1
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Treszoks J, Pal S. On the estimation of interval censored destructive negative binomial cure model. Stat Med 2023; 42:5113-5134. [PMID: 37706586 PMCID: PMC11099949 DOI: 10.1002/sim.9904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Revised: 08/18/2023] [Accepted: 09/01/2023] [Indexed: 09/15/2023]
Abstract
In this article, a competitive risk survival model is considered in which the initial number of risks, assumed to follow a negative binomial distribution, is subject to a destructive mechanism. Assuming the population of interest to have a cure component, the form of the data as interval-censored, and considering both the number of initial risks and risks remaining active after destruction to be missing data, we develop two distinct estimation algorithms for this model. Making use of the conditional distributions of the missing data, we develop an expectation maximization (EM) algorithm, in which the conditional expected complete log-likelihood function is decomposed into simpler functions which are then maximized independently. A variation of the EM algorithm, called the stochastic EM (SEM) algorithm, is also developed with the goal of avoiding the calculation of complicated expectations and improving performance at parameter recovery. A Monte Carlo simulation study is carried out to evaluate the performance of both estimation methods through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We demonstrate the proposed SEM algorithm as the preferred estimation method through simulation and further illustrate the advantage of the SEM algorithm, as well as the use of a destructive model, with data from a children's mortality study.
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Affiliation(s)
- Jodi Treszoks
- Department of Mathematics, University of Texas at Arlington, 411 S. Nedderman Drive, Arlington, TX, 76019, USA
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, 411 S. Nedderman Drive, Arlington, TX, 76019, USA
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2
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Pal S, Peng Y, Aselisewine W, Barui S. A support vector machine-based cure rate model for interval censored data. Stat Methods Med Res 2023; 32:2405-2422. [PMID: 37937365 PMCID: PMC10710011 DOI: 10.1177/09622802231210917] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2023]
Abstract
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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Affiliation(s)
- Suvra Pal
- Department of Mathematics, University of Texas at Arlington, TX, USA
| | - Yingwei Peng
- Department of Public Health Sciences, Queen’s University, Kingston, ON, Canada
| | | | - Sandip Barui
- Quantitative Methods and Operations Management Area, Indian Institute of Management Kozhikode, Kozhikode, KL, India
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3
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Aselisewine W, Pal S. On the integration of decision trees with mixture cure model. Stat Med 2023; 42:4111-4127. [PMID: 37503905 PMCID: PMC11099950 DOI: 10.1002/sim.9850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2023] [Accepted: 07/04/2023] [Indexed: 07/29/2023]
Abstract
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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Affiliation(s)
- Wisdom Aselisewine
- Department of Mathematics, University of Texas at Arlington, Texas, USA 76019
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, Texas, USA 76019
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4
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Pal S, Roy S. On the parameter estimation of Box-Cox transformation cure model. Stat Med 2023. [PMID: 37019798 DOI: 10.1002/sim.9739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Revised: 01/17/2023] [Accepted: 03/27/2023] [Indexed: 04/07/2023]
Abstract
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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Affiliation(s)
- Suvra Pal
- Department of Mathematics, University of Texas at Arlington, 411 S Nedderman Drive, Arlington, Texas, 76019, USA
| | - Souvik Roy
- Department of Mathematics, University of Texas at Arlington, 411 S Nedderman Drive, Arlington, Texas, 76019, USA
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5
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A Stochastic Version of the EM Algorithm for Mixture Cure Model with Exponentiated Weibull Family of Lifetimes. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2022. [DOI: 10.1007/s42519-022-00274-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
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6
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Treszoks J, Pal S. A destructive shifted Poisson cure model for interval censored data and an efficient estimation algorithm. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2067876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Jodi Treszoks
- Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
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7
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Fleming A, Coltrin JD, Medri J, Hilyard C, Tellez R, Symanzik J. Results and student perspectives on a web-scraping assignment from Utah State University's data technologies course to evaluate the African activity in the statistical computing community. Comput Stat 2022:1-25. [PMID: 35465358 PMCID: PMC9012946 DOI: 10.1007/s00180-022-01222-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 03/21/2022] [Indexed: 11/17/2022]
Abstract
In 2019, members of the Executive Committee of the International Association for Statistical Computing (IASC) were contacted by members of the IASC from Africa asking whether it would be feasible to establish a new regional IASC section in Africa. The establishment of a new regional section requires several steps that are outlined in the IASC Statutes at https://iasc-isi.org/statutes/. The approval likely depends on whether the proposed new regional section has the potential to conduct typical section activities, such as organizing regional conferences, workshops, and short courses. To establish whether it is feasible to add a regional section in Africa, the IASC must know whether there is currently enough high-level activity within African countries with respect to computational statistics. To answer this question, we looked at author affiliations of articles published in the Springer journal Computational Statistics (COST) and the Elsevier journal Computational Statistics & Data Analysis (CSDA) from 2015 to 2020 and used these data as a proxy to compare author productivity for authors with an affiliation in Africa in 2019 and 2020, compared to authors with an affiliation in Latin America in 2015 and 2016. This article looks at quantitative results to the questions above, provides insight on how students from Utah State University's STAT 5080/6080 "Data Technologies" course from the Fall 2019 semester used web scraping techniques in a homework assignment to gather author affiliations from COST and CSDA to answer these questions, and includes the evaluation of student feedback obtained after the end of the course.
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Affiliation(s)
- Adelyn Fleming
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322–3900 USA
| | - Joanna D. Coltrin
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322–3900 USA
| | - Jhonatan Medri
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322–3900 USA
| | - Cody Hilyard
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322–3900 USA
| | - Rigoberto Tellez
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322–3900 USA
| | - Jürgen Symanzik
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322–3900 USA
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8
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Wang P, Pal S. A two-way flexible generalized gamma transformation cure rate model. Stat Med 2022; 41:2427-2447. [PMID: 35262947 DOI: 10.1002/sim.9363] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2021] [Revised: 02/11/2022] [Accepted: 02/14/2022] [Indexed: 02/01/2023]
Abstract
We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.
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Affiliation(s)
- Pei Wang
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
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9
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Balakrishnan N, Barui S, Milienos FS. Piecewise linear approximations of baseline under proportional hazards based COM-Poisson cure models. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2032157] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - S. Barui
- Quantitative Methods and Operations Management Area, Indian Institute of Management Kozhikode, Kozhikode, Kerala, India
| | - F. S. Milienos
- Department of Sociology, Panteion University of Social and Political Sciences, Athens, Greece
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10
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Pal S, Roy S. A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate Model and a Simulation Study: Illustration with Negative Binomial Competing Risks. COMMUN STAT-SIMUL C 2022; 51:6866-6880. [PMID: 36568126 PMCID: PMC9782754 DOI: 10.1080/03610918.2020.1819321] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
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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Affiliation(s)
- Suvra Pal
- Department of Mathematics, University of Texas at Arlington, TX, 76019, USA.,Corresponding author. Tel.: 817-272-7163
| | - Souvik Roy
- Department of Mathematics, University of Texas at Arlington, TX, 76019, USA
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11
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Affiliation(s)
- Jia-Han Shih
- Institute of Statistical Science, Academia Sinica, Taipei, Taiwan
| | - Takeshi Emura
- Department of Information Management, Chang Gung University, Taoyuan, Taiwan
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12
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Pal S, Roy S. On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks. STAT NEERL 2021. [DOI: 10.1111/stan.12237] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Suvra Pal
- Department of Mathematics The University of Texas at Arlington Arlington Texas USA
| | - Souvik Roy
- Department of Mathematics The University of Texas at Arlington Arlington Texas USA
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13
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Shinohara S, Lin YH, Michimae H, Emura T. Dynamic lifetime prediction using a Weibull-based bivariate failure time model: a meta-analysis of individual-patient data. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1855449] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Sayaka Shinohara
- Department of Clinical Medicine (Biostatistics), Kitasato University, Tokyo, Japan
| | - Yuan-Hsin Lin
- Department of Information Management, Chang Gung University, Taoyuan City, Taiwan
| | - Hirofumi Michimae
- Department of Clinical Medicine (Biostatistics), Kitasato University, Tokyo, Japan
| | - Takeshi Emura
- Department of Information Management, Chang Gung University, Taoyuan City, Taiwan
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14
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Ramires TG, Ortega EM, Lemonte AJ, Hens N, Cordeiro GM. A flexible bimodal model with long-term survivors and different regression structures. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2018.1524902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Thiago G. Ramires
- Department of Mathematics, Federal University of Tecnology – Paraná, Apucarana, Brazil
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-Biostat), University of Hasselt, Hasselt, Belgium
| | - Edwin M.M. Ortega
- Department of Exact Sciences, University of São Paulo, São Paulo, Brazil
| | - Artur J. Lemonte
- Department of Statistics, Federal University of Rio Grande do Norte, Rio Grande do Norte, Brazil
| | - Niel Hens
- Department of Statistics, Federal University of Rio Grande do Norte, Rio Grande do Norte, Brazil
- Centre for Health Economic Research and Modelling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
| | - Gauss M. Cordeiro
- Department of Statistics, Federal University of Pernambuco, Pernambuco, Brazil
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15
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Davies K, Pal S, Siddiqua JA. Stochastic EM algorithm for generalized exponential cure rate model and an empirical study. J Appl Stat 2020; 48:2112-2135. [DOI: 10.1080/02664763.2020.1786676] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Katherine Davies
- Department of Statistics, University of Manitoba, Winnipeg, Canada
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, Arlington, TX, USA
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16
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Majakwara J, Pal S. On some inferential issues for the destructive COM-Poisson-generalized gamma regression cure rate model. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1642483] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Jacob Majakwara
- School of Statistics and Actuarial Science, University of the Witwatersrand, Johannesburg, South Africa
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
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18
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Wiangnak P, Pal S. Gamma lifetimes and associated inference for interval-censored cure rate model with COM–Poisson competing cause. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2017.1321769] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Piyachart Wiangnak
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
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19
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Pal S, Balakrishnan N. Likelihood inference for COM-Poisson cure rate model with interval-censored data and Weibull lifetimes. Stat Methods Med Res 2017; 26:2093-2113. [DOI: 10.1177/0962280217708686] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, we consider a competing cause scenario and assume the number of competing causes to follow a Conway–Maxwell Poisson distribution which can capture both over and under dispersion that is usually encountered in discrete data. Assuming the population of interest having a component cure and the form of the data to be interval censored, as opposed to the usually considered right-censored data, the main contribution is in developing the steps of the expectation maximization algorithm for the determination of the maximum likelihood estimates of the model parameters of the flexible Conway–Maxwell Poisson cure rate model with Weibull lifetimes. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination within the Conway–Maxwell Poisson distribution is addressed using the likelihood ratio test and information-based criteria to select a suitable competing cause distribution that provides the best fit to the data. A simulation study is also carried out to demonstrate the loss in efficiency when selecting an improper competing cause distribution which justifies the use of a flexible family of distributions for the number of competing causes. Finally, the proposed methodology and the flexibility of the Conway–Maxwell Poisson distribution are illustrated with two known data sets from the literature: smoking cessation data and breast cosmesis data.
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Affiliation(s)
- Suvra Pal
- Department of Mathematics, University of Texas, Arlington, TX, USA
| | - N Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada
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20
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Balakrishnan N, Barui S, Milienos FS. Proportional hazards under Conway–Maxwell-Poisson cure rate model and associated inference. Stat Methods Med Res 2017; 26:2055-2077. [DOI: 10.1177/0962280217708683] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Cure rate models or long-term survival models play an important role in survival analysis and some other applied fields. In this article, by assuming a Conway–Maxwell–Poisson distribution under a competing cause scenario, we study a flexible cure rate model in which the lifetimes of non-cured individuals are described by a Cox’s proportional hazard model with a Weibull hazard as the baseline function. Inference is then developed for a right censored data by the maximum likelihood method with the use of expectation-maximization algorithm and a profile likelihood approach for the estimation of the dispersion parameter of the Conway–Maxwell–Poisson distribution. An extensive simulation study is performed, under different scenarios including various censoring proportions, sample sizes, and lifetime parameters, in order to evaluate the performance of the proposed inferential method. Discrimination among some common cure rate models is then done by using likelihood-based and information-based criteria. Finally, for illustrative purpose, the proposed model and associated inferential procedure are applied to analyze a cutaneous melanoma data.
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Affiliation(s)
- N Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Canada
| | - S Barui
- Department of Mathematics and Statistics, McMaster University, Canada
| | - FS Milienos
- Department of Philosophy, Education and Psychology, University of Ioannina, Greece
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21
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A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling. Comput Stat Data Anal 2017. [DOI: 10.1016/j.csda.2016.10.001] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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22
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Ortega EMM, Cordeiro GM, Hashimoto EM, Suzuki AK. Regression models generated by gamma random variables with long-term survivors. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2017. [DOI: 10.5351/csam.2017.24.1.043] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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23
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Pal S, Balakrishnan N. An EM type estimation procedure for the destructive exponentially weighted Poisson regression cure model under generalized gamma lifetime. J STAT COMPUT SIM 2016. [DOI: 10.1080/00949655.2016.1247843] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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24
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Tahir MH, Cordeiro GM. Compounding of distributions: a survey and new generalized classes. JOURNAL OF STATISTICAL DISTRIBUTIONS AND APPLICATIONS 2016. [DOI: 10.1186/s40488-016-0052-1] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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25
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Barmalzan G, Najafabadi ATP, Balakrishnan N. Orderings for series and parallel systems comprising heterogeneous exponentiated Weibull-geometric components. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2016.1222432] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Ghobad Barmalzan
- Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran
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27
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Pal S, Balakrishnan N. Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data. Comput Stat 2016. [DOI: 10.1007/s00180-016-0660-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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28
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Gallardo DI, Bolfarine H, Pedroso-de-Lima AC. An EM algorithm for estimating the destructive weighted Poisson cure rate model. J STAT COMPUT SIM 2015. [DOI: 10.1080/00949655.2015.1071375] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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