Parametric and nonparametric methods for understanding the relationship between carcinogen-induced DNA adduct levels in distal and proximal regions of the colon
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abstract
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 diet. 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. Parametric and nonparametric methods are developed and applied to a dataset 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 article 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, whereas 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. 2001 American Statistical Association.
