STATISTICAL-ANALYSIS OF ABERRANT CRYPT ASSAYS FOR COLON-CANCER PROMOTION STUDIES

The size of aberrant crypt foci in rodent colons is a short-term assay for the promotion of colon carcinogenesis. An approximate model for t he number of aberrant crypts in a focus is derived by assuming a branc hing process with a gamma lifetime. Maximum likelihood estimation can be implemented using symbolic manipulation packages. Although in most cases the model provides a reasonable fit for the distribution of the number of aberrant crypts per focus, there is some evidence of lack of fit. A more robust analysis can be based on summarizing the data for each animal by their mean number of aberrant crypts per focus. The bra nching process with gamma lifetime is used to obtain expressions for t he functional relation between the variance of the number of aberrant crypts per focus and their mean. It is shown that in most cases this r elation is quadratic. The quadratic relation also holds for other life time distributions. The parameters of the quadratic relation can be es timated by pseudolikelihood. An experiment for assessing the promotion al effect of the compound HMF is used for illustration.