RESUMO
In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.
RESUMO
Cure fraction models have been widely used to model time-to-event data when part of the individuals survives long-term after disease and are considered cured. Most cure fraction models neglect the measurement error that some covariates may experience which leads to poor estimates for the cure fraction. We introduce a Bayesian promotion time cure model that accounts for both mismeasured covariates and atypical measurement errors. This is attained by assuming a scale mixture of the normal distribution to describe the uncertainty about the measurement error. Extending previous works, we also assume that the measurement error variance is unknown and should be estimated. Three classes of prior distributions are assumed to model the uncertainty about the measurement error variance. Simulation studies are performed evaluating the proposed model in different scenarios and comparing it to the standard promotion time cure fraction model. Results show that the proposed models are competitive ones. The proposed model is fitted to analyze a dataset from a melanoma clinical trial assuming that the Breslow depth is mismeasured.
Assuntos
Modelos Estatísticos , Teorema de Bayes , Simulação por Computador , Humanos , Distribuição NormalRESUMO
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.
Assuntos
Fragilidade , Melanoma , Brasil , Humanos , Funções Verossimilhança , Modelos Estatísticos , Modelos de Riscos Proporcionais , Análise de SobrevidaRESUMO
Different cure fraction models have been used in the analysis of lifetime data in presence of cured patients. This paper considers mixture and nonmixture models based on discrete Weibull distribution to model recurrent event data in presence of a cure fraction. The novelty of this study is the use of a discrete lifetime distribution in place of usual existing continuous lifetime distributions for lifetime data in presence of cured fraction, censored data, and covariates. In the verification of the fit of the proposed model it is proposed the use of randomized quantile residuals. An extensive simulation study is considered to evaluate the properties of the estimates of the parameters related to the proposed model. As an illustration of the proposed methodology, it is considered an application considering a medical dataset related to lifetimes in a retrospective cohort study conducted by Puchner et al. (2017) that consists of 147 consecutive cases with surgical treatment of a sarcoma of the pelvis between the years of 1980 and 2012.
Assuntos
Biometria/métodos , Modelos Estatísticos , Neoplasias Pélvicas/cirurgia , Sarcoma/cirurgia , Humanos , Funções Verossimilhança , Análise Multivariada , Estudos Retrospectivos , Resultado do TratamentoRESUMO
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.
Assuntos
Funções Verossimilhança , Neoplasias , Distribuição Normal , Neoplasias do Colo/mortalidade , Conjuntos de Dados como Assunto , Humanos , Estimativa de Kaplan-Meier , Leucemia/mortalidade , Melanoma/mortalidadeRESUMO
The presence of immune elements (generating a fraction of cure) in survival data is common. These cases are usually modeled by the standard mixture model. Here, we use an alternative approach based on defective distributions. Defective distributions are characterized by having density functions that integrate to values less than 1, when the domain of their parameters is different from the usual one. We use the Marshall-Olkin class of distributions to generalize two existing defective distributions, therefore generating two new defective distributions. We illustrate the distributions using three real data sets.
Assuntos
Modelos Estatísticos , Análise de Sobrevida , Teorema de Bayes , Simulação por Computador , Interpretação Estatística de Dados , Humanos , Funções Verossimilhança , Distribuição Normal , Processos EstocásticosRESUMO
The postmastectomy survival rates are often based on previous outcomes of large numbers of women who had a disease, but they do not accurately 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. We propose a new cure rate survival regression model for predicting breast carcinoma survival in women who underwent mastectomy. We assume that the unknown number of competing causes that can influence the survival time is given by a power series distribution and that the time of the tumor cells left active after the mastectomy for metastasizing follows the beta Weibull distribution. The new compounding regression model includes as special cases several well-known cure rate models discussed in the literature. The model parameters are estimated by maximum likelihood. Further, for different parameter settings, sample sizes, and censoring percentages, some simulations are performed. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess local influences. The potentiality of the new regression model to predict accurately breast carcinoma mortality is illustrated by means of real data.