Proportional Odds under Conway-Maxwell-Poisson Cure Rate Model and Associated Likelihood Inference

N. Balakrishnan; T. Feng

doi:10.19139/soic.v6i3.573

N. Balakrishnan Department of Mathematics and Statistics, McMaster University,Canada
T. Feng Department of Mathematics and Statistics, McMaster University,Canada

DOI: https://doi.org/10.19139/soic.v6i3.573

Keywords: Cure rate model, Long-term survivor, Conway-Maxwell-Poisson distribution, Weibull distribution, Log-logistic distribution, Maximum likelihood estimator, Expectation-Maximization algorithm, Profile likelihood, Akaike information criterion, Bayesian informa

Abstract

Cure rate models are useful while modelling lifetime data involving long time survivors. In this work, we discuss a flexible cure rate model by assuming the number of competing causes for the event of interest to follow the Conway-Maxwell Poisson distribution and the lifetimes of the non-cured individuals to follow a proportional odds model. The baseline distribution is considered to be either Weibull or log-logistic distribution. Under right censoring, we develop the maximum likelihood estimators using EM algorithm. Model discrimination among some well-known special cases are discussed under both likelihood- and information-based criteria. An extensive simulation study is carried out to examine the performance of the proposed model and the inferential methods. Finally, a cutaneous melanoma dataset is analyzed for illustrative purpose.

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