New contributions to joint models of longitudinal and survival outcomes : two-stage approaches
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2021
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Abstract
Joint models of longitudinal and survival outcomes have gained much popularity over the last three decades. This type of modeling consists of two submodels, one longitudinal and one survival, which are connected by some common term. Unsurprisingly, sharing information makes the inferential process highly time-consuming. This problem can be overcome by estimating the parameters of each submodel separately, leading to a natural reduction in the complexity of joint models, but often producing biased estimates. Hence, we propose different two-stage strategies that first fits the longitudinal submodel and then plug the shared information into the survival submodel. Our proposals are developed for both the frequentist and Bayesian paradigms. Specifically, our frequentist two-stage approach is based on the simulation-extrapolation algorithm. On the other hand, we propose two Bayesian approaches, one inspired by frailty models and another that uses maximum a posteriori estimations and longitudinal likelihood to calculate posterior distributions of random effects and survival parameters. Based on simulation studies and real applications, we empirically compare our two-stage approaches with their main competitors. The results show that our methodologies are very promising, since they reduce the estimation bias compared to other two-stage methods and require less processing time than joint specification approaches.
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Tesis (Doctor en Estadística)--Pontificia Universidad Católica de Chile, 2021