Abstract
In this paper, we develop the steps of the expectation maximization algorithm (EM algorithm) for the determination of the maximum likelihood estimates (MLEs) of the parameters of the destructive exponentially weighted Poisson cure rate model in which the lifetimes are assumed to be Weibull. This model is more flexible than the promotion time cure rate model as it provides an interesting and realistic interpretation of the biological mechanism of the occurrence of an event of interest by including a destructive process of the initial number of causes in a competitive scenario. The standard errors of the MLEs are obtained by inverting the observed information matrix. An extensive Monte Carlo simulation study is carried out to evaluate the performance of the developed method of estimation. Finally, a known melanoma data are analyzed to illustrate the method of inference developed here. With these data, a comparison is also made with the scenario when the destructive mechanism is not included in the analysis.
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The second author expresses his thanks to the Natural Sciences and Engineering Research Council of Canada for funding this research through an individual discovery grant. The authors are also thankful to the editor and anonymous reviewers for their useful comments and suggestions on an earlier version of this manuscript which led to this improved one.
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Appendix: Expressions useful in M-step
Appendix: Expressions useful in M-step
where
The above quantities are all defined for \(l,l^{\prime }=0,1,\ldots ,s,\,x_{i0}=1 \forall i=1,2,\ldots ,n,\) and \(k,k^{\prime }=1,2,\ldots ,s^\prime .\)
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Pal, S., Balakrishnan, N. Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data. Comput Stat 32, 429–449 (2017). https://doi.org/10.1007/s00180-016-0660-8
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DOI: https://doi.org/10.1007/s00180-016-0660-8