Statistical Modelling 5 (2005), 210215
Joint modelling of recurrence and progression of
adenomas: a latent variable approach
Chiu-Hsieh Hsu
Mel and Enid Zuckerman College of Public Health and Arizona Cancer Center
University of Arizona
Tucson, AZ 85724
U.S.A.
eMail:
phsu@azcc.arizona.edu
Abstract:
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.
Keywords:
latent variable; measurement error; mixture distribution;
robust weight function; variable
follow-up; zero-inflated poisson
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