Methods for statistical analysis of colonic crypt labelling.

In cancer prevention research, intermediate markers are often used. In colon cancer one such biomarker is the colon crypt labelling index which attempts to measure the proliferation rate for colon tissue. Another suggested biomarker is an upward shift in the location of cell proliferation occurring in the crypt columns. For each person on study, there a varying number of crypt columns available to study the biomarkers, where each crypt column contains on average sixty epithelial cells. The information available for each crypt column is an ordered sequence of zeroes and ones where a one indicates the cell is dividing and a zero indicates it is not. We consider modeling the probability of a cell dividing as some nonlinear function of its position in the crypt column and crypt-specific parameters. Several functions are fit to a large data set. The parameters are estimated using the conditional likelihood function assumed for each crypt column, called a two-stage estimation approach. From the functions considered, a particular model is chosen to be explored in more detail. To study the biomarkers, we reparameterize to the area under the curve and the mode. Through Monte Carlo simulations, the power of these proposed summary measures is compared to the power of the methods currently being used to study the biomarkers. We find that some of the methods currently being used are inappropriate. We also find that our proposed analysis outperforms the commonly used compartmental approaches in detecting an upward shift of cell proliferation, even in the case when the true function is different from the chosen model. A general conclusion from the simulation studies is that a difference in the cell proliferation rate between the groups may affect the analyses used to detect an upward shift. An alternative estimation approach, used instead to estimate person-specific parameters, is also briefly examined. This one-stage estimation approach is found to be much more computationally involved than the two-stage estimation approach. The proposed analysis is also used to analyze two different data sets