State Space and Hidden Markov Models of Human Colon Cancer Involving Multiple Pathways

• Activity Number: 171
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Wai-Yuan Tan and Y.W. Yan*+
• Companies: The University of Memphis and University of Memphis
• Keywords: State space model ; stochastic differential equations ; mixture model of carcinogenesis ; milti-level Gibbs sampling

Abstract

Molecular biologists and cancer researchers have shown that for human colon cancer tumors can either be derived through chromosomal instability pathways involving the APC gene in chromosome 5 or be derived through micro-satellite instability pathways involving mis-match repair genes. Given cancer incidence data such as the SEER data set from NCI/NIH, in this paper we will proceed to show that this process can be formulated in terms of a state space model or a hidden Markov model. In this state space model, the stochastic system model can be represented as a Markov process while the observation model is a statistical model for cancer incidence. This model is not Markov but is a function of a Markov process and hence is hidden Markov. Based on this model, we have formulated a generalized Bayesian procedure via Gibbs sampling to estimate parameters, which are consistent with cancer biology.