Joint quantile disease mapping with application to Malaria and G6PD deficiency

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 inferring 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 arise. 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, resulting in a
very efficient model even for large datasets. Finally, we illustrate the
applicability of the model by analyzing the malaria and G6PD deficiency
incidences, jointly, in 21 countries.