A Bayesian Analysis Involving Colonic Crypt Structure and Coordinated Response to Carcinogens Incorporating Missing Crypts

Jeffrey S. Morris, The University of Texas M.D. Anderson Cancer Center
Naisyin Wang, Texas A&M University
Joanne R. Lupton, Texas A&M University
Robert S. Chapkin, Texas A&M University
Nancy D. Turner, Texas A&M University
Mee-Young Hong, Texas A&M University
Raymond J. Carroll, Texas A&M University

Abstract

This paper is concerned with modeling the architecture of colonic crypts and the implications of this modeling for understanding possible coordinated response of carcinogen–induced DNA damage between various regions of the colon. The methods we develop to address these two issues are applied to a particular important example in colon carcinogenesis. We cast the problem as an unusual and not previously studied hierarchical mixed-effects model characterized by completely missing covariates in units at a structurally base level, except for some randomly selected units. Information concerning the missing covariates is available through certain known ordering constraints and surrogate measures. Our methods use Bayesian machinery. We exploit the biological structure of this problem to generate the missing covariates simultaneously and efficiently at the base levels, as opposed to the naive practice of generating units at the base levels one-at-a-time with Metropolis–Hastings steps.We apply our methods to show that different regions of the colon have different architectures, and to estimate an important but nonstandard function that measures the interrelationship of DNA damage mechanisms in different regions of the colon.