Calculating Age-Standardized Rate Trends

The age-standardized rate (ASR) is a critical and representative parameter when considering differences in the age structure of multiple populations. The ASR is a weighted mean of age-specific rates. The ASR is calculated on basis of the age structure of standard populations using the following formula: $$\text{ASR}=\frac{{\sum }_{i=1}^A{a}_i{w}_i}{{\sum }_{i=1}^A{w}_i}\times 100,000$$
where a_i is the age-specific rate in the i^th age group, w_i is the number of persons (or the weight) in the corresponding i^th age subgroup of the selected reference standard population, and A is the number of age groups.
The ASR trend is a widely accepted measure that estimates the changing patterns of disease burden. The estimated annual percentage change (EAPC) is a common index reflecting the temporal trend of ASR, which has been described in detail elsewhere [18 (link)]. A regression line was fitted to the natural logarithm of the ASR. EAPC and its 95% confidence interval (CI) were estimated with the linear regression model. The formula is as following: $$\text{y}=\alpha +\beta \text{x}+\epsilon$$ $$\text{EAPC}=100\times \left(\text{exp}\left(\beta \right)-1\right)$$
where y = ln (ASR), and x is the calendar year. The trends were judged: if the EAPC and its 95% CI were > 0, the ASR was in an increasing trend; if EAPC and its 95% CI were < 0, the ASR was in a decreasing trend; other values meant that the ASR was stable over time. For the aim to analyze the impact factors of EAPC, the respective associations between EAPCs and ASR in 2000, and between EAPCs and HDI in 2017, were calculated by using the Pearson correlation analysis in the Statistical Package for Social Sciences (SPSS; version 25.0; SPSS Inc., Chicago, IL, USA). The choropleth maps were drawn using the statistical software R 3.6.2 (Lucent Technologies, Jasmine Mountain, USA). A P value of less than 0.05 was deemed to be statistically significant.