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In employing spatial regression models for counts, we usually meet two issues. First, ignoring the inherent collinearity between covariates and the spatial effect would lead to causal inferences. Second, real count data usually reveal over or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining non-confounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data based on the gamma distribution assumption for waiting times. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation using the integrated nested Laplace approximation method. We also examine different popular approaches for handling spatial confounding and compare their performances in the presence of dispersion. We use the proposed methodology to analyze a clinical dataset related to stomach cancer incidence in Slovenia and perform a simulation study to understand the proposed approachs merits better.
Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. We outline a general approach to the estimation of causal quantities for settings with time-varying confound
Incorporating preclinical animal data, which can be regarded as a special kind of historical data, into phase I clinical trials can improve decision making when very little about human toxicity is known. In this paper, we develop a robust hierarchica
Most clinical trials involve the comparison of a new treatment to a control arm (e.g., the standard of care) and the estimation of a treatment effect. External data, including historical clinical trial data and real-world observational data, are comm
In causal mediation studies that decompose an average treatment effect into a natural indirect effect (NIE) and a natural direct effect (NDE), examples of post-treatment confounding are abundant. Past research has generally considered it infeasible t
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a Gaussian sp