Jeffrey Morris, Texas A&M University
Parametric and Nonparametric Methods For Understanding the
Relationship Between Carcinogen-Induced DNA Adduct Levels in Distal
and Proximal Regions of the Colon
An important problem in studying
the etiology of colon cancer is understanding the relationship between
DNA adduct levels (broadly, DNA damage) in cells within colonic crypts
in distal and proximal parts of the colon, following treatment with a
carcinogen and different types of diets. In particular, it is
important to understand whether rats who have elevated adduct levels
in particular positions in distal region crypts also have elevated
levels in the same positions of the crypts in proximal regions, and
whether this relationship depends on diet. We cast this problem as
estimating the correlation function of two responses as a function of
a covariate for studies where both responses are measured on the same
experimental units but not the same subsampling units. The
measurements of the responses are taken at the subsampling level for
various levels of the covariate. Parametric and nonparametric methods
are developed and applied to a data set from an ongoing study, leading
to potentially important and surprising biological
results. Theoretical calculations suggest that the nonparametric
method, based on nonparametric regression, should in fact have
statistical properties nearly the same as if the functions
nonparametrically estimated were known. The methodology used in this
paper can be applied to other settings when the goal of the study is
to model the correlation of two continuous repeated measurement
responses as a function of a covariate, while the two responses of
interest can be measured on the same experimental units but not on the
same subsampling units. In our example, the two responses were
measured in two different regions of the colon. (Joint work with:
Joanne R. Lupton, Allen Chair of Nutrition, Texas A&M University)