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Abstract:
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There are many applications in which interest lies in modeling the survival time of two variables from the same or matched pairs of subjects. For example the researcher may desire to model the time to failure of two organs in individuals, or the failure time of the same organ in twin studies. The focus of our research is in obtaining inference for the bivariate mean residual life (MRL) function, which characterizes the survival distribution through the inversion formula. While bivariate survival has been well-studied under classical and Bayesian perspectives, the focus has remained on inference for the joint survival rather than the MRL. Here, we present a Bayesian nonparametric bivariate survival model and obtain inference for the associated bivariate MRL function. Namely, we use a Dirichlet process mixture model with a bivariate gamma kernel having gamma marginals, which is known to have pointwise denseness on univariate MRL space. We explore the implied structure for the bivariate MRL under the model, and demonstrate the diversity of the functional shapes that can be obtained. We apply our model to a real data set, and compare our results to current bivariate survival models.
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