Joint modelling of recurrence and progression of adenomas: a latent variable approach

In this paper, we treat the number of recurrent adenomatous polyps as a latent variable and then use a mixture distribution to model the number of observed recurrent adenomatous polyps. This approach is equivalent to zero-inflated Poisson regression, which is a method used to analyse count data with excess zeros. In a zero-inflated Poisson model, a count response variable is assumed to be distributed as a mixture of a Poisson distribution and a distribution with point mass of one at zero. In many cancer studies, patients often have variable follow-up. When the disease of interest is subject to late onset, ignoring the length of follow-up will underestimate the recurrence rate. In this paper, we modify zero-inflated Poisson regression through a weight function to incorporate the length of follow-up into analysis. We motivate, develop, and illustrate the methods described here with an example from a colon cancer study.