A Stochastic Version of the EM Algorithm for Mixture Cure Model with Exponentiated Weibull Family of Lifetimes

Pal, Suvra; Barui, Sandip; Davies, Katherine F.; Mishra, Nutan

doi:10.1007/s42519-022-00274-8

Cited by 10 publications

(9 citation statements)

References 54 publications

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“…It will be interesting to see how the NCG algorithm performs in these cases and how it compares with the EM algorithm or a variation of the EM algorithm. [47][48][49] Regarding the complexity order of the NCG algorithm, it has been recently shown that computing the complexity of NCG algorithm is a challenging task for non-convex problems. 50 The only known complexity result is for finite dimensional convex quadratic problems, when the NCG algorithm converges in finitely many steps, much faster than other optimization algorithms.…”

Section: Discussionmentioning

confidence: 99%

“…The NCG algorithm may be useful for other complicated cure rate models, for example, the Conway‐Maxwell (COM) Poisson cure rate model and the destructive COM‐Poisson cure rate model, 15,22 where a profile likelihood approach has been proposed for the estimation of the COM‐Poisson shape parameter

\phi

due to the flatness of the likelihood surface with respect to

\phi

. It will be interesting to see how the NCG algorithm performs in these cases and how it compares with the EM algorithm or a variation of the EM algorithm 47‐49 . Regarding the complexity order of the NCG algorithm, it has been recently shown that computing the complexity of NCG algorithm is a challenging task for non‐convex problems 50 .…”

Section: Discussionmentioning

confidence: 99%

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On the parameter estimation of Box‐Cox transformation cure model

Pal

Roy

2023

Statistics in Medicine

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We propose an improved estimation method for the Box‐Cox transformation (BCT) cure rate model parameters. Specifically, we propose a generic maximum likelihood estimation algorithm through a non‐linear conjugate gradient (NCG) method with an efficient line search technique. We then apply the proposed NCG algorithm to BCT cure model. Through a detailed simulation study, we compare the model fitting results of the NCG algorithm with those obtained by the existing expectation maximization (EM) algorithm. First, we show that our proposed NCG algorithm allows simultaneous maximization of all model parameters unlike the EM algorithm when the likelihood surface is flat with respect to the BCT index parameter. Then, we show that the NCG algorithm results in smaller bias and noticeably smaller root mean square error of the estimates of the model parameters that are associated with the cure rate. This results in more accurate and precise inference on the cure rate. In addition, we show that when the sample size is large the NCG algorithm, which only needs the computation of the gradient and not the Hessian, takes less CPU time to produce the estimates. These advantages of the NCG algorithm allows us to conclude that the NCG method should be the preferred estimation method over the already existing EM algorithm in the context of BCT cure model. Finally, we apply the NCG algorithm to analyze a well‐known melanoma data and show that it results in a better fit when compared to the EM algorithm.

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Section: Discussionmentioning

confidence: 99%

\phi

due to the flatness of the likelihood surface with respect to

\phi

Section: Discussionmentioning

confidence: 99%

On the parameter estimation of Box‐Cox transformation cure model

Pal

Roy

2023

Statistics in Medicine

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“…In such a case, the Kaplan-Meier survival curve shows a long plateau that levels off to a non-zero value, indicating the presence of a cured subgroup. [1][2][3][4][5] To capture the mixture patient population, mixture cure model (MCM) and associated estimation methods have been proposed as extensions to the standard survival models; see the recent monograph by Peng and Yu for a book-length account on MCM. 6 The cured statuses of patients or their survival probabilities are often the primary parameters of interest in predictions and prognoses.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, the overall patient population can be regarded as a mixture of these two groups of patients. In such a case, the Kaplan‐Meier survival curve shows a long plateau that levels off to a non‐zero value, indicating the presence of a cured subgroup 1‐5 …”

Section: Introductionmentioning

confidence: 99%

On the integration of decision trees with mixture cure model

Aselisewine,

Pal

2023

Statistics in Medicine

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The mixture cure model is widely used to analyze survival data in the presence of a cured subgroup. Standard logistic regression‐based approaches to model the incidence may lead to poor predictive accuracy of cure, specifically when the covariate effect is non‐linear. Supervised machine learning techniques can be used as a better classifier than the logistic regression due to their ability to capture non‐linear patterns in the data. However, the problem of interpret‐ability hangs in the balance due to the trade‐off between interpret‐ability and predictive accuracy. We propose a new mixture cure model where the incidence part is modeled using a decision tree‐based classifier and the proportional hazards structure for the latency part is preserved. The proposed model is very easy to interpret, closely mimics the human decision‐making process, and provides flexibility to gauge both linear and non‐linear covariate effects. For the estimation of model parameters, we develop an expectation maximization algorithm. A detailed simulation study shows that the proposed model outperforms the logistic regression‐based and spline regression‐based mixture cure models, both in terms of model fitting and evaluating predictive accuracy. An illustrative example with data from a leukemia study is presented to further support our conclusion.

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“…Introduced by Boag 1 and exclusively studied by Berkson and Gage, 2 the mixture cure rate model is perhaps the most popular cure rate model. 3 If T * denotes the lifetime of a susceptible (not cured) subject, then, the actual lifetime T for any subject can be modeled by where J is a cure indicator with J = 0 if an individual is cured and J = 1 otherwise. Furthermore, considering S p false( t false) = P false( T > t false) and S u false( t false) = P false( T * > t false) as the respective survival functions corresponding to T and T *, we can express where π = P false( J = 1 false).…”

Section: Introductionmentioning

confidence: 99%

A support vector machine-based cure rate model for interval censored data

Pal,

Peng,

Aselisewine

et al. 2023

Stat Methods Med Res

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The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic function. This readily implies that the boundary classifying the cured and uncured subjects is linear. In this article, we propose a new mixture cure rate model based on interval censored data that uses the support vector machine to model the effect of covariates on the uncured or the cured probability (i.e. on the incidence part of the model). Our proposed model inherits the features of the support vector machine and provides flexibility to capture classification boundaries that are nonlinear and more complex. The latency part is modeled by a proportional hazards structure with an unspecified baseline hazard function. We develop an estimation procedure based on the expectation maximization algorithm to estimate the cured/uncured probability and the latency model parameters. Our simulation study results show that the proposed model performs better in capturing complex classification boundaries when compared to both logistic regression-based and spline regression-based mixture cure rate models. We also show that our model’s ability to capture complex classification boundaries improve the estimation results corresponding to the latency part of the model. For illustrative purpose, we present our analysis by applying the proposed methodology to the NASA’s Hypobaric Decompression Sickness Database.

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A Stochastic Version of the EM Algorithm for Mixture Cure Model with Exponentiated Weibull Family of Lifetimes

Cited by 10 publications

References 54 publications

On the parameter estimation of Box‐Cox transformation cure model

On the parameter estimation of Box‐Cox transformation cure model

On the integration of decision trees with mixture cure model

A support vector machine-based cure rate model for interval censored data

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