A truncated poisson regression model with applications to occurrence of adenomatous polyps

Adenomatous polyps are considered as the dominant precursor lesion of colorectal cancer. A phase III colorectal cancer prevention trial, conducted by the Arizona Cancer Center, concerns the ability of wheat bran fibre supplement to reduce the recurrence of adenomatous polyps. All participants in the study are to have had colorectal polyps detected and removed during a baseline (qualifying) colonoscopy within three months prior to enrolment. In this paper, our interest focuses on occurrence of adenomatous polyps at the baseline colonoscopy. We use a truncated Poisson model to fit these types of data. We develop a regression model to assess the effects of explanatory factors on the positive counting variable. We fit truncated Poisson parameters by a log-linear regression model and estimate regression parameters by the maximum likelihood procedure. Finally, we apply it to the baseline colonoscopy data from the Wheat Bran Fiber study.