Bivariate lifetime models in presence of cure fraction: a comparative study with many different copula functions.

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.

Developing a Hierarchical Model for the Spatial Analysis of PM10 Pollution Extremes in the Mexico City Metropolitan Area.

We implemented a spatial model for analysing PM 10 maxima across the Mexico City metropolitan area during the period 1995-2016. We assumed that these maxima follow a non-identical generalized extreme value (GEV) distribution and modeled the trend by introducing multivariate smoothing spline functions into the probability GEV distribution. A flexible, three-stage hierarchical Bayesian approach was developed to analyse the distribution of the PM 10 maxima in space and time. We evaluated the statistical model's performance by using a simulation study. The results showed strong evidence of a positive correlation between the PM 10 maxima and the longitude and latitude. The relationship between time and the PM 10 maxima was negative, indicating a decreasing trend over time. Finally, a high risk of PM 10 maxima presenting levels above 1000 µ g/m 3 (return period: 25 yr) was observed in the northwestern region of the study area.

Modelaje Bayesiano espacio-temporal de factores asociados con la incidencia del dengue en el área metropolitana de Maracay, Venezuela / Spatio-temporal Bayesian hierarchical modeling of Dengue incidence in the metropolitan area of Maracay, Venezuela

El dengue es uno de los mayores problemas de salud pública en el estado Aragua. La situación se ha deteriorado en los últimos años, reportándose la mayor epidemia durante el año 2001. En los años 2002 y 2003 las tasas de exposición y riesgos relativos en municipios que conforman al estado Aragua, muestran que el área metropolitana de Maracay concentra riesgos importantes. Los municipios Girardot (capital), Francisco Linares Alcántara y Santiago Mariño, son los que concentraron los mayores riesgos. Durante ese período el número de nuevos casos de dengue aumentó especialmente durante la época de lluvias, evidenciándose la existencia de un patrón estacional. Este trabajo propone Modelos Bayesianos Jerárquicos con estructura espacio temporal que incluye variables climáticas y socio-demográficas con las cuales se identificaron factores de mayor influencia en la incidencia del dengue y se determinaron las parroquias con mayores riesgos.Los ajustes de los modelos resultantes se obtuvieron mediante técnicas con cadenas Markov Monte Carlo (MCMC) y se compararon con el criterio de información de deviancia (DIC). Estos modelos constituyen una herramienta importante que expertos en epidemiología y miembros del sector de salud pública deben considerar para el control del vector Aedes aegypti Linnaeus en el estado Aragua.

Dengue fever is a major public health problem in Aragua State, Venezuela. The situation has worsened in recent years, with a major epidemic during 2001. During 2002 and 2003 the exposition rates and relative risks of the municipalities that encompass Aragua State showed the highest relative risk of infection in the metropolitan area of Maracay. The municipalities of Girardot (capital), Francisco Linares Alcántara and Santiago Mariño concentrated the highest risk. During 2002 and 2003 the number of new dengue cases increased especially during the rainy season, showing the existence of a seasonal pattern. The present work presents Bayesian Hierarchical Models with spatio-temporal structure that included climatic and socioeconomic explanatory variables used to identify factors of major influence on dengue incidence and determined the municipalities with higher risks. Models were fitted using Markov Chain Monte Carlo (MCMC) methods and selected using the deviance information criteria (DIC), respectively. These models constitute an important tool that epidemiologists and public health officers in Aragua State have to consider for the control of the vector Aedes aegypti Linnaeus.