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# 数据科学代写|高级数据分析代写Advanced Data Analysis代考|EES1137 Standardized incidence ratio (SIR)

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## 数据科学代写|高级数据分析代写Advanced Data Analysis代考|Standardized incidence ratio (SIR)

The risk of $\mathrm{TC}$ was represented through the production of maps showing the spatial distribution, for each census tract, of the standardized incidence ratio (SIR). The SIRs were calculated for each inhabited census tract by indirect standardization (Waller and Gotway 2004, pp. 12-15), using the incidence rate of TC observed in the same period (2003-2016) in the whole of eastern Sicily. SIR is the ratio between observed TC cases and expected TC cases in each census tract $i$
$$S I R=\frac{O_{i}}{E_{i}}$$
where $O_{i}$ is the number of cases observed for census tract $i$ and $E_{i}$ is the number of cases expected in the same census tract $i$. The number of expected cases is calculated as the product of the population at risk (and therefore the entire resident population) in the given census tract $i$ and the general incidence rate for the entire investigated area
$$E_{i}=P_{i} r_{+}$$

where $P_{i}$ is the population at risk in the specific census tract $i$ and $r_{+}$is the general incidence rate of TC, calculated for the four provinces of interest as a whole, as
$$r_{+}=\frac{O_{+}}{P_{+}}$$
where $O_{+}$corresponds to the number of cases of TC observed and $P_{+}$is the resident population in the whole of eastern Sicily. The subscript $+$ indicates that the variables are calculated for the totality of the study area. Hence, it follows that the SIR of a single census tract is thus calculated as
$$S I R=\frac{O_{i}}{P_{i} \frac{O_{+}}{P_{+}}}$$

## 数据科学代写|高级数据分析代写Advanced Data Analysis代考|Local Moran’s I statistic

The local Moran’s I indicator belongs to the so-called LISA (Local Indicators of Spatial Association) or local indicators of spatial autocorrelation proposed by Anselin (1995). It is calculated with the following formula:
$$I_{i}=\frac{\left(x_{i}-\bar{x}\right)}{S_{i}^{2}} \sum_{j=1, j \neq i}^{n}\left(w_{i j}\left(x_{j}-\bar{x}\right)\right)$$
where $n$ is the number of geographical units, $x_{i}$ is the value of the variable $x$ in region $i, x^{-}$is the sample mean of the variable, $x_{j}$ is the value of the variable $x$ in all other regions (where $j \neq i$ ), $S_{i}^{2}$ is the sample variance of the variable $x$ and $w_{i j}$ is a weight that can be defined as the inverse of the distance between the various regions. There are other ways to define $w_{i j}$, some contemplate choosing a limit distance to define the neighborhood of a given region: the regions that fall within the limit distance take on a weight equal to one, while the external regions take on a weight equal to zero.

Positive and high values of the local Moran’s I index indicate that a given region is surrounded by neighboring regions with similar high (or low) values of the variable under study. In this case, the spatial groups detected are defined as “high-high” (region with a high value surrounded by regions with high values) or “low-low” (region with low value surrounded by regions with low values). In terms of cancer risk, a “high-high” cluster would indicate a high-risk area, while a “low-low” cluster would denote a low-risk area. Negative values of the local Moran’s I reveal that the region under examination is a spatial outlier. A spatial outlier is an area that has a markedly different value from that of its neighbors (Cerioli and Riani 1999). Spatial outliers are divided into “high-low” (high value surrounded by neighbors with low values) and “low-high” (low value surrounded by neighbors with high values).

## 数据科学代写|高级数据分析代写Advanced Data Analysis代考|Standardized incidence ratio (SIR)

$$S I R=\frac{O_{i}}{E_{i}}$$

$$E_{i}=P_{i} r_{+}$$

$$r_{+}=\frac{O_{+}}{P_{+}}$$

$$S I R=\frac{O_{i}}{P_{i} \frac{O_{+}}{P_{+}}}$$

## 数据科学代写|高级数据分析代写Advanced Data Analysis代考|Local Moran’s I statistic

$$I_{i}=\frac{\left(x_{i}-\bar{x}\right)}{S_{i}^{2}} \sum_{j=1, j \neq i}^{n}\left(w_{i j}\left(x_{j}-\bar{x}\right)\right)$$

## MATLAB代写

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