Two new defective distributions based on the Marshall–Olkin extension

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

doi:10.1007/s10985-015-9328-x

Cited by 16 publications

(13 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

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

Section: Introductionmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…A third and recent way to introduce cure rate models is known in the literature as the improper models introduced by Balka et al 29 In these models, the parameter space of the distribution is extended producing an improper model in which the cumulative distribution function no longer approaches 1, but to p ∈ (0,1). More details in improper models extensions can be found in References 30‐34. However, differently from the competing risks or frailty approaches, improper models do not have an underlying motivation and further connections with real problems are more complicated.…”

Section: Introductionmentioning

confidence: 99%

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…In the literature, models with this property have recently been termed “defective,” when they accommodate a proportion of the cure fraction with dependence on a single parameter value. 32–37…”

Section: Introductionmentioning

confidence: 99%

Long-term frailty modeling using a non-proportional hazards model: Application with a melanoma dataset

Calsavara

Milani

Bertolli

et al. 2019

Stat Methods Med Res

Self Cite

View full text Add to dashboard Cite

The semiparametric Cox regression model is often fitted in the modeling of survival data. One of its main advantages is the ease of interpretation, as long as the hazards rates for two individuals do not vary over time. In practice the proportionality assumption of the hazards may not be true in some situations. In addition, in several survival data is common a proportion of units not susceptible to the event of interest, even if, accompanied by a sufficiently large time, which is so-called immune, “cured,” or not susceptible to the event of interest. In this context, several cure rate models are available to deal with in the long term. Here, we consider the generalized time-dependent logistic (GTDL) model with a power variance function (PVF) frailty term introduced in the hazard function to control for unobservable heterogeneity in patient populations. It allows for non-proportional hazards, as well as survival data with long-term survivors. Parameter estimation was performed using the maximum likelihood method, and Monte Carlo simulation was conducted to evaluate the performance of the models. Its practice relevance is illustrated in a real medical dataset from a population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil.

show abstract

Two new defective distributions based on the Marshall–Olkin extension

Cited by 16 publications

References 25 publications

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

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

Long-term frailty modeling using a non-proportional hazards model: Application with a melanoma dataset

Contact Info

Product

Resources

About