Likelihood Inference for Flexible Cure Rate Models in the Context of Infectious Diseases with Multiple Exposures
Abstract
Cure rate models are mostly used to study data arising from cancer clinical
trials. Its use in the context of infectious diseases has not been explored well. In 2007,
Tournoud and Ecochard rst proposed a mechanistic formulation of cure rate model in
the context of infectious diseases with multiple exposures to infection. However, they
assumed a simple Poisson distribution to capture the unobserved number of pathogens
at each exposure time. In this thesis, we propose a new
exible cure rate model
to study infectious diseases with discrete multiple exposures to infection. This new
model uses the Conway-Maxwell Poisson (COM-Poisson) distribution to model the
number of competing pathogens at each moment of exposure. This new formulation
takes into account both over-dispersion and under-dispersion with respect to the count
on pathogens at each time of exposure and includes the model proposed by Tournoud
and Ecochard as a special case. We also propose a new estimation algorithm based on
the expectation maximization (EM) algorithm to calculate the maximum likelihood
estimates of the model parameters. Infectious diseases data are often right censored,
and the EM algorithm can be utilized to e ciently determine the maximum likelihood
iv
estimates of the underlying model. We carry out a detailed Monte Carlo simulation
study to demonstrate the performance of the proposed estimation algorithm. The
exibility of our proposed model also allows us to carry out a model discrimination,
which we do using both likelihood ratio test and information-based criteria. Finally,
to illustrate our proposed model, we analyze a recently collected infectious data.