Vera Tomazella

Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data: Birnbaum-Saunders frailty regression models

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

New defective models based on the Kumaraswamy family of distributions with application to cancer data sets

An alternative to the standard mixture model is proposed for modeling data containing cured elements or a cure fraction. This approach is based on the use of defective distributions to estimate the cure fraction as a function of the estimated parameters. In the literature there are just two of these distributions: the Gompertz and the inverse Gaussian. Here, we propose two new defective distributions: the Kumaraswamy Gompertz and Kumaraswamy inverse Gaussian distributions, extensions of the Gompertz and inverse Gaussian distributions under the Kumaraswamy family of distributions. We show in fact that if a distribution is defective, then its extension under the Kumaraswamy family is defective too. We consider maximum likelihood estimation of the extensions and check its finite sample performance. We use three real cancer data sets to show that the new defective distributions offer better fits than baseline distributions.

Modeling categorical covariates for lifetime data in the presence of cure fraction by Bayesian partition structures

In this paper, we propose a Bayesian partition modeling for lifetime data in the presence of a cure fraction by considering a local structure generated by a tessellation which depends on covariates. In this modeling we include information of nominal qualitative variables with more than two categories or ordinal qualitative variables. The proposed modeling is based on a promotion time cure model structure but assuming that the number of competing causes follows a geometric distribution. It is an alternative modeling strategy to the conventional survival regression modeling generally used for modeling lifetime data in the presence of a cure fraction, which models the cure fraction through a (generalized) linear model of the covariates. An advantage of our approach is its ability to capture the effects of covariates in a local structure. The flexibility of having a local structure is crucial to capture local effects and features of the data. The modeling is illustrated on two real melanoma data sets.

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

Defective distributions model cure rates by changing the usual domain of its parameters in a way that their survival functions converge to a value p∈(0,1). A new way to generate defective distributions to model cure fractions is proposed. The new way relies on a property derived from the Marshall–Olkin family of distributions. To exemplify this new result we use the extended Weibull distribution and introduce ten new defective distributions. A regression approach for these models is also proposed. Estimation by maximum likelihood is discussed and their asymptotes verified through simulations. Practical use is illustrated by applications to four real data sets.

Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data: A cure rate model with frailties and its diagnostics

Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. Our proposal consists of incorporating frailty into a cure rate model, as an alternative to the existing models to describe this type of data, based on the Birnbaum-Saunders distribution. Such a distribution has theoretical arguments to model medical data and has shown empirically to be a good option for their analysis. An advantage of the proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. In addition, the number of competing causes is described by the negative binomial distribution, which absorbs several particular cases. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for this model. We assess local influence on the parameter estimates under different perturbation schemes. Deriving diagnostic tools is needed in all statistical modeling, which is another novel aspect of our proposal. Numerical evaluation of the considered model is performed by Monte Carlo simulations and by an illustration with melanoma data, both of which show its good performance and its potential applications. Particularly, the illustration confirms the importance of statistical diagnostics in the modeling.

Accelerated lifetime modelling with frailty in a non-homogeneous Poisson Process for analysis of recurrent events data

In survival analysis, the hazard function for each individual may be influenced by risk variables, but commonly we have some variables that cannot be observed nor measured. Besides, when lifetime data present more than one observed event for each individual, frailty is a common factor among such recurrence times. In this paper, we present a natural extension of the conventional accelerated failure time (AFT) model for recurrent events with frailty, in order to take into account possible correlations and heterogeneity between event times. We include the effects of covariates on the intensity function of the non-homogeneous Poisson process for recurrent events. The proposed model retains the direct physical interpretation of the original AFT model in that the role of the covariates is to accelerate or decelerate the time to each recurrence. These include parametric approaches to model fitting, we consider to estimate the vector of regression parameters under this model and the parameter in the baseline hazard functions. This methodology is illustrated with a simulation study and also with a known real dataset.

Bayesian Estimation of the Kumaraswamy InverseWeibull Distribution

The Kumaraswamy Inverse Weibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy Inverse Weibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive treatment of the mathematical properties of the Kumaraswany Inverse Weibull distribution and derive expressions for its moment generating function and the

Frailty models power variance function with cure fraction and latent risk factors negative binomial

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

-th generalized moment. Some properties of the model with some graphs of density and hazard function are discussed. We also discuss a Bayesian approach for this distribution and an application was made for a real data set.

Biparametric Zero-Modified Power Series Distributions: Bayesian Analysis under a Reference Prior Approach

ABSTRACT In this article, we propose a flexible cure rate model, which is an extension of Cancho et al. (2011) model, by incorporating a power variance function (PVF) frailty term in latent risk. The model is more flexible in terms of dispersion and it also quantifies the unobservable heterogeneity. The parameter estimation is reached by maximum likelihood estimation procedure and Monte Carlo simulation studies are considered to evaluate the proposed model performance. The practical relevance of the model is illustrated in a real data set of preventing cancer recurrence.