Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.32211513

Assessing influence in survival data with a cure

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed

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Modelos lineares mistos tem sido frequentemente usados na análise de dados onde as respostas são agrupadas, pelo fato de serem flexíveis para modelar a correlação entre e intra-indivíduos (ou grupos). A normalidade (simetria) dos efeitos e erros aleatórios é uma suposição rotineira em modelos lineares mistos, que pode ser não realista e obscurecer importantes características da variação entre e intra-indivíduos (ou grupos). Neste trabalho relaxamos a suposição de normalidade considerando que tanto os erros como os efeitos aleatórios seguem uma distribuição normal-assimétrica, que inclui a distribuição normal como caso especial e fornece flexibilidade em capturar uma ampla variedade de comportamentos não normais, por simplesmente adicionar um parâmetro que controla o grau de assimetria. A densidade marginal das quantidades observadas é encontrada e mostramos que tem forma fechada, de modo que inferências podem ser abordadas usando programas computacionais conhecidos (R, S-plus, Matlab) e técnicas de otimização padrão. Explorando propriedades estatísticas do modelo considerado implementando o algoritmo EM que fornece algumas vantagens sobre a maximização direta da função log-verossimilhança. Apresentamos também, para esta distribuição normal-assimétrica multivariada, vários resultados relacionados com a teoria da distribuição das formas quadráticas, transformações lineares, densidade marginal e condicionamento. Em um segundo estágio do trabalho, usando uma segunda versão de distribuiçào normal-assimétrica multivariada, os modelos lineares mistos normal assimétricos bayesianos são definidos e procedimentos relacionados com o método Monte Carlo via cadeias de Markov (MCMC) são apresentados fazendo da inferência bayesiana uma alternativa viável para tais modelos. Em ambos os casos, resultados de estudo de simulação e aplicações a conjuntos de dados reais são fornecidos mostrando que os critérios de informação padrão, tais como AIC, BIC e HQ podem ser usados para detectar afastamentos da normalidade (simetria). Finalmente, apresentamos métodos para estimação em modelos lineares mistos com erros nas variáveis, baseados na função escore corrigido de Nakamura (1990), simulação-extrapolação (SIMEX) de Stefanski e Cook (1995) e máxima verossimilhança. Um estudo de simulação comparando os métodos SIMEX e escore corrigido é apresentado.not availabl

mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions

We present the R package mixsmsn, which implements routines for maximum likeli- hood estimation (via an expectation maximization EM-type algorithm) in finite mixture models with components belonging to the class of scale mixtures of the skew-normal distribution, which we call the FMSMSN models. Both univariate and multivariate re- sponses are considered. It is possible to fix the number of components of the mixture to be fitted, but there exists an option that transfers this responsibility to an automated procedure, through the analysis of several models choice criteria. Plotting routines to generate histograms, plug-in densities and contour plots using the fitted models output are also available. The precision of the EM estimates can be evaluated through their esti- mated standard deviations, which can be obtained by the provision of an approximation of the associated information matrix for each particular model in the FMSMSN family. A function to generate artificial samples from several elements of the family is also supplied. Finally, two real data sets are analyzed in order to show the usefulness of the package

mixsmsn

We present the R package mixsmsn, which implements routines for maximum likeli- hood estimation (via an expectation maximization EM-type algorithm) in finite mixture models with components belonging to the class of scale mixtures of the skew-normal distribution, which we call the FMSMSN models. Both univariate and multivariate re- sponses are considered. It is possible to fix the number of components of the mixture to be fitted, but there exists an option that transfers this responsibility to an automated procedure, through the analysis of several models choice criteria. Plotting routines to generate histograms, plug-in densities and contour plots using the fitted models output are also available. The precision of the EM estimates can be evaluated through their esti- mated standard deviations, which can be obtained by the provision of an approximation of the associated information matrix for each particular model in the FMSMSN family. A function to generate artificial samples from several elements of the family is also supplied. Finally, two real data sets are analyzed in order to show the usefulness of the package

Dataset for: Multivariate longitudinal data analysis with censored and intermittent missing responses

The multivariate linear mixed model (MLMM) has emerged as an important analytical tool for longitudinal data with multiple outcomes. However, the analysis of multivariate longitudinal data could be complicated by the presence of censored measurements due to a detection limit of the assay in combination with unavoidable missing values arising when subjects miss some of their scheduled visits intermittently. This paper presents a generalization of the MLMM approach, called the MLMM-CM, for a joint analysis of the multivariate longitudinal data with censored and intermittent missing responses. A computationally feasible EM-based procedure is developed to carry out maximum likelihood estimation within the MLMM-CM framework. Moreover, the asymptotic standard errors of fixed effects are explicitly obtained via the information-based method. We illustrate our methodology by using simulated data and a case study from an AIDS clinical trial. Experimental results reveal that the proposed method is able to provide more satisfactory performance as compared to the traditional MLMM approach

Dataset for: Influence Diagnostics in Spatial Models with Censored Response

Environmental data are often spatially correlated and sometimes include observations below or above detection limits (i.e., censored values reported as less or more than a level of detection). Existing research mainly concentrate on parameter estimation using Gibbs sampling, and most researches conducted from a frequentist perspective in spatial censored models are elusive. In this paper, we propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed effects and variance components, using a stochastic approximation of the EM (SAEM) algorithm (Delyon et al., 1999). This approach permits estimation of the parameters of spatial linear models when censoring is present in an easy and fast way. As a byproduct, predictions of unobservable values of the response variable are possible. Motivated by this algorithm, we develop local and global influence measures on the basis of the conditional expectation of the complete-data log-likelihood function which eliminates the complexity associated with the approach of Cook (1977, 1986) for spatial censored models. Some useful perturbation schemes are discussed. The newly developed method is illustrated using data from a dioxin contaminated site in Missouri that contain left-censored data as well as a dataset related to depths of a geological horizon that contains both left- and right-censored observations. In addition, a simulation study is presented that, explores the accuracy of the proposed measures in detecting influential observations under different perturbation schemes. The methodology addressed in this paper is implemented in the R package CensSpatial