spelling corrections basic statistics

07-basic_statistics.qmd

@@ -4,11 +4,11 @@ bibliography: references.bib
 
 # Basic statistics for spatial analysis
 
-This section aims at providing some basic statistical tools to study the spatial distribution of epidemiological data. If you wish to go further into these analysis and their limitations you can consult the tutorial "[Spatial Epidemiology](https://mkram01.github.io/EPI563-SpatialEPI/index.html)" from M. Kramer from which the statistical analysis of his section were adapted. 
+This section aims at providing some basic statistical tools to study the spatial distribution of epidemiological data. If you wish to go further into spatial statistics applied to epidemiology and their limitations you can consult the tutorial "[Spatial Epidemiology](https://mkram01.github.io/EPI563-SpatialEPI/index.html)" from M. Kramer from which the statistical analysis of this section was adapted. We will use 
 
 ## Import and visualize epidemiological data
 
-In this section, we load data that reference the cases of an imaginary disease throughout Cambodia. Each point correspond to the geolocalisation of a case.
+In this section, we load data that reference the cases of an imaginary disease, the W fever, throughout Cambodia. Each point corresponds to the geo-localization of a case.
 
 ```{r load_cases, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=8, class.output="code-out", warning=FALSE, message=FALSE}
 library(dplyr)
@@ -43,7 +43,7 @@ mf_map(x = cases, lwd = .5, col = "#990000", pch = 20, add = TRUE)
 
 ```
 
-In epidemiology, the true meaning of point is very questionable. If it usually gives the location of an observation, its not clear if this observation represents an event of interest (e.g. illness, death, ...) or a person at risk (e.g. a participant that may or may not experience the disease). Considering a ratio of event compared to a population at risk is often more informative than just considering cases. Administrative divisions of countries appears as great areal units for cases aggregation since they make available data on population count and structures. In this study, we will use the district as the areal unit of the study.
+In epidemiology, the true meaning of point is very questionable. If it usually gives the location of an observation, we cannot precisely tell if this observation represents an event of interest (e.g., illness, death, ...) or a person at risk (e.g., a participant that may or may not experience the disease). Considering a ratio of event compared to a population at risk is often more informative than just considering cases. Administrative divisions of countries appear as great areal units for cases aggregation since they make available data on population count and structures. In this study, we will use the district as the areal unit of the study.
 
 ```{r district_aggregate, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=8, class.output="code-out", warning=FALSE, message=FALSE}
 # Aggregate cases over districts
@@ -51,7 +51,7 @@ district$cases <- lengths(st_intersects(district, cases))
 
 ```
 
-The incidence ($\frac{cases}{population}$) is commonly use to represent cases distribution related to population density but other indicators exists. As example, the standardized incidence ratios (SIRs) represents the deviation of observed and expected number of cases and is expressed as $SIR = \frac{Y_i}{E_i}$ with $Y_i$, the observed number of cases and $E_i$, the expected number of cases. In this study, we computed the expected number of cases in each district by assuming infections are homogeneously distributed across Cambodia, i.e. the incidence is the same in each district. The SIR therefore represents the deviation of incidence compared to the averaged average incidence across Cambodia.
+The incidence ($\frac{cases}{population}$) expressed per 100,000 population is commonly use to represent cases distribution related to population density but other indicators exists. As example, the standardized incidence ratios (SIRs) represent the deviation of observed and expected number of cases and is expressed as $SIR = \frac{Y_i}{E_i}$ with $Y_i$, the observed number of cases and $E_i$, the expected number of cases. In this study, we computed the expected number of cases in each district by assuming infections are homogeneously distributed across Cambodia, i.e., the incidence is the same in each district. The SIR therefore represents the deviation of incidence compared to the average incidence across Cambodia.
 
 ```{r indicators, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=8, fig.height=4, class.output="code-out", warning=FALSE, message=FALSE}
 
@@ -86,12 +86,13 @@ mf_map(x = district,
        var = "incidence",
        type = "choro",
        pal = "Reds 3",
+       breaks = exp(mf_get_breaks(log(district$incidence+1), breaks = "pretty"))-1,
        leg_title = "Incidence \n(per 100 000)")
 mf_layout(title = "Incidence of W Fever")
 
 # Plot SIRs
 # create breaks and associated color palette
-break_SIR <- c(0, exp(mf_get_breaks(log(district$SIR), nbreaks = 8, breaks = "pretty")))
+break_SIR <- c(0,exp(mf_get_breaks(log(district$SIR), nbreaks = 8, breaks = "pretty")))
 col_pal <- c("#273871", "#3267AD", "#6496C8", "#9BBFDD", "#CDE3F0", "#FFCEBC", "#FF967E", "#F64D41", "#B90E36")
 
 mf_map(x = district,
@@ -104,7 +105,7 @@ mf_map(x = district,
 mf_layout(title = "Standardized Incidence Ratio of W Fever")
 ```
 
-These maps illustrates the spatial heterogenity of the cases. The incidence shows how the disease vary from one district to another while the SIR highlight districts that have :
+These maps illustrate the spatial heterogeneity of the cases. The incidence shows how the disease vary from one district to another while the SIR highlight districts that have:
 
 -   higher risk than average (SIR \> 1) when standardized for population
 
@@ -113,20 +114,22 @@ These maps illustrates the spatial heterogenity of the cases. The incidence show
 -   average risk (SIR \~ 1) when standardized for population
 
 ::: callout-tip
-### To go futher ...
+### To go further ...
 
-In this example, we standardized the cases distribution for population count. This simple standardization assume that the risk of contracting the disease is similar for each person. However, assumption does not hold for all diseases and for all observed events since confounding effects can create nuisance into the interpretations (e.g. the number of childhood illness and death outcomes in a district are usually related to the age pyramid) and you should keep in mind that other standardization can be performed based on variables known to have an effect but that you don't want to analyze (e.g. sex ratio, occupations, age pyramid).
+In this example, we standardized the cases distribution for population count. This simple standardization assumes that the risk of contracting the disease is similar for each person. However, assumption does not hold for all diseases and for all observed events since confounding effects can create nuisance into the interpretations (e.g., the number of childhood illness and death outcomes in a district are usually related to the age pyramid) and you should keep in mind that other standardization can be performed based on variables known to have an effect but that you don't want to analyze (e.g., sex ratio, occupations, age pyramid).
+
+In addition, one can wonder what does an $SIR \~ 1$ means, i.e., what is the threshold to decide whether the SIR is greater, lower or equivalent to 1. The significant of the SIR can be tested globally (to determine whether or not the incidence is homogeneously distributed) and locally in each district (to determine Which district have an SIR different than 1). We won't perform these analyses in this tutorial but you can look at the function `?achisq.test()` (from `Dcluster` package [@DCluster]) and `?probmap()` (from `spdep` package [@spdep]) to compute these statistics.
 :::
 
 ## Cluster analysis
 
 ### General introduction
 
-Why studying clusters in epidemiology ? Cluster analysis help identifying unusual patterns that occurs during a given period of time. The underlying ultimate goal of such analysis is to explain the observation of such patterns. In epidemiology, we can distinguish two types of process that would explain heterogeneity in case distribution :
+Why studying clusters in epidemiology? Cluster analysis help identifying unusual patterns that occurs during a given period of time. The underlying ultimate goal of such analysis is to explain the observation of such patterns. In epidemiology, we can distinguish two types of process that would explain heterogeneity in case distribution:
 
--   The **1st order effects** are the spatial variations of cases distribution caused by underlying properties of environment or the population structure itself. In such process individual get infected independently from the rest of the population. Such process includes the infection through a environment at risk as, for example, air pollution, contaminated waters or soils and UV exposition. This effect assume that the observed pattern are caused by a difference in risk intensity.
+-   The **1st order effects** are the spatial variations of cases distribution caused by underlying properties of environment or the population structure itself. In such process individual get infected independently from the rest of the population. Such process includes the infection through an environment at risk as, for example, air pollution, contaminated waters or soils and UV exposition. This effect assume that the observed pattern is caused by a difference in risk intensity.
 
--   The **2nd order effects** describes process of spread, contagion and diffusion of diseases caused by interactions between individuals. This includes transmission of infectious disease by proximity, but also the transmission of non-infectious disease, for example, with the diffusion of social norms within networks. This effect assume that the observed pattern are caused by correlations or co-variations.
+-   The **2nd order effects** describes process of spread, contagion and diffusion of diseases caused by interactions between individuals. This includes transmission of infectious disease by proximity, but also the transmission of non-infectious disease, for example, with the diffusion of social norms within networks. This effect assume that the observed pattern is caused by correlations or co-variations.
 
 No statistical methods could distinguish between these competing processes since their outcome results in similar pattern of points. The cluster analysis help describing the magnitude and the location of pattern but in no way could answer the question of why such patterns occurs. It is therefore a step that help detecting cluster for description and surveillance purpose and rising hypothesis on the underlying process that will lead further investigations.
 
@@ -135,11 +138,11 @@ Knowledge about the disease and its transmission process could orientate the cho
 ::: callout-note
 ### Statistic tests and distributions
 
-In statistics, problems are usually expressed by defining two hypothesis : the null hypothesis (H0), i.e. an *a priori* hypothesis of the studied phenomenon (e.g. the situation is a random) and the alternative hypothesis (HA), e.g. the situation is not random. The main principle is to measure how likely the observed situation belong to the ensemble of situation that are possible under the H0 hypothesis.
+In statistics, problems are usually expressed by defining two hypotheses: the null hypothesis (H0), i.e., an *a priori* hypothesis of the studied phenomenon (e.g., the situation is a random) and the alternative hypothesis (HA), e.g., the situation is not random. The main principle is to measure how likely the observed situation belong to the ensemble of situation that are possible under the H0 hypothesis.
 
-In mathematics, a probability distribution is a mathematical expression that represents what we would expect due to random chance. The choice of the probability distribution relies on the type of data you use (continuous, count, binary). In general, three distribution a used while studying disease rates, the Binomial, the Poisson and the Poisson-gamma mixture (a.k.a negative binomial) distributions.
+In mathematics, a probability distribution is a mathematical expression that represents what we would expect due to random chance. The choice of the probability distribution relies on the type of data you use (continuous, count, binary). In general, three distribution a used while studying disease rates, the Binomial, the Poisson and the Poisson-gamma mixture (also known as negative binomial) distributions.
 
-Many the statistical tests assume by default that data are normally distributed. It implies that your variable is continuous and that all data could easily be represented by two parameters, the mean and the variance, i.e. each value have the same level of certainty. If many measure can be assessed under the normality assumption, this is usually not the case in epidemiology with strictly positives rates and count values that 1) does not fit the normal distribution and 2) does not provide with the same degree of certainty since variances likely differ between district due to different population size, i.e. some district have very sparse data (with high variance) while other have adequate data (with lower variance).
+Many the statistical tests assume by default that data are normally distributed. It implies that your variable is continuous and that all data could easily be represented by two parameters, the mean and the variance, i.e., each value have the same level of certainty. If many measure can be assessed under the normality assumption, this is usually not the case in epidemiology with strictly positives rates and count values that 1) does not fit the normal distribution and 2) does not provide with the same degree of certainty since variances likely differ between district due to different population size, i.e., some district have very sparse data (with high variance) while other have adequate data (with lower variance).
 
 ```{r distribution, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=6, class.output="code-out", warning=FALSE, message=FALSE}
 
@@ -154,7 +157,7 @@ points(0:max(district$incidence), dpois(0:max(district$incidence), m_cases),type
 legend("topright", legend = c("Normal distribution", "Poisson distribution", "Observed distribution"), col = c("blue", "red", "black"),pch = c(NA, 20, NA), lty = c(1, 2, 1))
 ```
 
-In this tutorial, we used the poisson distribution in our statistical tests.
+In this tutorial, we used the Poisson distribution in our statistical tests.
 :::
 
 ### Test for spatial autocorrelation (Moran's I test)
@@ -166,26 +169,26 @@ A popular test for spatial autocorrelation is the Moran's test. This test tells
 ::: callout-note
 ##### Moran's I test
 
-The Moran's statistics is :
+The Moran's statistics is:
 
-$$I = \frac{N}{\sum_{i=1}^N\sum_{j=1}^Nw_{ij}}\frac{\sum_{i=1}^N\sum_{j=1}^Nw_{ij}(Y_i-\bar{Y})(Y_j - \bar{Y})}{\sum_{i=1}^N(Y_i-\bar{Y})^2}$$ with :
+$$I = \frac{N}{\sum_{i=1}^N\sum_{j=1}^Nw_{ij}}\frac{\sum_{i=1}^N\sum_{j=1}^Nw_{ij}(Y_i-\bar{Y})(Y_j - \bar{Y})}{\sum_{i=1}^N(Y_i-\bar{Y})^2}$$ with:
 
 -   $N$: the number of polygons,
 
--   $w_{ij}$: is a matrix of spatial weight with zeroes on the diagonal (i.e., $w_{ii}=0$). For example, if polygons are neighbors, the weight takes the value $1$ otherwise it take the value $0$.
+-   $w_{ij}$: is a matrix of spatial weight with zeroes on the diagonal (i.e., $w_{ii}=0$). For example, if polygons are neighbors, the weight takes the value $1$ otherwise it takes the value $0$.
 
 -   $Y_i$: the variable of interest,
 
 -   $\bar{Y}$: the mean value of $Y$.
 
-Under the Moran's test, the statistics hypothesis are :
+Under the Moran's test, the statistics hypotheses are:
 
--   **H0** : the distribution of cases is spatially independent, i.e. $I=0$.
+-   **H0**: the distribution of cases is spatially independent, i.e., $I=0$.
 
--   **H1**: the distribution of cases is spatially autocorrelated, i.e. $I\ne0$.
+-   **H1**: the distribution of cases is spatially autocorrelated, i.e., $I\ne0$.
 :::
 
-We will compute the Moran's statistics using `spdep`[@spdep] and `Dcluster`[@DCluster] packages. `spdep` package provides a collection of functions to analyze spatial correlations of polygons and works with sp objects. In this example, we use `poly2nb()` and `nb2listw()`. These function respectively detect the neighboring polygons and assign weight corresponding to $1/\#\ of\ neighbors$. `Dcluster` package provides a set of functions for the detection of spatial clusters of disease using count data.
+We will compute the Moran's statistics using `spdep`[@spdep] and `Dcluster`[@DCluster] packages. `spdep` package provides a collection of functions to analyze spatial correlations of polygons and works with sp objects. In this example, we use `poly2nb()` and `nb2listw()`. These functions respectively detect the neighboring polygons and assign weight corresponding to $1/\#\ of\ neighbors$. `Dcluster` package provides a set of functions for the detection of spatial clusters of disease using count data.
 
 ```{r MoransI, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=8, class.output="code-out", warning=FALSE, message=FALSE}
 
@@ -212,17 +215,17 @@ The Moran's statistics is here $I =$ `r signif(m_test$t0, 2)`. When comparing it
 
 #### Moran's I local test
 
-The global Moran's test provides us a global statistical value informing whether autocorrelation occurs over the territory but does not inform on where does these correlation occurs, i.e. what is the locations of the clusters. To identify such cluster we can decompose the Moran's I statistic to extract local informations of the level of correlation of each district and its neighbors. This is called the Local Moran's I LISA statistic. Because the Local Moran's I LISA statistic test each district for autocorrelation independently, concern are raised about multiple testing limitations that increase the Type I error ($\alpha$) of the statistical tests. The use of local test should therefore be study in light of explore and describes clusters once the global test detected autocorrelation.
+The global Moran's test provides us a global statistical value informing whether autocorrelation occurs over the territory but does not inform on where does these correlations occurs, i.e., what is the locations of the clusters. To identify such cluster, we can decompose the Moran's I statistic to extract local information of the level of correlation of each district and its neighbors. This is called the Local Moran's I LISA statistic. Because the Local Moran's I LISA statistic test each district for autocorrelation independently, concern is raised about multiple testing limitations that increase the Type I error ($\alpha$) of the statistical tests. The use of local test should therefore be study in light of explore and describes clusters once the global test detected autocorrelation.
 
 ::: callout-note
 ##### Statistical test
 
-For each district $i$, the Moran's statistics is :
+For each district $i$, the Local Moran's I statistics is:
 
 $$I_i = \frac{(Y_i-\bar{Y})}{\sum_{i=1}^N(Y_i-\bar{Y})^2}\sum_{j=1}^Nw_{ij}(Y_j - \bar{Y}) \text{ with }  I = \sum_{i=1}^NI_i/N$$
 :::
 
-The `localmoran()`function from the package `spdep` treats the variable of interest as if it was normally distributed. In some cases, this assumption could be reasonable for incidence rate, especially when the areal units of analysis have sufficiently large population count suggesting that the values have similar level of variances. Unfortunately, the local moran's test has not been implemented for poisson distribution (population not large enough in some districts) in `spdep` package. However Bivand **et al.** [@bivand2008applied] provided some code to manual perform the analysis using poisson distribution and was further implemented in the course "[Spatial Epidemiology](https://mkram01.github.io/EPI563-SpatialEPI/index.html)" .
+The `localmoran()`function from the package `spdep` treats the variable of interest as if it was normally distributed. In some cases, this assumption could be reasonable for incidence rate, especially when the areal units of analysis have sufficiently large population count suggesting that the values have similar level of variances. Unfortunately, the local Moran’s test has not been implemented for Poisson distribution (population not large enough in some districts) in `spdep` package. However, Bivand **et al.** [@bivand2008applied] provided some code to manual perform the analysis using Poisson distribution and was further implemented in the course "[Spatial Epidemiology](https://mkram01.github.io/EPI563-SpatialEPI/index.html)”.
 
 
 
@@ -271,15 +274,15 @@ district$pval_lm <- punif((diff + 1) / (nsim + 1))
 
 For each district, we obtain a p-value based on permutations process
 
-A conventional way of plotting these results is to classify the districts into 5 classes based on local Moran's I outputs. The classification of cluster that are significantly autocorrelated to their neighbors is performed based on a comparison of the scaled incidence in the district compared to the scaled weighted averaged incidence of it neighboring districts (computed with `lag.listw()`) :
+A conventional way of plotting these results is to classify the districts into 5 classes based on local Moran's I output. The classification of cluster that are significantly autocorrelated to their neighbors is performed based on a comparison of the scaled incidence in the district compared to the scaled weighted averaged incidence of it neighboring districts (computed with `lag.listw()`):
 
 -    Districts that have higher-than-average rates in both index regions and their neighbors and showing statistically significant positive values for the local $I_i$ statistic are defined as __High-High__ (hotspot of the disease)
 
--   Districts that have lower-than-average rates in both index regions and their neighbors adn showing statistically significant positive values for the local $I_i$ statistic are defined as  __Low-Low__ (coldspot of the disease).
+-   Districts that have lower-than-average rates in both index regions and their neighbors and showing statistically significant positive values for the local $I_i$ statistic are defined as  __Low-Low__ (cold spot of the disease).
 
 -   Districts that have higher-than-average rates in the index regions and lower-than-average rates in their neighbors, and showing statistically significant negative values for the local $I_i$ statistic are defined as  __High-Low__(outlier with high incidence in an area with low incidence).
 
--   Districts that have lower-than-average rates in the index regions and  higher-than-average rates in their neighbors, and showing statistically significant negative values for the local $I_i$ statistic are defined as  __Low-High__(outlier of low incidence in area with high incidence). 
+-   Districts that have lower-than-average rates in the index regions and higher-than-average rates in their neighbors, and showing statistically significant negative values for the local $I_i$ statistic are defined as  __Low-High__ (outlier of low incidence in area with high incidence). 
 
 -   Districts with non-significant values for the $I_i$ statistic are defined as __Non-significant__.
 
@@ -314,7 +317,7 @@ mf_map(x = district,
        pal = c("#6D0026" , "blue",  "white") , # "#FF755F","#7FABD3" ,
        leg_title = "Clusters")
 
-mf_layout(title = "Cluster using Local moran'I statistic")
+mf_layout(title = "Cluster using Local Moran's I statistic")
 
 
 
@@ -324,17 +327,17 @@ mf_layout(title = "Cluster using Local moran'I statistic")
 
 ### Spatial scan statistics
 
-While Moran's indice focuses on testing for autocorrelation between neighboring polygons (under the null assumption of spatial independance), the spatial scan statistic aims at identifying an abnormal higher risk in a given region compared to the risk outside of this region (under the null assumption of homogeneous distribution). The conception of a cluster is therefore different between the two methods.
+While Moran's indices focus on testing for autocorrelation between neighboring polygons (under the null assumption of spatial independence), the spatial scan statistic aims at identifying an abnormal higher risk in a given region compared to the risk outside of this region (under the null assumption of homogeneous distribution). The conception of a cluster is therefore different between the two methods.
 
 The function `kulldorff` from the package `SpatialEpi` [@SpatialEpi] is a simple tool to implement spatial-only scan statistics. Briefly, the kulldorff scan statistics scan the area for clusters using several steps:
 
-1.  It create a circular window of observation by defining a single location and an associated radius of the windows varying from 0 to a large number that depends on population distribution (largest radius could includes 50% of the population).
+1.  It create a circular window of observation by defining a single location and an associated radius of the windows varying from 0 to a large number that depends on population distribution (largest radius could include 50% of the population).
 
 2.  It aggregates the count of events and the population at risk (or an expected count of events) inside and outside the window of observation.
 
 3.  Finally, it computes the likelihood ratio to test whether the risk is equal inside versus outside the windows (H0) or greater inside the observed window
 
-4.  These 3 steps are repeted for each location and each possible windows-radii.
+4.  These 3 steps are repeated for each location and each possible windows-radii.
 
 ```{r spatialEpi, eval = TRUE, echo = TRUE, nm = TRUE, class.output="code-out", warning=FALSE, message=FALSE}
 
@@ -342,7 +345,7 @@ library("SpatialEpi")
 
 ```
 
-The use of R spatial object is not implementes in `kulldorff()` function. It uses instead matrix of xy coordinates that represents the centroids of the districts. A given district is included into the observed circular window if its centroids falls into the circle.
+The use of R spatial object is not implements in `kulldorff()` function. It uses instead matrix of xy coordinates that represents the centroids of the districts. A given district is included into the observed circular window if its centroids fall into the circle.
 
 ```{r kd_centroids, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=6, class.output="code-out", warning=FALSE, message=FALSE}
 
@@ -353,7 +356,7 @@ head(district_xy)
 
 ```
 
-We can then call kulldorff function (you are strongly encourage to call `?kulldorff` to properly call the function). The `alpha.level` threshold filter for the secondary clusters that will be retained. The most-likely cluster will be saved whatever its significance.
+We can then call kulldorff function (you are strongly encouraged to call `?kulldorff` to properly call the function). The `alpha.level` threshold filter for the secondary clusters that will be retained. The most-likely cluster will be saved whatever its significance.
 
 ```{r kd_test, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=6, class.output="code-out", warning=FALSE, message=FALSE}
 
@@ -367,7 +370,7 @@ kd_Wfever <- kulldorff(district_xy,
 
 ```
 
-All outputs are saved into an R object, here called `kd_Wfever`. Unfortunately the package did not developed any summary and visualization of the results but we can explore the output object.
+All outputs are saved into an R object, here called `kd_Wfever`. Unfortunately, the package did not develop any summary and visualization of the results but we can explore the output object.
 
 ```{r kd_outputs, eval = TRUE, echo = TRUE, nm = TRUE, fig.width=6, class.output="code-out", warning=FALSE, message=FALSE}
 names(kd_Wfever)
@@ -390,7 +393,7 @@ kd_Wfever$most.likely.cluster$expected.cases
 
 ```
 
-`r length(kd_Wfever$most.likely.cluster$location.IDs.included)` districts belong to the cluster and its number of cases is `r signif(kd_Wfever$most.likely.cluster$SMR, 2)` times higher than the expected number of case.
+`r length(kd_Wfever$most.likely.cluster$location.IDs.included)` districts belong to the cluster and its number of cases is `r signif(kd_Wfever$most.likely.cluster$SMR, 2)` times higher than the expected number of cases.
 
 Similarly, we could study the secondary clusters. Results are saved in a list.
 
@@ -415,7 +418,7 @@ We only have one secondary cluster composed of one district.
 # create empty column to store cluster informations
 district$k_cluster <- NA
 
-# save cluster informations from kulldorff outputs
+# save cluster information from kulldorff outputs
 district$k_cluster[kd_Wfever$most.likely.cluster$location.IDs.included] <- 'Most likely cluster'
 
 for(i in 1:length(kd_Wfever$secondary.clusters)){
@@ -440,7 +443,7 @@ mf_layout(title = "Cluster using kulldorf scan statistic")
 ```
 
 ::: callout-tip
-#### To go futher ...
+#### To go further ...
 
 In this example, the expected number of cases was defined using the population count but note that standardization over other variables as age could also be implemented with the `strata` parameter in the `kulldorff()` function.
 

public/01-introduction.html

@@ -2,7 +2,7 @@
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
 
 <meta charset="utf-8">
-<meta name="generator" content="quarto-1.1.251">
+<meta name="generator" content="quarto-1.1.189">
 
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
@@ -302,12 +302,12 @@ div.csl-indent {
 <div class="cell">
 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(sf)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Linking to GEOS 3.10.2, GDAL 3.4.3, PROJ 8.2.1; sf_use_s2() is TRUE</code></pre>
+<pre><code>Linking to GEOS 3.9.3, GDAL 3.5.2, PROJ 8.2.1; sf_use_s2() is TRUE</code></pre>
 </div>
 <div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>district <span class="ot">&lt;-</span> <span class="fu">st_read</span>(<span class="st">"data_cambodia/district.shp"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre class="code-out"><code>Reading layer `district' from data source 
-  `/home/lucas/Documents/ForgeIRD/rspatial-for-onehealth/data_cambodia/district.shp' 
+  `C:\Users\UNiK\Documents\R_works\IRD\Rspatial\rspatial-for-onehealth\data_cambodia\district.shp' 
   using driver `ESRI Shapefile'
 Simple feature collection with 197 features and 10 fields
 Geometry type: MULTIPOLYGON
@@ -348,7 +348,7 @@ Available layers:
 <div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>road <span class="ot">&lt;-</span> <span class="fu">st_read</span>(<span class="st">"data_cambodia/cambodia.gpkg"</span>, <span class="at">layer =</span> <span class="st">"road"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre class="code-out"><code>Reading layer `road' from data source 
-  `/home/lucas/Documents/ForgeIRD/rspatial-for-onehealth/data_cambodia/cambodia.gpkg' 
+  `C:\Users\UNiK\Documents\R_works\IRD\Rspatial\rspatial-for-onehealth\data_cambodia\cambodia.gpkg' 
   using driver `GPKG'
 Simple feature collection with 6 features and 9 fields
 Geometry type: MULTILINESTRING