Advertisement

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
Article
  • 253 Downloads

Abstract

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.

Keywords

Disease natural history Marked endpoints Competing risks Semiparametric regression Survival analysis 

Notes

Acknowledgements

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)

References

  1. American Cancer Society (2016) Cancer facts and figures 2016. American Cancer Society, AtlantaGoogle Scholar
  2. 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
  3. Andersen PK, Keiding N (2002) Multi-state models for event history analysis. Stat Methods Med Res 11(2):91–115CrossRefzbMATHGoogle Scholar
  4. Biki B, Mascha E, Moriarty DC, Fitzpatrick JM, Sessler DI, Buggy DJ (2008) Anesthetic technique for radical prostatectomy surgery affects cancer recurrence: a retrospective analysis. J Am Soc Anesthesiol 109(2):180–187CrossRefGoogle Scholar
  5. Chen YH (2009) Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models. Biometrika 96(3):591–600MathSciNetCrossRefzbMATHGoogle Scholar
  6. Chen YH (2012) Maximum likelihood analysis of semicompeting risks data with semiparametric regression models. Lifetime Data Anal 18(1):36–57MathSciNetCrossRefzbMATHGoogle Scholar
  7. 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(1):141–151MathSciNetCrossRefzbMATHGoogle Scholar
  8. Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94(446):496–509MathSciNetCrossRefzbMATHGoogle Scholar
  9. Fine JP, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88(4):907–919MathSciNetCrossRefzbMATHGoogle Scholar
  10. Govindarajulu US, Lin H, Lunetta KL, D’Agostino R (2011) Frailty models: applications to biomedical and genetic studies. Stat Med 30(22):2754–2764MathSciNetCrossRefGoogle Scholar
  11. Hougaard P, Hougaard P (2000) Analysis of multivariate survival data, vol 564. Springer, New YorkCrossRefzbMATHGoogle Scholar
  12. Hu C, Tsodikov A (2014a) Joint modeling approach for semicompeting risks data with missing nonterminal event status. Lifetime Data Anal 20(4):563–583MathSciNetCrossRefzbMATHGoogle Scholar
  13. Hu C, Tsodikov A (2014b) Semiparametric regression analysis for time-to-event marked endpoints in cancer studies. Biostatistics 15(3):513–525CrossRefGoogle Scholar
  14. Kalbfleisch JD, Prentice RL (2011) The statistical analysis of failure time data, vol 360. Wiley, HobokenzbMATHGoogle Scholar
  15. Liu L, Wolfe RA, Huang X (2004) Shared frailty models for recurrent events and a terminal event. Biometrics 60(3):747–756MathSciNetCrossRefzbMATHGoogle Scholar
  16. Mehlen P, Puisieux A (2006) Metastasis: a question of life or death. Nat Rev 6:449–458CrossRefGoogle Scholar
  17. Meira-Machado L, de Uña-Álvarez J, Cadarso-Suárez C (2006) Nonparametric estimation of transition probabilities in a non-markov illness-death model. Lifetime Data Anal 12(3):325–344MathSciNetCrossRefzbMATHGoogle Scholar
  18. Neeman E, Ben-Eliyahu S (2013) Surgery and stress promote cancer metastasis: new outlooks on perioperative mediating mechanisms and immune involvement. Brain Behav Immun 30:S32–S40CrossRefGoogle Scholar
  19. Nelsen RB (1999) An introduction to copulas. Springer, BerlinCrossRefzbMATHGoogle Scholar
  20. 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
  21. Oakes D (1989) Bivariate survival models induced by frailties. J Am Stat Assoc 84(406):487–493MathSciNetCrossRefzbMATHGoogle Scholar
  22. O’Reilly MS, Holmgren L, Shing Y, Chen C, Rosenthal RA, Moses M, Lane WS, Cao Y, Sage EH, Folkman J (1994) Angiostatin: a novel angiogenesis inhibitor that mediates the suppression of metastases by a lewis lung carcinoma. Cell 79(2):315–328CrossRefGoogle Scholar
  23. Peng L, Fine JP (2007) Regression modeling of semicompeting risks data. Biometrics 63(1):96–108MathSciNetCrossRefzbMATHGoogle Scholar
  24. Smolle J, Soyer HP, Smolle-Jüttner F, Rieger E, Kerl H (1997) Does surgical removal of primary melanoma trigger growth of occult metastases? An analytical epidemiological approach. Dermatol Surg 23(11):1043–1046CrossRefGoogle Scholar
  25. Tsodikov A (2003) Semiparametric models: a generalized self-consistency approach. J R Stat Soc Ser B Stat Methodol 65(3):759–774MathSciNetCrossRefzbMATHGoogle Scholar
  26. Xu J, Kalbfleisch JD, Tai B (2010) Statistical analysis of illness-death processes and semicompeting risks data. Biometrics 66(3):716–725MathSciNetCrossRefzbMATHGoogle Scholar
  27. Zeng D, Lin D (2006) Efficient estimation of semiparametric transformation models for counting processes. Biometrika 93(3):627–640MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity of MichiganAnn ArborUSA

Personalised recommendations