Exploratory Research In Distribution Of Tuberculosis Based On Spatial Lag Model

Tuberculosis is known as "white plague", of which the occurrence, infection and spread is a kind of spatial phenomenon and closely related to factors such as environment, population, and climate. Some researches have shown that there exists spatial correlation and heterogeneity in the distribution of tuberculosis. Therefore, it’s very necessary to explore spatial pattern and influencing factors of tuberculosis distribution from a point of quantitative view, by using the method of spatial epidemiology and statistics.Firstly, we apply Spatial Autocorrelation Analysis to explore spatial pattern of tuberculosis distribution from both global and local perspective by using the GeoDa software. Then based on the spatial dependence, we construct Spatial Lag Model to explore the potential factors influencing the distribution of tuberculosis. Thirdly we define a ternary weight matrix to highlight the influence of adjacent tuberculosis zone of high incidence, construct the Spatial Lag Model and compare with binary weighted spatial lag model.The results are shown as follows:1. The global Moran’s Ⅰ autocorrelation index from2005to2011are respectively0.2590,0.2551,0.3081,0.2516,0.3424,0.3925,0.4512and all of them are statistically significant. This shows that there exists spatial aggregation phenomenon, which is more and more obvious, in the distribution of tuberculosis.2. Local indicator of spatial analysis shows that from2005to2011, the number of high-high type tuberculosis zone which is statistically significant, increases from1to5. Concretely, they are Hunan province in2005, Hunan and Chongqing in2008, Hunan, Sichuan, Tibet, Qinghai and Xinjiang in2011. But the number of low-low type tuberculosis zone which is statistically significant has no noticeable change. They are mostly located still in Beijing-Tianjin-Hebei region.3. Both urban-rural resident deposits and investment on three industrial castoffs have a significant impact on tuberculosis incidence. Specifically, every increase of100billion RMB in urban-rural resident deposits will lead to increasing1.8tuberculosis patients per100000populations, while every increase of10million RMB in investment on three industrial castoffs will lead to decreasing2.4tuberculosis patients per100000populations.4. The absolute value of log likelihood function in Spatial Lag Model is136.131, less than that of OLS regression model(138.75); and the Moran’s1index of residuals in Spatial Lag Model is0.0258, without statistical significance. This shows that Spatial Lag Model is superior to the OLS regression model and it eliminates the spatial dependence of residuals, which lead to the regression error term satisfying the classical assumptions (independent identically distributed).5. In ternary weighted Spatial Lag Model, the absolute value of log likelihood function is between135.74-135.85and the sum of residuals is between11037-11366, both of which is less than that of binary weighted Spatial Lag Model(136.131and14886respectively). This indicates that ternary weighted Spatial Lag Model is better than binary weighted spatial lag model, and different weight values have little impact on model fitting effect.The innovation of this article is that we bring up the definition of ternary weight matrix based on both geographical adjacent relations and attribute values of spatial units, which highlight the effect of adjacent tuberculosis zone of high incidence and optimize the fitting effect of Spatial Lag Model. This will have a guiding significance in the further study of spatial lag regression model.