Standard Article

Three-State Carcinogenicity Model

Environmental Health

  1. Gregg E. Dinse

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vac005.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Dinse, G. E. 2013. Three-State Carcinogenicity Model . Encyclopedia of Environmetrics. 6.

Author Information

  1. National Institute of Environmental Health Sciences, Research Triangle Park, NC, USA

Publication History

  1. Published Online: 15 JAN 2013


A common stochastic model for animal carcinogenicity data has three states: N (alive with no tumor), T (alive with tumor), and D (dead from natural causes). The intensity rates for N [RIGHTWARDS ARROW] T, T [RIGHTWARDS ARROW] D, and N [RIGHTWARDS ARROW] D transitions at time t are denoted by λ(t), α(t), and β(t), respectively, which correspond to the hazard rates for times from birth to tumor onset, from tumor onset to natural death, and from birth to natural death without a tumor. Carcinogenesis refers to the development of new tumors; so analyses of carcinogenicity data should focus on the tumor incidence rate, λ(t). Three factors complicate tumor incidence analyses: all onset times are censored if tumors are occult; tumor lethality makes censoring informative; and differential mortality exacerbates biases arising from inadequate survival or lethality adjustment. The most appropriate analysis of tumor incidence data depends on what information is available and what assumptions are reasonable. This article describes a variety of scenarios and, in each case, outlines approaches for comparing tumor incidence rates across treatment groups.


  • carcinogenesis;
  • cause of death;
  • differential mortality;
  • fatal tumor;
  • incidental tumor;
  • occult tumor;
  • sacrifice;
  • survival;
  • tumor incidence;
  • tumor lethality;
  • tumor onset;
  • tumor prevalence