An EM algorithm for estimating the destructive weighted Poisson cure rate model

Gallardo, Diego I.; Bolfarine, Heleno; Pedroso-de-Lima, Antonio Carlos

doi:10.1080/00949655.2015.1071375

Cited by 18 publications

(15 citation statements)

References 21 publications

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“…Since this pioneering work, few other researchers have proposed extensions of this destructive cure rate model. In this regard, interested readers may refer to Gallardo et al (2016) and Balakrishnan (2016, 2017); see also Cancho et al (2013) and Pal et al (2018). In the context of these aforementioned works on cure rate models and destructive cure rate models, the development of the expectation maximization (EM) algorithm or, simply, the direct numerical maximization of the log-likelihood function turns out to be the commonly used tools for maximum likelihood estimation of the model parameters.…”

Section: Introductionmentioning

confidence: 99%

“…In the context of destructive cure rate models, Gallardo et al (2016) developed a variation of the EM algorithm, where they showed that the objective function to be maximized can be decomposed into simpler functions and each simple function can be maximized separately. Although this turned out to be an advantage over the EM algorithms developed by Balakrishnan (2016, 2017), the authors still had to depend on the profile likelihood technique, also called the grid search technique.…”

Section: Introductionmentioning

confidence: 99%

“…Although this turned out to be an advantage over the EM algorithms developed by Balakrishnan (2016, 2017), the authors still had to depend on the profile likelihood technique, also called the grid search technique. In this regard, Gallardo et al (2017) took a specific example of negative binomial competing risks and showed how the profile likelihood approach can be avoided in the development of the EM algorithm, which is a much preferred procedure when compared to the EM algorithms of Gallardo et al (2016) and Pal and Balakrishnan (2016).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…As far as developing the likelihood inference and finding the maximum likelihood estimates (MLEs) are concerned in the given context, the expectation maximization (EM) algorithm is a very popular technique. Interested readers may refer to Cancho et al (2013), Gallardo et al (2016), Pal and Balakrishnan (2017b), and Wiangnak and Pal (2018).…”

Section: Introductionmentioning

confidence: 99%

A Simplified Stochastic EM Algorithm for Cure Rate Model with Negative Binomial Competing Risks: An Application to Breast Cancer Data

Pal¹

2020

Preprint

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In this paper, we consider a long-term survival model under a competing risks scenario. Since the number of competing risks is unobserved, we assume it to follow a negative binomial distribution that can capture both over-and under-dispersion we usually encounter when modeling count data. The distribution of the progression time, corresponding to each competing risk, is associated with a set of risk factors that allow us to capture the non-homogeneous patient population. We also provide flexibility in modeling the cure or the long-term survival rate, which is considered as a function of risk factors. Considering the latent competing risks as missing data, we develop a variation of the well-known expectation maximization (EM) algorithm, called the stochastic EM algorithm (SEM), which is the main contribution of this paper. We show that the SEM algorithm avoids calculation of complicated expectations, which is a major advantage of the SEM algorithm over the EM algorithm. Our proposed procedure allows the objective function to be maximized to be split into two simpler functions, one corresponding to the parameters associated with the cure rate and the other corresponding to the parameters associated with the progression times. The advantage of this approach is that each function, with lower parameter dimension, can be maximized independently. Through an extensive Monte Carlo simulation study we show the performance of the proposed SEM algorithm through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We also show that the SEM algorithm is not sensitive to the choice of the initial values. Finally, for illustration, we analyze a breast cancer survival data.

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“…is expectation taken with respect to the Poisson pmf. Gallardo et al (2016) developed an EM algorithm based technique for the same model for estimating the parameters for the three special cases, viz., destructive length-biased Poisson, destructive exponentially weighted Poisson and destructive negative binomial cure models. An extension of this model was described by Borges et al (2012) by creating a correlation structure between the initiated cells using the generalized power series distribution.…”

Section: Introductionmentioning

confidence: 99%

Destructive cure rate models under proportional odds and associated likelihood inference

Tian

2019

Communications in Statistics: Case Studies, Data Analysis and A

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In survival analysis, cure models have gained much importance due to rapid advancements in medical sciences. More recently, a subset of cure models, called destructive cure models, have been studied extensively under competing risks scenario wherein initial competing risks undergo a destructive process, such as under a chemotherapy. In this article, we study destructive cure models by assuming a flexible weighted Poisson distribution (exponentially weighted Poisson, length biased Poisson and negative binomial distributions) for the initial number of competing causes and with lifetimes of the susceptible individuals following proportional hazards. The expectation-maximization (EM) algorithm and profile likelihood approach are made use of for estimating the model parameters. An extensive simulation study is carried out under various parameter settings to examine the properties of the models, and the accuracy and robustness of the proposed estimation technique. Effects of model mis-specification on the parameter estimates are also discussed in detail. Finally, for the illustration of the proposed methodology, a real-life cutaneous melanoma data set is analyzed.

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An EM algorithm for estimating the destructive weighted Poisson cure rate model

Cited by 18 publications

References 21 publications

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

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

A Simplified Stochastic EM Algorithm for Cure Rate Model with Negative Binomial Competing Risks: An Application to Breast Cancer Data

Destructive cure rate models under proportional odds and associated likelihood inference

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