A Projected Non-Linear Conjugate Gradient Algorithm for Destructive Negative Binomial Cure Rate Model
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In this paper, we propose a new estimation methodology based on a projected non-linear conjugate gradient (PNCG) algorithm for the destructive negative binomial cure rate model. We show that the PNCG algorithm can simultaneously maximize all model parameters even though the likelihood surface is flat with respect to some model parameters, where, in such a scenario, a profile likelihood approach has been proposed in the literature. We compare the performance of the PNCG algorithm with the well studied expectation maximization (EM) algorithm and show, in particular, that the PNCG algorithm results in more precise and accurate estimates of cure rates. We further show that the PNCG algorithm is computationally less expensive when compared to the EM algorithm with profile likelihood. Finally, we apply the proposed PNCG algorithm on a well-known melanoma data.
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