A weighted zero-inflated Poisson model for estimation of recurrence of adenomas

In this article, a weighted zero-inflated Poisson (W-ZIP) approach to modelling colorectal adenoma data is used in which the number of recurrent adenomas is subject to measurement error and some participants might have their follow-up colonoscopy conducted before the end of trial. The weights are used to adjust for varying follow-up and obtained from a nonparametric survival function derived from the lengths of follow-up. It is shown that logistic regression (LR) and survival analysis tend to underestimate recurrence rate due to measurement error on the status of recurrence. A simulation study shows that the W-ZIP model is robust to the assumption of the underlying distribution of time-to-recurrence and is less affected by misclassification at follow-up colonoscopy when compared with LR and survival analysis approaches. The method described here is illustrated with an example from a colon cancer study.