Anais - V WASA - Workshop em Análise de Sobrevivência e Aplicações

A Destructive Survival Model for Predicting Breast Carcinoma Survival with Long-Term Survivors - Link direto para esse trabalho
Gladys D.C. Barriga, Vicente G. Cancho, Edwin M.M. Ortega , Gauss C. Cordeiro, Michael W. Kattan

A new flexible cure rate survival model is developed where the initial number of competing causes of the event of interest (say lesions or altered cells) follows a power series distribution. This model provides a realistic interpretation of the biological mechanism of the event of interest as it models a destructive process of the initial competing risk factors and records only the damaged portion of the original number of risk factors. Our proposed survival models are used for predicting breast carcinoma survival in women who underwent mastectomy. The postmastectomy survival rates are often based on previous outcomes of large numbers of women who had a disease, but they cannot predict what will happen in any particular patient's case. Pathologic explanatory variables such as disease multifocality, tumor size, tumor grade, lymphovascular invasion and enhanced lymph node staining are prognostically significant to predict these survival rates.
Palavras-Chave: Cure rate models; power series distribution; proportional hazard models;

A flexible cure rate model based on the polylogarithm distribution (não consegui carregar o arquivo pdf!) - Link direto para esse trabalho
Diego I. Gallardo; Yolanda M. Gómez; Mário de Castro

Models for dealing with survival data in the presence of a cured fraction of individuals have attracted the attention of many researchers and practitioners in recent years. In this paper, we propose a cure rate model under the competing risks scenario. For the number of causes that can lead to the event of interest, we assume the polylogarithm distribution. The model is flexible in the sense it encompasses some well known models, which can be tested using large sample test statistics applied to nested models. Maximum likelihood estimation based on the EM algorithm and hypotheses testing are investigated. Results of simulation studies designed to gauge the performance of the estimation method and of two test statistics are reported. The methodology is applied in the analysis of a data set.
Palavras-Chave: EM algorithm; Geometric distribution; Logarithmic distribution; Negative binomial distribution; Power series family;

A new Nadarajah-Haghighi generalization with applications in survival analysis - Link direto para esse trabalho
Fernando A. Peña-Ramírez; Renata Rojas Guerra; Gauss M. Cordeiro.

We propose a new continuous distribution based on compounding the Lindley and Nadarajah-Haghighi distributions. The new distribution is very competitive to other lifetime models. Some of its properties are investigated including moments, mean residual life, mean deviations, Bonferroni and Lorenz curves and generating function. We discuss the estimation of the model parameters by maximum likelihood. We provide a simulation study and two applications to real data for illustrative purposes. We prove empirically that the proposed distribution yields good fits to both data sets, and it can be a useful alternative for other classical lifetime models.
Palavras-Chave: Compounding approach; Exponential distribution; Lifetime data; Lindley distribution; Nadarajah-Haghighi distribution;

A new extension of the Birnbaum-Saunders model - Link direto para esse trabalho
Maria do Carmo Soares de Lima; Gauss Moutinho Cordeiro; Edwin M. M. Ortega; Alice B. V. Mello

An extended fatigue life model called the odd log-logistic Birnbaum-Saunders-Poisson distribution is proposed. It extends the Birnbaum-Saunders and odd log-logistic Birnbaum-Saunders distribu- tions. We obtain some structural properties of the new model including explicit expressions for the moments and generating function. The method of maximum likelihood is used to estimate the model parameters. Further, we define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum-Saunders-Poisson random variable. The usefulness of the proposed models is illustrated by means of three real data sets.
Palavras-Chave: Birnbaum-Saunders distribution; Fatigue life distribution; Lifetime data; Maximum likelihood estimation;

Analysis of Bivariate Lifetime Data in Presence of Censoring and Covariates: A Review Using Bivariate Parametric Distributions - Link direto para esse trabalho
Ricardo Puziol de Oliveira; Jorge Alberto Achcar; Danielle Peralta; Josmar Mazucheli

The analysis of bivariate lifetime time covers the field where independence between survival times cannot be assumed, that is, the dependence structure of the data must be considered and plays a vital role in the data analysis. The dependence can occur for very different kinds of data, especially in medical data. In this study, considering some applications involving real survival medical data, we present a review of some bivariate continuous and discrete models under a Bayesian approach to analyze bivariate lifetimes in presence of censored data and covariates assuming dependence structures. In order to discriminate the proposed models it is used the popular discrimination criteria DIC and comparisons of the fitted marginal survival curves with Kaplan-Meier nonparametric estimators for the marginal survival functions. The posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) simulations methods and R2jags library of R software. Despite the existing differences among continuous and discrete bivariate distributions, the data analysis show great similarities but in general, the discrete models have simpler mathematical expressions when compared to the continuous case and better accuracy in the obtained inference results for bivariate lifetimes in presence of censored data and covariates.
Palavras-Chave: bivariate lifetimes; Bayesian analysis; survival analysis; right-censored data;

Avaliação de produtos baseada na presença de m >= 1 características - Link direto para esse trabalho
Démerson André Polli; Carlos Alberto Ribeiro Diniz

Um produto (ou um serviço) pode ser avaliado através da verificação de que m >= 1 características são satisfeitas. Pelo menos dois cenários distintos de avaliação são possíveis: (1) os avaliadores atribuem, para cada item, um valor entre 0 e m correspondente à contagem de características consideradas satisfatórias, ou (2) os avaliadores atribuem, para cada item, um vetor de m variáveis dicotômicas correspondentes à cada característica. Os avaliadores pertencem à diferentes populações que consideram níveis distintos de importância para as características ou atribuem as respostas para cada característica ao acaso (sem julgar a satisfação da referida categoria). Este resumo mostra alguns modelos simples para tratar estes 2 cenários de avaliação citados.
Palavras-Chave: modelos de mistura; modelos bayesianos; avaliação de produtos;

Defective Regression Models for Cure Rate Modeling with Interval-Censored Data - Link direto para esse trabalho
Vinicius F. Calsavara; Agatha S. Rodrigues; Ricardo Rocha; Vera Tomazella; Francisco Louzada Neto

The regression models in survival analysis are most commonly applied for right-censored survival data. However, in some situations the time to the event is not exactly observed but it is known that the event occurred between two observed times. In practical problems, it is common to assume the moment of observation as the event occurrence time, ignoring the interval-censored mechanism. We present a cure rate defective model for interval-censored event-time data. Defective distribution is characterized by density function whose integration assumes values less than one when the domain of their parameters is different from the usual one. We consider the Gompertz and inverse Gaussian defective distributions which allow to model data containing cured elements. The parameter estimation is reached by maximum likelihood estimation procedure and Monte Carlo simulation studies are considered in order to evaluate the proposed models performance. The practice relevance of the models is illustrated through the ovarian cancer recurrence and oral lesion in children after liver transplantation datasets. Both studies were performed at A.C.Camargo Cancer Center, São Paulo, Brazil.
Palavras-Chave: Defective distributions; Gompertz distribution; Inverse Gaussian distribution; Interval-censored data; Long-term survivors;

Estimating nonlinear effects in the presence of cure fraction using the semi-parametric Weibull regression model - Link direto para esse trabalho
Ana Julia Righetto;Luiz Ricardo Nakamura;Thiago Gentil Ramires;Rodrigo Rosseto Pescim

Nonlinear effects between explanatory and response variables are increasingly present in new surveys. Here, we propose a flexible three-parameter semi-parametric cure rate survival based on the Weibull distribution. The proposed model is based on the generalized additive models for location, scale and shape, for which any or all parameters of the distribution are parametric linear and/or nonparametric smooth functions of explanatory variables. The new model is used to fit the nonlinear behavior between explanatory variables and cure rate. The flexibility of the proposed model is illustrated by predicting lifetime and cure rate proportion as well as identifying factors associated to women diagnosed with breast cancer.
Palavras-Chave: Cure rate models; GAMLSS; Long-term survivors; P-spline;

Estimation of Reliability of Multicomponent Stress-Strength of a Bathtub Shape or Increasing Failure Rate Function - Link direto para esse trabalho
Sanku Dey ; Fernando A. Moala

This work deals with the Bayesian and non-Bayesian estimation of multicomponent stress-strength reliability by assuming the Chen distribution. Both stress and strength are assumed to have a Chen distribution with common shape parameter. The reliability of such a system is obtained by the methods of maximum likelihood and Bayesian approach and the results are compared using MCMC technique for both small and large samples. Finally, two data sets are analyzed for illustrative purposes.
Palavras-Chave: Chen distribution; Reliability of multicomponent; Bayesian estimation; Maximum likelihood estimation;

Heteroscedastic models applied into the medical field - Link direto para esse trabalho
Luiz R. Nakamura; Thiago G. Ramires; Ana J. Righetto; Edwin M.M. Ortega; Gauss M. Cordeiro

In this work, we use the generalized additive models for location, scale and shape (GAMLSS) framework based on the Weibull distribution in order to identify the associated factors in patients with renal disease in a Brazilian city.
Palavras-Chave: GAMLSS; renal insufficiency; risk factors;

Influência do saneamento básico e pluviosidade na incidência de dengue em Sergipe. - Link direto para esse trabalho
Joyce Dalline Silva Andrade¹; José Rodrigo dos Santos Silva¹*; Joas Silva dos Santos¹; Lorena França Andrade¹, Elizeu Junio Dantas Alves¹.

A dengue é a uma doença infecciosa viral prevalente em países tropicais em desenvolvimento, transmitida pelo vetor Aedes aegypti. Neste sentido, o objetivo do estudo foi desenvolver um modelo de regressão, afim, de determinar o grau de influência do saneamento básico e pluviosidade na incidência de dengue em Sergipe de 2001 a 2012. Com esta finalidade foram selecionadas cerca de oito variáveis para a construção do modelo. Mediante análise preliminar de correlação, foi observada a presença de multicolinearidade. Desta forma, foi necessária a aplicação do método de componentes principais, resultando em 3 fatores, estes foram ajustados a um modelo de regressão linear múltipla onde foi possível observar que a deficiência no esgotamento sanitário e serviços essenciais (água, esgoto e coleta de lixo), implicam no aumento da incidência de dengue. Por outro lado, o aumento da precipitação eleva o número de casos da doença. O resultado da análise de variância mostra que a equação obtida, é significativamente aderente. Sendo assim, concluímos que o estudo de indicadores sanitários e pluviométricos podem ser de suma importância para subsidiar as ações de saúde pública no controle da dengue
Palavras-Chave: Aedes Aegypt; Análise estatística; Dengue; Epidemiologia;

Joint modeling of longitudinal measurements and event time data: a dynamic generalized hierarchical approach - Link direto para esse trabalho
Pamela Chiroque Solano; Helio Migon

This paper introduced a broad class of dynamic generalized hierarchical models for the joint behavior of a sequence of longitudinal measurements and event times. The distribution of event times is conditional to the longitudinal measurements and both follow a dynamic generalized hierarchical structure. This class includes and extends a number of specific models proposed in the last decade literature. A fully Bayesian inference is implemented via Markov chain Monte Carlo methods. The proposed model is illustrated using results from two classical clinical trials. One is for the treatment of schizophrenia and the treatment of AIDS.\\
Palavras-Chave: teste; teste2; testando; Dynamic model; Hierarchical model; Longitudinal and time-to-event data;

Modelos de regressão com erros de medida e dados censurados considerando a distribuição t-Student - Link direto para esse trabalho
Alejandro Guillermo Monzón Montoya; Lourdes Coral Contreras Montenegro

Neste trabalho estudamos a abordagem de influência local para modelos de regressão com erro de medida para respostas multivariadas censuradas sob a distribuição t-Student. Embora a distribuição normal é geralmente assumida para os erros e a variável com erros, tal suposição deixa a inferência mais vulnerável a “outliers”. Usamos o algoritmo ECM para obter os estimadores de máxima verossimilhança. A função de log-verossimilhança dos dados completos é utilizada para obter as medidas de influência local baseadas na metodologia proposta por Zhu e Lee (2001). Finalmente, as metodologias propostas são usadas na análise de dados reais que ilustra a utilidade da abordagem.
Palavras-Chave: Dados censurados; Algoritmo ECM; Modelos com erro de medida; Distribuição t-Student; Influência local;

Objective Bayesian Estimation Method in a Repairable System Subject to Competing Risks - Link direto para esse trabalho
Almeida, M.P. ; Tomazella, V.L.D. ; Avalle, G.L.G.

Objective Bayesian methods are proposed to analyze the minimal repair framework for competing risks. We analyzed the recurrence of failures in a reparable system subject to a variety of failure modes and with a minimal repair type of corrective maintenance assumption. The intensity function for each of modes is described by a power law process. The estimation of the parameters of the model is done using objective Bayesian analysis methodology. Under orthogonality of the parameters we obtain a single prior distribution for any parameter of interest of model. We derive other non-informative prior using formal rules, such as Jeffreys prior to show that are remarkably identical. The posterior reference distribution follows a product of independent gamma distributions. The methodology described is applied to a real data set.
Palavras-Chave: Repairable system; competing risks; power law process; overall objective prior;

Prior Specifications to Handle Monotone Likelihood in the Cox Regression Model - Link direto para esse trabalho

The monotone likelihood is a phenomenon that may affect the fitting process of well-established regression models such as the Cox proportional hazards model. In short, the problem occurs when the likelihood converges to a finite value, while at least one parameter estimate diverges to +- infinity. In survival analysis, monotone likelihood primarily appears in samples with substantial censored times and containing many categorical covariates; it is often observed when one level of a categorical covariate has not experienced any failure. A solution suggested in the literature (known as Firth correction) is an adaptation of a method originally created to reduce the bias of maximum likelihood estimates. The method leads to a finite estimate by means of a penalized maximum likelihood procedure. In this case, the penalty might be interpreted as a Jeffreys type of prior widely used in the Bayesian context. However, this approach has some drawbacks, especially biased estimators and high standard errors. In this paper, we explore other penalties for the partial likelihood function in the flavor of Bayesian prior distributions. A simulated study is developed, based on Monte Carlo replications and distinct sample sizes, to evaluate the impact of the suggested priors in terms of inference. A real application is also presented to illustrate the analysis using a melanoma skin data set.
Palavras-Chave: Firth correction; MCMC; Partial likelihood; Survival analysis;

Refinamento de inferências na distribuiçao Burr X escalonada para dados censurados tipo II - Link direto para esse trabalho
Renilma Pereira da Silva; Audrey H. M. A. Cysneiros

Este artigo apresenta dois diferentes ajustes para a função de verossimilhança perfilada com o objetivo de obter inferências mais confiáveis sobre o parâmetro de forma da distribuição Burr X escalonada. Especificamente, derivamos a função de verossimilhança perfilada e suas versões ajustadas para fazer estimação pontual e teste de hipóteses com base na estatística da razão de verossimilhanças (RV), sob o enfoque de censura do tipo II. O estudo também inclui dois testes da RV corrigidos por bootstrap paramétrico. Os resultados de simulação indicam que em pequenas amostras as inferências baseadas nas funções de verossimilhança perfilada ajustadas são mais precisas. Duas aplicações a conjuntos de dados reais são apresentados para ilustrar a teoria desenvolvida.
Palavras-Chave: Burr X escalonada; Censura tipo II; Estimação pontual; Teste de hipóteses; Verossimilhança perfilada ajustada;

Teste de Bondade de Ajuste para a Distribuição Birnbaum-Saunders Baseado na informação de Kullback-Leibler na Presença de CPII - Link direto para esse trabalho
Ednário Barbosa de Mendonça; Michelli Karinne Barros da Silva; Joelson da Cruz Campos

Neste trabalho, propomos um teste de bondade de ajuste baseado na informação de Kullback-Leibler (KL) para o modelo Birnbaum-Saunders, em que foram considerados dados com censura progressiva do tipo II (CPII). Em tal estudo, foram obtidas as estatísticas de teste, de modo que o processo de estimação dos parâmetros do modelo teve como base o método da máxima verossimilhança. Além disso, também foram avaliados os tamanhos e os poderes do teste por meio de estudos de simulação, isso considerando diferentes tamanhos amostrais, diferentes esquemas de censura e diferentes alternativas para a função de risco. Por fim, fizemos uma aplicação com um conjunto de dados reais.
Palavras-Chave: Distribuição Birnbaum-Saunders; Teste de bondade de ajuste; Informação de Kullback-Leibler; Censura progressiva do tipo II;

The Beta-pG family of distributions for cure rate regression models - Link direto para esse trabalho
Juliana Scudilio; Ricardo Rocha; Vera Tomazella; Francisco Louzada

In this paper we propose a general family of distributions to model cure rate data, called Beta-pG family of distributions. This approach is based in including a parameter p in the Beta-G family of distributions, in order to make it a cure rate model. We propose a regression approach for this new family to accommodate covariate information. Inference by maximum likelihood is suggested. We take a special attention when G comes from an exponential distribution, that is, when we have the Beta-pExp distribution. We use some simulation studies to show the finite sample convergence of the parameters in the distribution, as well to compare the proposed model with the standard mixture approach. We use two real cancer related data sets to show that the new family can outperform the standard mixture model.
Palavras-Chave: Beta-G family of distributions; Beta-Exponencial distributions; Cured fraction; Long -term survivors; Survival analysis;

The Nadarajah-Haghihi Gompertz distribution: properties and applications - Link direto para esse trabalho
Maria do Carmo Soares de Lima; Alice Buarque Vieira de Mello

A new four-parametric Nadarajah-Haghighi-Gompertez distribution is proposed. It extends the Gompertz distribution that is applied in several areas as biology, demography and actuary. We obtain some structural properties of the new model including explicit expressions for the moments and quantile function. The method of maximum likelihood is used to estimate the model parameters. A simulation study is realized to verify the asymptotic properties of the parameters and the usefulness of the proposed model is illustrated by means of two real data sets.
Palavras-Chave: Gompertz distribution; Lifetime data; Maximum likelihood estimation;

The Odd Log-Logistic Geometric Family with Applications in Regression Models - Link direto para esse trabalho
Maria do Carmo S. Lima; Fábio Prataviera; Edwin M. M. Ortega;

We obtain some mathematical properties of a new generator of continuous distributions with two additional shape parameters called the odd log-logistic geometric family. We present some special models and investigate the asymptotes and shapes. The family density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive a power series for its quantile function. We provide explicit expressions for the ordinary and incomplete moments and generating function. We estimate the model parameters by maximum likelihood. We propose a useful heteroscedastic regression model to fit real data.
Palavras-Chave: Geometric family; Heteroscedastic regression model; Maximum likelihood estimation; Odd log-logistic family;

The exponentiated exponential with cure fraction: application to breast cancer data with covariates - Link direto para esse trabalho
Marcos Vinicius de Oliveira Peres;Jorge Alberto Achcar;Edson Zangiacomi Martinez

In traditional survival analysis, if the individual is accompanied by a sufficiently long period, it is assume that the event of interest will happen, in this way all the individuals in study are subject to the event of interest. However, there are situations where this assumption is not valid. The class of models that consider this proportion of cured or immune are known by cure fraction models. In this work, we present estimates of maximum likelihood for the mixture cure fraction model based on the exponentiated exponential distribution considering a breast cancer data of young women, in the presence and not presence of the estrogen receptor. Considering an application of the model to a real data set from breast cancer study, we can note that the model satisfactorily fitted the data.
Palavras-Chave: Survival analysis; Cure fraction; Estrogen receptor;

The heteroscedastic odd log-logistic generalized gamma regression model for censored data - Link direto para esse trabalho
Fábio Prataviera;Edwin M. M. Ortega;Gauss M. Cordeiro;Altemir da Silva Braga

We propose a four-parameter extended generalized gamma model, which includes as special cases some important distributions and it is very useful for modeling lifetime data. A advantage is that it can represent the error distribution for a new heteroscedastic log-odd log-logistic generalized gamma regression model. The proposed heteroscedastic regression model can be used more effectively in the analysis of survival data since it includes as special models several widely-known regression models. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. Overall, the new regression model is very useful to the analysis of real data.
Palavras-Chave: Censored data; log-gamma generalized regression; odd log-logistic distribution; survival function;

The logistic Burr XII distribution: properties and applications to income data - Link direto para esse trabalho
Renata Rojas Guerra; Fernando A. Peña-Ramı́rez; Gauss M. Cordeiro

We introduce the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as baseline in the logistic-X family and may be a useful alternative to model income distribution and applied to other areas. We prove that the new distribution can have decreasing and upside-down bathtub hazard functions and that its density function is an infinite linear combination of Burr XII densities. Some mathematical properties of the proposed model are determined such as the quantile function, ordinary and incomplete moments and generating function. We also obtain the maximum likelihood estimators of the model parameters and perform a Monte Carlo simulation study. The potentiality of the new distribution is illustrated by means of two applications to income data sets.
Palavras-Chave: teste; teste2; testando; Burr XII distribution; income distribution; logistic-X family; maximum likelihood estimation; moments;

Tatiana Reis Icuma; Isabela Panzeri Carlotti Buzatto; Daniel Guimarães Tiezzi; Jorge Alberto Achcar.

Introdução: A análise de dados de sobrevivência na área médica tem exigido cada vez mais o uso de modelos estatísticos mais precisos. Uma situação frequente em dados de câncer são dados bivariados, onde tem-se dois tempos de sobrevivência de interesse. O modelo de Cox é muito utilizado na área médica, porém a violação da suposição básica, que é a de taxas de falha proporcionais, pode acarretar em sérios vícios na estimação dos coeficientes de regressão do modelo. Objetivo: Apresentar alternativas para a análise de dados de sobrevivência bivariados baseada em distribuições bivariadas assumindo dados contínuos ou discretos. Métodos: Alguns modelos bivariados foram utilizados para evidenciar fatores que possam afetar os tempos de sobrevida livre da doença (SLD) e total (ST) de um estudo retrospectivo realizado no HC-FMRP-USP, referente a 54 pacientes com câncer de mama localmente avançado com superexpressão do Her-2 que iniciaram a quimioterapia neoadjuvante associada com o medicamento Herceptin® (Trastuzumabe) no período de 2008 a 2012. Utilizaram-se modelos assumindo uma estrutura de dependência entre os tempos observados, baseados na distribuição exponencial bivariada de Block Basu, na distribuição geométrica bivariada de Arnold e na distribuição geométrica bivariada de Basu-Dhar. Resultados: Usando as três distribuições bivariadas as análises evidenciam que o estágio da doença afeta ambos os tempos (SLD e ST) e utilizando a distribuição de Arnold, também se evidencia que a covariável tipo de cirurgia afeta o tempo de ST. Conclusões: Dos resultados obtidos da análise estatística usando os modelos bivariados contínuos ou discretos foram obtidas melhores inferências quando comparados ao uso de técnicas tradicionais semi-paramétricas como o modelo de riscos proporcionais de Cox assumindo tempos independentes.
Palavras-Chave: Bivariados; Métodos Bayesianos; Análise de sobrevivência;

pexm: a JAGS module for applications involving the piecewise exponential distribution - Link direto para esse trabalho
Vinícius Diniz Mayrink; João Daniel Nunes Duarte; Fábio Nogueira Demarqui

The piecewise exponential (PE) model is extensively used in survival analysis and reliability to approximate the distribution of event-time data; possibly investigating the association of the time response with explanatory variables. In this study, we present a new module built for those users interested in the BUGS language to develop a Bayesian analysis for a model assuming the piecewise exponential (PE) distribution. The module is an extension to the open-source program JAGS by which a Gibbs sampler can be applied without requiring the derivation of complete conditionals and the subsequent implementation of strategies to draw samples from unknown distributions. Currently, the PE distribution can only be implemented in JAGS through methods to indirectly specify likelihoods based on the Poisson or Bernoulli probabilities. Our module provides a more straightforward implementation and is thus more attractive to those researchers focused on the Bayesian data analysis and willing to avoid demanding codes. Here, we describe how to use the module taking advantage of the interface between R and JAGS. A short simulated study is developed to ensure that the module is correctly working, and a real application is presented to explore and illustrate two frailty models.
Palavras-Chave: Survival analysis; Semiparametric; Piecewise exponential; Bayesian inference;