Defective models induced by gamma frailty term for survival data with cured fraction

Scudilio, Juliana; Calsavara, Vinícius Fernando; Rocha, Ricardo; Louzada, Francisco; Tomazella, Vera; Rodrigues, Agatha Sacramento

doi:10.1080/02664763.2018.1498464

Cited by 24 publications

(22 citation statements)

References 40 publications

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“…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. Defective distributions are obtained from standard distributions by changing parameter domains in such a way that their survival functions limit to

p_{0} \in false(0, 1 false)

.…”

Section: Introductionmentioning

confidence: 99%

“…Defective models offer one strategy for modeling interval-censored data in the context of a cured fraction. McNicholas (2009, 2011) and Louzada (2016, 2017a); Rocha, Nadarajah, Tomazella, Louzada, and Eudes (2017b); Scudilio et al (2019) recently popularized the term "defective," although previous papers had used the same idea. Defective distributions are obtained from standard distributions by changing parameter domains in such a way that their survival functions limit to 0 ∈ (0, 1).…”

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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p_{0} \in false(0, 1 false)

.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…To finalize this chapter, three real databases are presented to illustrate the proposed distribution compared to the standard mixture models. This chapter is based on the paper of Scudilio et al (2019).…”

Section: Objective and Overviewmentioning

confidence: 99%

“…In this application, one model only with the covariate N, because is the only one without missing values. For more details about this data see Scudilio et al (2019). 1 TIL = 0 then TIL ≤ 10%, TIL = 1 otherwise.…”

Section: Breast Cancer Datamentioning

confidence: 99%

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Cure rate models: alternatives methods to estimate the cure rate

Rodrigues¹

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Cure rate models in survival data studies has formed an important field in the area and has attracted the attention of researchers. In the search for new models of cure rate, the objective of this work is to propose alternative methods to model the cure rate. For this two methods are presented. The first use the methodology of the defective models and the last method use the concept the distributions family. Then, in the first method propose the defective models induced by a frailty term. Defective models have the advantage of modeling the proportion of cured without adding any extra parameters in the model, in contrast to the most models from the literature. Models with a frailty term incorporate an unobserved heterogeneity among individuals and this incorporation brings advantages for the estimated model, because it incorporates the influence of unobserved covariates in a proportional hazard model. It is showed that the new defective distributions are induced when using the gamma frailty term. The last method proposed in this work, is to use distribution families to calculate the cure rate. For this, a parameter "p" is included in the Beta-G family in order to create a new family of cure rate models, the new family can be more flexible for modeling cure rate than the standard mixture models.

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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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Defective models induced by gamma frailty term for survival data with cured fraction

Cited by 24 publications

References 40 publications

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

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

Cure rate models: alternatives methods to estimate the cure rate

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

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