The Influence Of Temperature, Humidity On Influenza Like Illness In Shanghai

Objective:To propose GAMAR (Generalized Additive Model with Autoregressive terms, and assess the impact of temperature and humidity on daily ILI (Influenza Like Illness) in Shanghai.Significance:ILI series is a time series that needs to be analyzed based on its past values. However, the predominantly used GLM and GAM are probabilistic models, and never use the autocorrelation information of dependent variable. In addition, using maximum likelihood to estimate GLM and GAM, we often assume independence among observations, which isn’t always true. GAMAR can explain autocorrelation of dependent variables. And it can not only fit data in our study, but also shed lights on other similar studies. Influenza is a kind of disease that is greatly harmful to human health. Experiments had proved the close connection between climate factors and transmission of influenza virus. But there are scarcely any epidemiological studies concerning connection between climate factors and ILI. Shanghai is an international metropolis, facing risks of seasonal influenza and influenza outbreak. Knowing the effect of climate factors is conducive to control the influenza epidemics, to reduce the risks of influenza outbreaks, to deploy resources properly and to give warning signals of influenza outbreak.Statistical Methods:Propose Generalized Additive Model with Autoregressive terms, and compare the performances of GAM and GAMAR when applied to data with autocorrelated dependent variable.Modeling:First using Poisson GAM with natural cubic splines presenting long term trend, the nonlinear effect of daily temperature, relative humidity, daily pressure, air pollutant PM10, S02, N02, dummy variable describing week effect, to analyze the association between ILI and climate factors. Since its Pearson residuals are autocorrelated, we use GAMAR for modeling. Predict Model:The former models both contain a long time trend spline, so they can’t be used for prediction. If we predict future ILI by GAM, the uncertainty of future trend would influence prediction accuracy. But if we use GAMAR, since AR terms already incorporate past information, so GAMAR can use past information to predict the future trend. To j ustify this, cross-validation is performed for ILI before and after time trend adjustment by GAM/GAMAR.Results and Conclusions:We proposed GAMAR for time series from environmental epidemiology, simulation study has proved for data with autocorrelation, GAM gave wrong results while GAMAR gave correct estimation. Then we used GAM to model the reliance of ILI on climate and air pollution, however we found its Pearson residuals are severely autocorrelated, thus violate the model assumption of GAM; so we use GAMAR instead. Pearson residuals given by GAMAR are hardly autocorrelated. And we found the estimated effect curves from GAMAR are more flat than GAM. For GAMAR, temperature in23days ago at10℃and30℃correspond to the highest ILI, at15～25℃correspond to the lowest ILI, so the effect curve is bimodal. When relative humidity in4days ago is low, the ILI is high, and ILI decline with rise of relative humidity. It fluctuates when relative humidity is between65～80%, then declines with rise of relative humidity when it’s higher than80%. Since we don’t know the future trend in the future, so model for prediction can’t contain time spline for trend, naturally GAMAR that can use the past information is a better choice. We found GAMAR was more robust than GAM with respect to long term trend adjustment. Additionally, GAMAR performed better in cross-validation than GAM irrespective of such adjustment.