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Biostatistics 3:529-546 (2002)
© 2002 Oxford University Press

A Bayesian analysis of colonic crypt structure and coordinated response to carcinogen exposure incorporating missing crypts

Jeffrey S. Morris*, Naisyin Wang, Joanne R. Lupton, Robert S. Chapkin, Nancy D. Turner, Meeyoung Hong and Raymond J. Carroll

Jeffrey S. Morris. Department of Biostatistics, University of Texas, M.D. Anderson Cancer Center, 1515 Holcombe, Boulevard, Box 447, Houston, TX 77030-4009, USA jeffmo{at}mdanderson.org
Naisyin Wang. Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA
Joanne R. Lupton, Robert S. Chapkin, Nancy D. Turner, Meeyoung Hong. Faculty of Nutrition, Texas A&M University, College Station, TX 77843-2471, USA
Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA

*To whom correspondence should be addressed

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 non-standard function that measures the interrelationship of DNA damage mechanisms in different regions of the colon.

Keywords: Bayesian inference; Carcinogenesis; Colon cancer; Correlation; Functional data analysis; Gibbs sampler; Markov chain Monte Carlo; Missing covariates; Nutrition; Surrogate variables


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