Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: A Bayesian approach |
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Authors: | Taban Baghfalaki Mojtaba Ganjali Damon Berridge |
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Affiliation: | 1. Department of Statistics, Shahid Beheshti University, , Tehran, 1983963113 Iran;2. Department of Mathematics and Statistics, Fylde College, Lancaster University, , Lancaster, UK |
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Abstract: | Joint modeling of longitudinal data and survival data has been used widely for analyzing AIDS clinical trials, where a biological marker such as CD4 count measurement can be an important predictor of survival. In most of these studies, a normal distribution is used for modeling longitudinal responses, which leads to vulnerable inference in the presence of outliers in longitudinal measurements. Powerful distributions for robust analysis are normal/independent distributions, which include univariate and multivariate versions of the Student's t, the slash and the contaminated normal distributions in addition to the normal. In this paper, a linear‐mixed effects model with normal/independent distribution for both random effects and residuals and Cox's model for survival time are used. For estimation, a Bayesian approach using Markov Chain Monte Carlo is adopted. Some simulation studies are performed for illustration of the proposed method. Also, the method is illustrated on a real AIDS data set and the best model is selected using some criteria. |
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Keywords: | Bayesian approach Cox's proportional hazard model Joint models Longitudinal data Markov Chain Monte Carlo Normal/independent distributions Time to event data |
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