  Statistical analysis based on quantile regression methods is more
comprehensive, flexible, and less sensitive to outliers when compared to mean
regression methods. When the link between different diseases are of interest,
joint disease mapping is useful for measuring directional correlation between
them. Most studies study this link through multiple correlated mean
regressions. In this paper we propose a joint quantile regression framework for
multiple diseases where different quantile levels can be considered. We are
motivated by the theorized link between the presence of Malaria and the gene
deficiency G6PD, where medical scientist have anecdotally discovered a possible
link between high levels of G6PD and lower than expected levels of Malaria
initially pointing towards the occurrence of G6PD inhibiting the occurrence of
Malaria. This link cannot be investigated with mean regressions and thus the
need for flexible joint quantile regression in a disease mapping framework. Our
joint quantile disease mapping model can be used for linear and non-linear
effects of covariates by stochastic splines, since we define it as a latent
Gaussian model. We perform Bayesian inference of this model using the INLA
framework embedded in the R software package INLA. Finally, we illustrate the
applicability of model by analyzing the malaria and G6PD deficiency incidences
in 21 African countries using linked quantiles of different levels.
