¹Universidad Nacional de Colombia, Statistics School, Medellín, Colombia. PhD. Email: mcjarami@unal.edu.co
²Universidad Nacional de Colombia, Statistics School, Medellín, Colombia. PhD. Email: jcsalaza@unal.edu.co

Usually, the exact time at which an event occurs cannot be observed for several reasons; for instance, it is not possible to constantly monitor a characteristic of interest. This generates a phenomenon known as censoring that can be classified as having a left censor, right censor or interval censor. When one is working with survival data in the presence of arbitrary censoring, the survival time of interest is defined as the elapsed time between an initial event and the next event that is generally unknown. This problem has been widely studied in the statistic literature and some progress has been made, toward resolving and the formulation of a bivariate likelihood to estimate parameters in a parametric regression model offers positive development opportunities. In this paper, we construct a bivariate likelihood for the Weibull regression model in the presence of interval censoring. Finally, its performance is illustrated by means of a simulation study.

Key words: Biostatistics, Confidence Bands, Goodness of Fit, Regression Models, Simulation, Survival Analysis.

Usualmente, el tiempo exacto en el que ocurre un evento no se puede observar por diversas razones; por ejemplo, no es posible un monitoreo constante de las características de interés. Esto genera un fenómeno conocido como censura que puede ser de tres tipos: a izquierda, a derecha, o de intervalo. En datos de tiempo de vida con censura arbitraria (censura a izquierda, a derecha, o de intervalo), el tiempo de supervivencia de interés es definido como el lapso de tiempo entre un evento inicial y el evento siguiente, el cuál generalmente es desconocido. Este problema ha sido ampliamente estudiado en la literatura estadística, y se evidencian avances importantes. Sin embargo, la construcción de una verosimilitud bivariada para la estimación de los parámetros de modelos de regresión paramétricos, ofrece oportunidades de desarrollo. En este trabajo se construye una verosimilitud bivariada para el modelo de regresión Weibull, en presencia de censura arbitraria. Finalmente se ilustra su desempeño por medio de un estudio de simulación.

Palabras clave: análisis de supervivencia, bandas de confianza, bioestadística, modelos de regresión, simulación.

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