Comparison of different methods in dealing with HIV viral load data with diversified missing value mechanism on HIV positive MSM / 中华流行病学杂志

Objective To compare results of different methods in organizing HIV viral load (VL) data with missing values mechanism. Methods We used software SPSS 17.0 to simulate complete and missing data with different missing value mechanism from HIV viral loading data collected from MSM in 16 cities in China in 2013. Maximum Likelihood Methods Using the Expectation and Maximization Algorithm (EM), regressive method, mean imputation, delete method, and Markov Chain Monte Carlo (MCMC) were used to supplement missing data respectively. The results of different methods were compared according to distribution characteristics, accuracy and precision. Results HIV VL data could not be transferred into a normal distribution. All the methods showed good results in iterating data which is Missing Completely at Random Mechanism (MCAR). For the other types of missing data, regressive and MCMC methods were used to keep the main characteristic of the original data. The means of iterating database with different methods were all close to the original one. The EM, regressive method, mean imputation, and delete method under-estimate VL while MCMC overestimates it. Conclusion MCMC can be used as the main imputation method for HIV virus loading missing data. The iterated data can be used as a reference for mean HIV VL estimation among the investigated population.

Comparison of different methods in dealing with HIV viral load data with diversified missing value mechanism on HIV positive MSM / 中华流行病学杂志

Objective To compare results of different methods in organizing HIV viral load (VL) data with missing values mechanism. Methods We used software SPSS 17.0 to simulate complete and missing data with different missing value mechanism from HIV viral loading data collected from MSM in 16 cities in China in 2013. Maximum Likelihood Methods Using the Expectation and Maximization Algorithm (EM), regressive method, mean imputation, delete method, and Markov Chain Monte Carlo (MCMC) were used to supplement missing data respectively. The results of different methods were compared according to distribution characteristics, accuracy and precision. Results HIV VL data could not be transferred into a normal distribution. All the methods showed good results in iterating data which is Missing Completely at Random Mechanism (MCAR). For the other types of missing data, regressive and MCMC methods were used to keep the main characteristic of the original data. The means of iterating database with different methods were all close to the original one. The EM, regressive method, mean imputation, and delete method under-estimate VL while MCMC overestimates it. Conclusion MCMC can be used as the main imputation method for HIV virus loading missing data. The iterated data can be used as a reference for mean HIV VL estimation among the investigated population.

Population Forecasts for Bangladesh, Using a Bayesian Methodology.

Population projection for many developing countries could be quite a challenging task for the demographers mostly due to lack of availability of enough reliable data. The objective of this paper is to present an overview of the existing methods for population forecasting and to propose an alternative based on the Bayesian statistics, combining the formality of inference. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique for Bayesian methodology available with the software WinBUGS. Convergence diagnostic techniques available with the WinBUGS software have been applied to ensure the convergence of the chains necessary for the implementation of MCMC. The Bayesian approach allows for the use of observed data and expert judgements by means of appropriate priors, and a more realistic population forecasts, along with associated uncertainty, has been possible.

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.

Análise Bayesiana no estudo do tempo de retorno das precipitações pluviais máximas em Jaboticabal (SP) / Bayesian analysis for estimating the return period of maximum precipitation at Jaboticabal São Paulo state, Brazil

Dados históricos de precipitação máxima são utilizados para realizar previsões de chuvas extremas, cujo conhecimento é de grande importância na elaboração de projetos agrícolas e de engenharia hidráulica. A distribuição generalizada de valores extremos (GEV) tem sido aplicada com freqüência nesses tipos de estudos, porém, algumas dificuldades na obtenção de estimativas confiáveis sobre alguma medida dos dados têm ocorrido devido ao fato de que, na maioria das situações, tem-se uma quantidade escassa de dados. Uma alternativa para obter melhorias na qualidade das estimativas seria utilizar informações dos especialistas de determinada área em estudo. Sendo assim, objetiva-se neste trabalho analisar a aplicação da Inferência Bayesiana com uma distribuição a priori baseada em quantis extremos, que facilite a incorporação dos conhecimentos fornecidos por especialistas, para obter as estimativas de precipitação máxima para os tempos de retorno de 10 e 20 anos e seus respectivos limites superiores de 95 por cento, para o período anual e para os meses da estação chuvosa em Jaboticabal (SP). A técnica Monte Carlo, via Cadeias de Markov (MCMC), foi empregada para inferência a posteriori de cada parâmetro. A metodologia Bayesiana apresentou resultados mais acurados e precisos, tanto na estimação dos parâmetros da distribuição GEV, como na obtenção dos valores de precipitação máxima provável para a região de Jaboticabal, apresentando-se como uma boa alternativa na incorporação de conhecimentos a priori no estudo de dados extremos.

Historical maximum rainfall data are used to forecast extreme rainfall, which is important to elaborate agricultural and hydraulic engineering projects. Generalized Extreme Value Distribution (GEV) has been applied in such type of studies. Since those values are extracted from the upper (or lower) tail of the original distribution, a scarce amount of data is obtained in most cases, which may be a problem acquiring reliable estimates about some measure of interest. An alternative to overcome this potential problem would be the use of information available from experts in the area. Therefore, this paper intended to analyze the application of the Bayesian Inference using a priori distribution based on extreme quantiles, which facilitates the incorporation of the information supplied by the experts in order to determine the punctual and the 95 percent upper limit estimates of the probable maximum precipitation for return periods of 10 and 20 years, yearly and monthly in Jaboticabal, São Paulo State, Brazil. Markov Chain Monte Carlo (MCMC) methods were used to a posterior inference of each parameter. Bayesian inference yielded more suitable and accurate results in the estimation of the parameters of the GEV distribution as well as in the determination of the values of the probable maximum precipitation estimates for Jaboticabal. It turned out as an interesting way of incorporating prior knowledge to the study of extreme data.