Applied Mixed Generalized Additive Model to Assess the Effect of Temperature on the Incidence of Bacillary Dysentery and Its Forecast

Background: Association between bacillary dysentery (BD) disease and temperature has been reported in some studies applying Poisson regression model, however the effect estimation might be biased due to the data autocorrelation. Furthermore the temperature effect distributed in the time of different lags has not been studied either. The purpose of this work was to obtaining the association between the BD counts and the climatic factors such as temperature in the form of the weighted averages, concerning the autocorrelation pattern of the model residuals, and to make short term predictions using the model. The data was collected in the city of Shanghai from 2004 to 2008. Methods: We used mixed generalized additive model (MGAM) to analyze data on bacillary dysentery, temperature and other covariates with autoregressive random effect. Short term predictions were made using MGAM with the moving average of the BD counts. Main Results: Our results showed that temperature was significant linearly associated with the logarithm of BD count for temperature in the range from 12°C to 22°C. Optimal weights in the temperature effect have been obtained, in which the one of 1-day-lag was close to 0, and the one of 2-days-lag was the maximum (p-value of the difference was less than 0.05). The predictive model was showing good fitness on the internal data with R2 value 0.875, and the good short term prediction effect on the external data with correlation coefficient to be 0.859. Conclusion: According to the model estimation, corresponding Risk Ratio to affect BD was close to 1.1 when temperature effect goes up for 1°C in the range from 12°C to 22°C. And the 1-day incubation period could be inferred from the model estimation. Good prediction has been made using the predictive MGAM.