew University of JerusalemJerusalemIsrael
  4. 4.Department of Biostatistics and Computational BiologyDana Farber Cancer Institute BostonUSA
  5. 5.Department of BiostatisticsHarvard School of Public HealthBostonUSA

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