Lifetime Data Analysis

, Volume 24, Issue 3, pp 385–406 | Cite as

A joint model of cancer incidence, metastasis, and mortality

  • Qui Tran
  • Kelley M. Kidwell
  • Alex Tsodikov


Many diseases, especially cancer, are not static, but rather can be summarized by a series of events or stages (e.g. diagnosis, remission, recurrence, metastasis, death). Most available methods to analyze multi-stage data ignore intermediate events and focus on the terminal event or consider (time to) multiple events as independent. Competing-risk or semi-competing-risk models are often deficient in describing the complex relationship between disease progression events which are driven by a shared progression stochastic process. A multi-stage model can only examine two stages at a time and thus fails to capture the effect of one stage on the time spent between other stages. Moreover, most models do not account for latent stages. We propose a semi-parametric joint model of diagnosis, latent metastasis, and cancer death and use nonparametric maximum likelihood to estimate covariate effects on the risks of intermediate events and death and the dependence between them. We illustrate the model with Monte Carlo simulations and analysis of real data on prostate cancer from the SEER database.


Disease natural history Marked endpoints Competing risks Semiparametric regression Survival analysis 



This research was supported by National Cancer Institute’s grants U01CA199338 (CISNET) and P50CA186786 (SPORE).

Supplementary material

10985_2017_9407_MOESM1_ESM.pdf (221 kb)
Supplementary material 1 (pdf 221 KB)


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity of MichiganAnn ArborUSA

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