Abstract:
Disease mapping models have found wide range of applications to epidemiology and
public health. These models typically extend from generalized linear models (GLM)
and are usually implemented using a Bayesian approach. Most of the disease mapping
models incorporate random effects that assume either a Gaussian exchangeable prior
for the spatially unstructured heterogeneity or the popular Gaussian CAR priors for
the spatially structured variability. However, this Gaussian assumption is often violated
since random effects can be skewed. This thesis proposed models that relax the
usual normality assumption on the spatially unstructured random effect by using skew
normal and skew-t distributions. In the analysis of 2016 HIV and AID data in Kenya,
it was found out that models whose unstructured random effects follow asymmetric
skewed distributions perform better than models with corresponding symmetric distributed
unstructured random effects. Classical random-effects models for count data
includes the Poisson-gamma model, that utilizes the conjugate feature between the
Poisson and Gamma distributions to attain closed-form posterior distribution but accounts
only for overdispersion or extra variation, and the Gaussian conditional autoregressive
(CAR) models, that model spatial correlation but does not have a closed-form
posterior distribution. This thesis also considers an alternative model that combines
a Poisson-gamma model with a spatially structured skew-t random effect in the same
model thus accounting for the extra variability, spatial correlation and skewness in the
data. In the analysis of 2016 Kenya HIV and AIDS data, the skew-t spatial combined
random effects model was found to provide a better alternative to the classical disease
mapping models. Simulation studies also show that the proposed models perform better
than the classical disease mapping models. To model spatio-temporal variation,
this thesis considered Leroux CAR (LCAR) prior for spatial random effect and implemented
Bayesian analysis using integrated nested Laplace approximations (INLA).
In the analysis of spatio-temporal variation of HIV and AIDS in Kenya for the period
2013–2016, it was found out that counties located in theWestern region of Kenya show
significantly higher HIV and AIDS risks as compared to the other counties.
