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 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.