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In this paper, we propose a new estimation methodology based on a projectednon-linear conjugate gradient (PNCG) algorithm with an efficient line searchtechnique. We develop a general PNCG algorithm for a survival modelincorporating a proportion cure under a competing risks setup, where theinitial number of competing risks are exposed to elimination after an initialtreatment (known as destruction). In the literature, expectation maximization(EM) algorithm has been widely used for such a model to estimate the modelparameters. Through an extensive Monte Carlo simulation study, we compare theperformance of our proposed PNCG with that of the EM algorithm and show theadvantages of our proposed method. Through simulation, we also show theadvantages of our proposed methodology over other optimization algorithms(including other conjugate gradient type methods) readily available as Rsoftware packages. To show these we assume the initial number of competingrisks to follow a negative binomial distribution although our general algorithmallows one to work with any competing risks distribution. Finally, we apply ourproposed algorithm to analyze a well-known melanoma data.

A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate  Model and a Simulation Study: Illustration with Negative Binomial Competing  Risks