Motivated by a real data example on renal graft failure, we propose a new semiparametric multivariate joint model that relates multiple longitudinal outcomes to a time-to-event. To allow for greater flexibility, key components of the model are modelled nonparametrically. In particular, for the subject-specific longitudinal evolutions we use a spline-based approach, the baseline risk function is assumed piecewise constant, and the distribution of the latent terms is modelled using a Dirichlet Process prior formulation. Additionally, we discuss the choice of a suitable parameterization, from a practitioner's point of view, to relate the longitudinal process to the survival outcome. Specifically, we present three main families of parameterizations, discuss their features, and present tools to choose between them.

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The asymmetric Laplace density (ALD) is used as a working likelihood for Bayesian quantile regression. Sriram et al. (2013) derived posterior consistency for Bayesian linear quantile regression based on the misspecified ALD. While their paper also argued for √ n−consistency, (2017) highlighted that the argument was only valid for n α rate for α < 1/2. However, √ n−rate is necessary to carry out meaningful Bayesian inference based on the ALD. In this paper, we give sufficient conditions for √ n−consistency in the more general setting of Bayesian non-linear quantile regression based on ALD. In particular, we derive √ n−consistency for the Bayesian linear quantile regression. Our approach also enables an interesting extension of the linear case when number of parameters p increases with n, where we obtain posterior consistency at the rate n α for α < 1/2. Sriram and Ramamoorthi

Summary We develop a spatial Poisson hurdle model to explore geographic variation in emergency department (ED) visits while accounting for zero inflation. The model consists of two components: a Bernoulli component that models the probability of any ED use (i.e., at least one ED visit per year), and a truncated Poisson component that models the number of ED visits given use. Together, these components address both the abundance of zeros and the right-skewed nature of the nonzero counts. The model has a hierarchical structure that incorporates patient- and area-level covariates, as well as spatially correlated random effects for each areal unit. Because regions with high rates of ED use are likely to have high expected counts among users, we model the spatial random effects via a bivariate conditionally autoregressive (CAR) prior, which introduces dependence between the components and provides spatial smoothing and sharing of information across neighboring regions. Using a simulation study, we show that modeling the between-component correlation reduces bias in parameter estimates. We adopt a Bayesian estimation approach, and the model can be fit using standard Bayesian software. We apply the model to a study of patient and neighborhood factors influencing emergency department use in Durham County, North Carolina.