New framework of Getis-Ord's indexes associating spatial autocorrelation with interaction

Exploring the County Level Mortality Pattern Variations in Rural Areas of Iran (2006-2016)

BACKGROUND

Mortality rate in rural areas is a useful measure of the health of the population and the function of the health system, which varies over space and time. The objective of this research is to explore the spatial and temporal variations in the rural mortality rate in Iran at the county level in 2006, 2011, and 2016.

METHODS

data were gathered from the rural population and mortality statistics published by the Statistical Centre of Iran (SCI) and the National Organization for Civil Registration (NOCR). Global spatial patterns were assessed using the global Moran's I and local clusters through the local Moran's I.

RESULTS

Spatial distribution of rural mortality rate shows that during the years under study the number of counties with a lower rate has increased. The counties with rate of less form continuous areas in the southwest, central and east regions. The excess risk map reveals significant variations in both value and extent. Also, the values of Moran's index increased from 0.1848 in 2006 to 0.4041 in 2016, which indicates the strengthening of the cluster spatial pattern of the overall rural mortality rate. Local patterns have undergone substantial changes over space and time.

CONCLUSION

The findings indicate significant spatial and temporal variations in rural mortality rates in Iran. Policy-makers can use this information to plan and enhance healthcare infrastructure in specific counties. The findings serve for evaluating the effectiveness of health policies, enabling policy-makers to make informed decisions, allocate resources efficiently and design targeted interventions for improved public health outcomes.

Spatial epidemiological analysis of the burden of liver cancer in China

Background

Liver cancer is one of the most common cancers in the world, with unique regional variations in disability-adjusted life years (DALY) rate, nearly 50% of liver cancer cases occur in China. Therefore, understanding the epidemiological characteristics of liver cancer is of utmost importance. In this study, to analyze the spatial distribution characteristics and clustering of the DALY rate of liver cancer in 1990 and 2017 in China based on provincial administrative divisions, and to explore its possible influencing factor.

Methods

The DALY rate data of liver cancer at the provincial level in China were collected, the global autocorrelation of the DALY rate was analyzed by Moran's I, the local autocorrelation of the DALY rate was analyzed by Getis-Ord-Gi*, and the influencing factors related to the DALY rate were analyzed by the least squares regression model.

Results

The DALY rate of liver cancer in China generally showed an increasing trend. The DALY rate increased in 22 provinces and decreased in nine provinces. In 2017, the distribution of DALY rate in all provinces showed heterogeneity, with the highest DALY rate in Guangxi (1,363.37/100,000) and the lowest in Beijing (315.78/100,000). In 2017, the low and low clustering were mainly concentrated in Inner Mongolia, Ningxia, Shanxi, Hebei, and Tianjin. The low and high clustering in Yunnan, Guizhou, and Guangdong, were surrounded by the high clustering in neighboring provinces, high and high concentration is mainly concentrated in Hunan and neighboring provinces. The results of the least square regression model showed that the per capita years of education, hepatitis B incidence and the proportion of population over 65 years old had an impact on the DALY rate of liver cancer (P<0.05).

Conclusions

The DALY rate of liver cancer in China showed an overall increasing trend. In 2017, the DALY rate of liver cancer in China had a spatial aggregation in the whole country, and the per capita years of education, the incidence of hepatitis B and the proportion of population over 65 years old had an impact on the DALY rate of liver cancer in space.

Spatial autocorrelation equation based on Moran's index

Moran's index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran's index is chiefly a statistical measurement rather than a mathematical model. This paper is devoted to establishing spatial autocorrelation models by means of linear regression analysis. Using standardized vector as independent variable, and spatial weighted vector as dependent variable, we can obtain a set of normalized linear autocorrelation equations based on quadratic form and vector inner product. The inherent structure of the models' parameters are revealed by mathematical derivation. The slope of the equation gives Moran's index, while the intercept indicates the average value of standardized spatial weight variable. The square of the intercept is negatively correlated with the square of Moran's index, but omitting the intercept does not affect the estimation of the slope value. The datasets of a real urban system are taken as an example to verify the reasoning results. A conclusion can be reached that the inner product equation of spatial autocorrelation based on Moran's index is effective. The models extend the function of spatial analysis, and help to understand the boundary values of Moran's index.

Geospatial modelling to estimate the territory at risk of establishment of influenza type A in Mexico - An ecological study

The aim of this study was to estimate the territory at risk of establishment of influenza type A (EOITA) in Mexico, using geospatial models. A spatial database of 1973 outbreaks of influenza worldwide was used to develop risk models accounting for natural (natural threat), anthropic (man-made) and environmental (combination of the above) transmission. Then, a virus establishment risk model; an introduction model of influenza A developed in another study; and the three models mentioned were utilized using multi-criteria spatial evaluation supported by geographically weighted regression (GWR), receiver operating characteristic analysis and Moran's I. The results show that environmental risk was concentrated along the Gulf and Pacific coasts, the Yucatan Peninsula and southern Baja California. The identified risk for EOITA in Mexico were: 15.6% and 4.8%, by natural and anthropic risk, respectively, while 18.5% presented simultaneous environmental, natural and anthropic risk. Overall, 28.1% of localities in Mexico presented a High/High risk for the establishment of influenza type A (area under the curve=0.923, P<0.001; GWR, r2=0.840, P<0.001; Moran's I =0.79, P<0.001). Hence, these geospatial models were able to robustly estimate those areas susceptible to EOITA, where the results obtained show the relation between the geographical area and the different effects on health. The information obtained should help devising and directing strategies leading to efficient prevention and sound administration of both human and financial resources.

An analytical process of spatial autocorrelation functions based on Moran's index

A number of spatial statistic measurements such as Moran’s I and Geary’s C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary’s coefficient and Getis’ index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.