A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling

Rocha, Ricardo; Nadarajah, Saraless; Tomazella, Vera; Louzada, Francisco

doi:10.1016/j.csda.2016.10.001

Cited by 29 publications

(20 citation statements)

References 38 publications

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“…This algorithm is similar to that presented by Rocha et al (2017). An R function for generating random samples based on these steps is presented in the Appendix.…”

Section: A Simulation Methods For a Random Variable With A Modified Gomentioning

confidence: 99%

“…In this paper we propose Bayesian and frequentist approaches to a model based on the modified Gompertz distribution, considering survival data in presence of a cure fraction. More recently a number of new families of defective distributions have been proposed in the literature, such as those based on the Kumaraswamy Rocha et al (2015) and the Marshall-Olkin families Rocha et al (2017). However, in the present study, the modified Gompertz distribution was preferred because of its computational simplicity and the ease of interpretation of their parameters.…”

Section: Introductionmentioning

confidence: 94%

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Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Application to the Cervical Carcinoma Study

Santos

Achcar

Martínez

2017

CeN

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Survival analysis is a class of statistical methods to study the time until the occurrence of a specified event. The usual methods assume that all individuals under study are subjects to the event the interest. However, there are situations where this case is unrealistic. For example, in a clinical research, a proportion of patients could respond favourably to the treatment under investigation and consequently they would not die from the disease. Models based on defective distributions are a suitable way to analyse data with these characteristics. In this paper, we present Bayesian and maximum likelihood inference for the defective Gompertz cure rate model in presence of covariates. An example with application to disease-free survival of women treated for cervical carcinoma is used to illustrate the proposed methodology. In the Bayesian analysis, posterior distributions of parameters are estimated using the Markov chain Monte Carlo (MCMC) method. R, SAS and OpenBUGS codes are provided in the appendix at the end of the paper so that reader can carry out their own analysis.

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“…This algorithm is similar to that presented by Rocha et al (2017). An R function for generating random samples based on these steps is presented in the Appendix.…”

Section: A Simulation Methods For a Random Variable With A Modified Gomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Application to the Cervical Carcinoma Study

Santos

Achcar

Martínez

2017

CeN

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show abstract

“…(); Borges (); dos Santos, Achcar, and Martinez (); Martinez and Achcar (); Rocha et al. (, ) and Martinez and Achcar ().…”

Section: Introductionmentioning

confidence: 98%

“…Defective models offer one strategy for modeling interval‐censored data in the context of a cured fraction. Balka, Desmond, and McNicholas (, ) and Rocha, Nadarajah, Tomazella, and Louzada (, ); Rocha, Nadarajah, Tomazella, Louzada, and Eudes (); Scudilio et al. () recently popularized the term “defective,” although previous papers had used the same idea.…”

Section: Introductionmentioning

confidence: 99%

“…Until recently, only two distributions in the literature had this property: the Gompertz and inverse Gaussian distributions. These models were studied in the context of right-censored observations by Haybittle (1959); Whitmore (1979); Cantor and Shuster (1992), Gieser, Chang, Rao, Shuster, & Pullen (1998); Balka et al (2009Balka et al ( , 2011; Rocha et al (2016); Borges (2017); dos Santos, Achcar, and Martinez (2017); Martinez and Achcar (2017); Rocha et al (2017aRocha et al ( , 2017b and Martinez and Achcar (2018).…”

Section: Introductionmentioning

confidence: 99%

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Defective regression models for cure rate modeling with interval‐censored data

et al. 2019

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Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.

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A new cure rate model with flexible competing causes with applications to melanoma and transplantation data

Leão

Bourguignon

Gallardo

et al. 2020

Statistics in Medicine

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In this article, we introduce a long-term survival model in which the number of competing causes of the event of interest follows the zero-modified geometric (ZMG) distribution. Such distribution accommodates equidispersion, underdispersion, and overdispersion and captures deflation or inflation of zeros in the number of lesions or initiated cells after the treatment. The ZMG distribution is also an appropriate alternative for modeling clustered samples when the number of competing causes of the event of interest consists of two subpopulations, one containing only zeros (cure proportion), while in the other (noncure proportion) the number of competing causes of the event of interest follows a geometric distribution. The advantage of this assumption is that we can measure the cure proportion in the initiated cells. Furthermore, the proposed model can yield greater or lower cure proportion than that of the geometric distribution when modeling the number of competing causes. In this article, we present some statistical properties of the proposed model and use the maximum likelihood method to estimate the model parameters. We also conduct a Monte Carlo simulation study to evaluate the performance of the estimators. We present and discuss two applications using real-world medical data to assess the practical usefulness of the proposed model.

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A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling

Cited by 29 publications

References 38 publications

Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Application to the Cervical Carcinoma Study

Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Application to the Cervical Carcinoma Study

Defective regression models for cure rate modeling with interval‐censored data

A new cure rate model with flexible competing causes with applications to melanoma and transplantation data

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