A Stochastic and State Space Model for Tumour Growth and Applications. Issue 2 (2009)

• Record Type: Journal Article
• Authors: Tan, Wai-Yuan; Ke, Weiming; Webb, G.
• Is Part Of: Computational and mathematical methods in medicine. Volume 10:Issue 2(2009)
• Page Start: 117
• Page End: 138
• Publication Date: 2009
• Subjects: generalized Bayesian approach -- Gompertz growth of cancer tumour -- multilevel Gibbs sampling procedure -- probability distributions -- statistical model -- state space model -- stochastic model; Medicine -- Computer simulation -- Periodicals; Medicine -- Mathematical models -- Periodicals; 610.11
• DOI: 10.1080/17486700802200784
• Languages: English
• ISSNs: 1748-670X

Abstract

Abstract : We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.