Estimating the effects of the factors underlying the progression of Familial Adenomatous Polyposis using Longitudinal Com-­‐Poisson Model

Abstract

This paper aims at developing a statistical model capable of quantifying the effects of various factors on the progression of Familial Adenomatous Polyposis (FAP), a genetic disorder affecting the colon and rectum in human beings. The progression of FAP in affected individuals is monitored by counting the number of polyps developed over a period of time. These count responses repeatedly observed over time are over-­‐dispersed and highly correlated resulting into a complicated longitudinal count data structure, which render the application of commonly, used Gaussian regression model useless. We designed a statistical model based on Com-­‐ Poisson distribution, which can efficiently analyze such a data structure. The estimates of over-­‐dispersion as well as correlation parameters confirm the nature of real data. Analysis of the model indicates that males are 50% more at risk to develop polyps than females. With respect to the type of treatment, the application of vitamin C and E with high fiber treatment is a better remedy followed by vitamin C and E only as compared to placebo. In men as well as in women, initial polyp counts positively affect the polyp counts at a given time.

KEY WORDS: Familial adenomatous polyposis; Longitudinal responses; Correlation and overdispersion; Com-­ ‐Poisson model