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The present study considers non-mixture models based on the discrete Burr XIII distribution to model recurrent event data in the presence of a cure fraction. In this context, we provide an alternative to the standard Cox proportional hazards model using a discretized distribution to analyze lifetime data assuming a non-mixture structure for cure rates. In a Bayesian setting, the proposed methodology was considered for analyzing a real dataset from a retrospective cohort study that aimed to evaluate specific clinical conditions that affect the lifetimes of 299 heart failure patients admitted to the Institute of Cardiology and Allied Hospital – Faisalabad, Pakistan (April-December, 2015). The model validation process was addressed using the Cox-Snell residuals, which allowed us to identify the suitability of the proposed non-mixture cure rate model. [ABSTRACT FROM AUTHOR]

In many practical situations, clinical diagnostic procedures include two or more biological traits whose outcomes are expressed on a continuous scale and are then dichotomized using a cut point. As measurements are performed on the same individual there is a likely correlation between the continuous underlying traits that can go unnoticed when the parameter estimation is done with the resulting binary variables. In this paper, we compare the performance of two different indexes developed to evaluate the dependence between diagnostic clinical tests that assume binary structure in the results with the performance of the binary covariance and two copula dependence parameters.Muchos procedimientos de diagnóstico clínico médico exigen la evaluación de dos o mas rasgos biológicos que se ven alterados ante la presencia de fenómenos de enfermedad o infección, los cuales se expresan en una escala continúa de medición con posterior dicotomización usando de un valor límite o punto de corte. Dado que las mediciones son realizadas en el mismo individuo, los resultados probablemente presenten dependencia de algún tipo, lo cual puede ser ignorado en la etapa de análisis de datos dada la presentación binaria de los datos. En este estudio comparamos el comportamiento de dos parámetros de dependencia presentes en funciones de cópula con el de la covarianza binaria y dos índices creados para medir dependencia entre pruebas diagnósticas de respuesta dicótoma.

In this paper, we show different parameters estimation forms for multiple linear regression model. We used clinical data, where the interest was to verify the relationship among the mechanical assay maximum stress with femoral mass, femoral diameter and group of ovariectomized Wistar rats. We used three inference methods: Classic inference, based on the least square method; bayesian inference, based on the Bayes theorem; and bootstrap inference, based on resampling processes.En este trabajo se muestran diferentes formas de estimación de parámetros para el modelo de regresión lineal múltiple. Para estimar los parámetros del modelo se utilizaron los datos de un ensayo clínico donde el interés era verificar la relación entre la tensión mecánica máxima del fémur con la masa y el diámetro femoral en un grupo experimental de ratas ovariectomizadas de la raza Rattus norvegicus albinos, variedad Wistar. Para estimar los parámetros del modelo se compararon tres métodos: la metodología clásica basada en el método de mínimos cuadrados, la metodología bayesiana, basada en el teorema de Bayes y la inferencia bootstrap basada en los procesos de remuestreo.Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

The statistical literature presents many continuous probability distributions with only one parameter, which are extensively used in the analysis of lifetime data, such as the exponential, the Lindley, and the Rayleigh distributions. Alternatively, the use of discretized versions of these distributions can provide a better fit for the data in many applications. As the novelty of this study, we present inferences for the discrete Bilal distribution (DB) with one parameter introduced by Altun et al. (2020) in the presence of right-censored data and cure fraction. We assume standard maximum likelihood methods based on asymptotic normality of the maximum likelihood estimators and also a Bayesian approach based on MCMC (Markov Chain Monte Carlo) simulation methods to get inferences for the parameters of the discrete BD distribution. The use of the proposed model was illustrated with three examples considering real medical lifetime data sets. From these applications, we concluded that the proposed model based on the discrete DB distribution has good performance even with the inclusion of a cure fraction in comparison to other existing discrete models, such as the DsFx-I, Lindley, Rayleigh, and Burr-Hatke probability distributions. Moreover, the model can be easily implemented in standard existing software, such as the R package. Under a Bayesian approach, we assumed a gamma prior distribution for the parameter of the DB discrete distribution. We also provided a brief sensitivity analysis assuming the half-normal distribution in place of the gamma distribution for the parameter of the DB distribution. From the obtained results of this study, we can conclude that the proposed methodology can be very useful for researchers dealing with medical discrete lifetime data in the presence of right-censored data and cure fraction. [ABSTRACT FROM AUTHOR]

En este artículo se presenta una breve descripción de modelos GARCH multivariados y se realizan inferencias de la volatilidad de series de tiempo usando un enfoque Bayesiano, utilizando algoritmos de simulación de Monte Carlo (MCMC). Como una aplicación para ilustrar la metodología propuesta, se analizan los log-retornos de IBOVESPA y Dow Jones Industrial en una base semanal de 04/27/1993 para 11/03/2008.