|
Abstract:
|
For regionally aggregated disease incidence data, Bayesian hierarchical regression models involve region-specific latent random effects modelled jointly as having a multivariate Gaussian distribution. To model the spatial dependence between regions in the precision matrix, we propose an autoregressive model based upon directed acyclic graphs (DAGAR). Compared to the widely used improper and proper CAR model, DAGAR guarantees positive definiteness and improves interpretability of spatial correlation. In this talk, I'll briefly discuss the underlying idea behind DAGAR and extend it to multiple diseases. We will now allow spatial dependence between sites and among multiple diseases. We propose two multivariate DAGAR models using conditional and joint probability laws. In multivariate DAGAR, for each disease, the spatial random effects have a conditional multivariate Gaussian distribution given random effects of other diseases, with precision matrix following a DAGAR model. The joint multivariate DAGAR model using latent factors. We will demonstrate and compare them with existing multivariate CAR models with simulation experiments and with public health applications to disease mapping.
|
