The Conway–Maxwell–Poisson-generalized gamma regression model with long-term survivors

Cancho, Vicente G.; Ortega, Edwin M. M.; Barriga, Gladys Dorotea Cacsire; Hashimoto, Elizabeth M.

doi:10.1080/00949655.2010.491827

Cited by 8 publications

(5 citation statements)

References 27 publications

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“…. , ∞; γ > 0, (1) where f (π , γ ) = ∞ n=0 π n (n!) γ is the normalizing constant and infinite series and π is the location parameter.…”

Section: Figurementioning

confidence: 99%

“…Figure 1 presents the probability mass function (PMF) for different simulated data from the COMP distribution. It is noted that the COMP (3,1) is equivalent to the Poisson with a parameter of π = 3, and COMP(0.55,0) is equivalent to the geometric distribution with a parameter of π = 0.55. In the following two cases, COMP (3,1.5) and COMP (3,0.85) refer to the cases of under-and over-dispersion in the COMP distribution, respectively.…”

Section: Figurementioning

confidence: 99%

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Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Abonazel

Awwad²,

Eldin³

et al. 2023

Front. Appl. Math. Stat.

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The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. The theoretical comparison of the proposed estimator with the ridge, Liu, and modified one-parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and to compare it with the ridge, Liu, and modified one-parameter Liu estimators. The results showed the superiority of the proposed estimator as it has the smallest MSE value.

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“…. , ∞; γ > 0, (1) where f (π , γ ) = ∞ n=0 π n (n!) γ is the normalizing constant and infinite series and π is the location parameter.…”

Section: Figurementioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Abonazel

Awwad²,

Eldin³

et al. 2023

Front. Appl. Math. Stat.

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“…Rodrigues et al (2009) proposed a unification of the mixture cure rate model and the promotion time cure rate model by assuming a Conway Maxwell Poisson (COM-Poisson) distribution for the latent risk factors. For the use of the COM-Poisson distribution in the context of cure rate models, interested readers may refer to the works of Cancho et al (2011), Balakrishnan and Pal (2015a); ; see also Balakrishnan and Feng (2018). For developing estimation methods and inference, researchers have relied on different frameworks.…”

Section: Introductionmentioning

confidence: 99%

On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks

Pal

Roy

2021

Statistica Neerlandica

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A new estimation method is proposed founded upon a nonlinear conjugate gradient-type algorithm having an efficient line search technique for cure rate models with competing risks, which are subject to elimination. An extensive simulation study is carried out to compare the performance of the proposed algorithm with some existing algorithms, including other conjugate gradient-type algorithms and the expectation maximization algorithm. For this purpose, it is assumed that the initial competing risks follow an exponentially weighted Poisson distribution. In particular, it is shown that that the proposed algorithm produces estimates that are more accurate and efficient (i.e., the bias and root mean square errors are smaller), specifically with respect to the parameters related to the cure rate. Although for the purpose of simulation study an exponentially weighted Poisson competing risks distribution is assumed, the proposed algorithm incorporates a generic framework that can accommodate any competing risks distribution. Finally, a real data application is provided.

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“…In this case, the cure rate is given by 1 Z(η,φ) . Note that if φ → ∞ in (3), the COM-Poisson model reduces to the mixture model in (1) with p 0 = 1 1+η , whereas, if φ = 1 in (3), the COM-Poisson model reduces to the promotion time model in (2); see Cancho et al (2011), Balakrishnan and Pal (2015), , and Balakrishnan and Feng (2018) for some recent works on cure rate model using COM-Poisson distribution. To develop the associated inferential procedures, several approaches have been proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

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

Pal¹,

Roy²

2019

Preprint

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

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The Conway–Maxwell–Poisson-generalized gamma regression model with long-term survivors

Cited by 8 publications

References 27 publications

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks

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

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