Comparación de los métodos de imputación múltiple, Bayesianos y el algoritmo ICM (Iterative Convex Minorant) para datos con censura en intervalos
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Bustos Giraldo, Olga Alexandra
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Los datos con censura en intervalos son comunes en varias áreas del conocimiento, tales como: epidemiología, finanzas, demografía, medicina, entre otros. Ocurren cuando el evento de interés, el tiempo de falla, no se observa exactamente, sino que se encuentra dentro de algún intervalo del tiempo de observación. La solución para esta situación es realizar imputación de los datos que no se conocen exactamente. Las alternativas propuestas son los métodos de imputación simple y múltiple, los métodos Bayesianos y el algoritmo ICM (Iterative Convex Minorant) bajo el modelo de riesgos proporcionales de Cox fueron estudiados en esta investigación. En esta tesis se realizará una comparación vía simulación de los métodos anteriormente descritos. La comparación se realizará utilizando el error cuadrático medio (ECM) de las respectivas estimaciones de los parámetros de interés y la probabilidad de cobertura con un nivel de confianza nominal del 95% y finalmente se realizará una aplicación con datos reales
Abstract: Interval-censored data are common in several areas of knowledge, such as: epidemiology, _nance, demography and medicine. These data occur when the event of interest, the time of failure, is not observed exactly, but it is within a known interval of observation times. A solution for this situation is to impute the data that is not known exactly. The proposed alternatives are simple and multiple imputation methods. Bayesian methods and the ICM (Iterative Convex Minorant) algorithm under the proportional hazards model of Cox were studied in this research. In this thesis, a comparison will be made via simulation of the methods described above. The comparison will be made using the mean square error (MSE) of the respective estimators of the parameters of interest and the probability of coverage with a nominal con_dence level of 95 %. Finally an application will be made with real data.
Abstract: Interval-censored data are common in several areas of knowledge, such as: epidemiology, _nance, demography and medicine. These data occur when the event of interest, the time of failure, is not observed exactly, but it is within a known interval of observation times. A solution for this situation is to impute the data that is not known exactly. The proposed alternatives are simple and multiple imputation methods. Bayesian methods and the ICM (Iterative Convex Minorant) algorithm under the proportional hazards model of Cox were studied in this research. In this thesis, a comparison will be made via simulation of the methods described above. The comparison will be made using the mean square error (MSE) of the respective estimators of the parameters of interest and the probability of coverage with a nominal con_dence level of 95 %. Finally an application will be made with real data.