Predicting seasonal influenza transmission using functional regression models with temporal dependence

This paper proposes a novel approach that uses meteorological information to predict the incidence of influenza in Galicia (Spain). It extends the Generalized Least Squares (GLS) methods in the multivariate framework to functional regression models with dependent errors. These kinds of models are useful when the recent history of the incidence of influenza are readily unavailable (for instance, by delays on the communication with health informants) and the prediction must be constructed by correcting the temporal dependence of the residuals and using more accessible variables. A simulation study shows that the GLS estimators render better estimations of the parameters associated with the regression model than they do with the classical models. They obtain extremely good results from the predictive point of view and are competitive with the classical time series approach for the incidence of influenza. An iterative version of the GLS estimator (called iGLS) was also proposed that can help to model complicated dependence structures. For constructing the model, the distance correlation measure was employed to select relevant information to predict influenza rate mixing multivariate and functional variables. These kinds of models are extremely useful to health managers in allocating resources in advance to manage influenza epidemics.本研究提出一种全新方法，借助气象信息对西班牙加利西亚（Galicia）地区的流感发病率进行预测。该方法将多元框架下的广义最小二乘法（Generalized Least Squares，GLS）拓展至带有相依误差的函数型回归模型。当流感发病率的近期历史数据难以获取时（例如，因与健康信息报送方的通信延迟导致数据滞后），此类模型可通过修正残差的时间相依性，并利用更易获取的变量来构建预测，因而具备实际应用价值。仿真实验结果表明，相较于经典模型，广义最小二乘估计量对回归模型相关参数的估计效果更优；从预测性能来看，该方法表现极佳，且与针对流感发病率的经典时间序列方法相比颇具竞争力。本研究还提出了广义最小二乘估计量的迭代版本（记为iGLS），可用于建模复杂的相依结构。在模型构建过程中，本研究采用距离相关测度来筛选相关信息，以融合多元变量与函数型变量对流感发病率进行预测。此类模型可帮助卫生管理者提前调配资源以应对流感疫情，具备极高的实用价值。