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.

与均值回归（mean regression）方法相比，基于分位数回归（quantile regression）的统计分析更为全面、灵活，且对异常值（outliers）的敏感性更低。当研究者关注不同疾病间的关联时，联合疾病地图分析（joint disease mapping）可用于推断疾病间的相关性。现有多数研究通过多组关联均值回归模型探究此类疾病关联。本文针对多疾病场景提出一种可适配不同分位数水平的联合分位数回归框架。本研究的研究动机源于疟疾（Malaria）与G6PD基因缺乏症之间的理论关联——此前有医学研究者通过零散观察发现，G6PD水平偏高与疟疾发病率低于预期存在关联，这一现象最初指向G6PD可抑制疟疾的发生。此类关联无法通过均值回归模型开展探究，因此亟需在疾病地图分析框架中引入灵活的联合分位数回归方法。由于我们将该模型定义为隐高斯模型（latent Gaussian model），因此本研究提出的联合分位数疾病地图分析模型可通过随机样条（stochastic splines）实现协变量的线性与非线性效应建模。我们依托R语言软件包INLA内置的集成嵌套拉普拉斯近似（INLA）框架对该模型开展贝叶斯推断，即便针对大规模数据集，该模型也能实现高效运算。最后，我们通过对21个国家的疟疾与G6PD缺乏症发病情况开展联合分析，验证了该模型的适用性。