A joint model of cancer incidence, metastasis, and mortality
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.
KeywordsDisease 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).
- American Cancer Society (2016) Cancer facts and figures 2016. American Cancer Society, AtlantaGoogle Scholar
- Andersen PK, Hansen LS, Keiding N (1991) Non-and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process. Scand Stat 18(2):153–167Google Scholar
- Nielsen GG, Gill RD, Andersen PK, Sørensen TIA (1992) A counting process approach to maximum likelihood estimation in frailty models. Scand J Stat 19(1):25–43Google Scholar