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<title>Mapping and spatial analyses in R for One Health studies - 7&nbsp; Basic statistics for spatial analysis</title>
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  <li><a href="#import-and-visualize-epidemiological-data" id="toc-import-and-visualize-epidemiological-data" class="nav-link active" data-scroll-target="#import-and-visualize-epidemiological-data"><span class="toc-section-number">7.1</span>  Import and visualize epidemiological data</a></li>
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  <li><a href="#basics-statistics" id="toc-basics-statistics" class="nav-link" data-scroll-target="#basics-statistics"><span class="toc-section-number">7.2</span>  Basics statistics</a>
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  <li><a href="#spatial-autocorrelation-morans-i-test" id="toc-spatial-autocorrelation-morans-i-test" class="nav-link" data-scroll-target="#spatial-autocorrelation-morans-i-test"><span class="toc-section-number">7.2.1</span>  Spatial autocorrelation (Moran’s I test)</a></li>
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<p>This section aims at providing some basic statistical tools to study the spatial distribution of the cases.</p>
<section id="import-and-visualize-epidemiological-data" class="level2" data-number="7.1">
<h2 data-number="7.1" class="anchored" data-anchor-id="import-and-visualize-epidemiological-data"><span class="header-section-number">7.1</span> Import and visualize epidemiological data</h2>
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<p>In this section, we load data that reference the cases of an imaginary disease throughout Cambodia.</p>
<div class="cell" data-nm="true">
<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>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="co">#Import Cambodia country border</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>country <span class="ot">=</span> <span class="fu">st_read</span>(<span class="st">"data_cambodia/cambodia.gpkg"</span>, <span class="at">layer =</span> <span class="st">"country"</span>, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="co">#Import provincial administrative border of Cambodia</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>education <span class="ot">=</span> <span class="fu">st_read</span>(<span class="st">"data_cambodia/cambodia.gpkg"</span>, <span class="at">layer =</span> <span class="st">"education"</span>, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="co">#Import district administrative border of Cambodia</span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>district <span class="ot">=</span> <span class="fu">st_read</span>(<span class="st">"data_cambodia/cambodia.gpkg"</span>, <span class="at">layer =</span> <span class="st">"district"</span>, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Import locations of cases from an imaginary disease</span></span>
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<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>cases <span class="ot">=</span> <span class="fu">st_read</span>(<span class="st">"data_cambodia/cambodia.gpkg"</span>, <span class="at">layer =</span> <span class="st">"cases"</span>, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>cases <span class="ot">=</span> <span class="fu">subset</span>(cases, Disease <span class="sc">==</span> <span class="st">"W fever"</span>)</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="co"># Aggregate cases over districts</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a>district<span class="sc">$</span>cases <span class="ot">&lt;-</span> <span class="fu">lengths</span>(<span class="fu">st_intersects</span>(district, cases))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</div>
<p>The first step of any statistical analysis always consists on visualizing the data to check they were correctly loaded and to observe general pattern of the cases.</p>
<div class="cell" data-nm="true">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># View the cases object</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(cases)</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>Simple feature collection with 6 features and 2 fields
Geometry type: MULTIPOINT
Dimension:     XY
Bounding box:  xmin: 255891 ymin: 1179092 xmax: 506647.4 ymax: 1467441
Projected CRS: WGS 84 / UTM zone 48N
  id Disease                           geom
1  0 W fever MULTIPOINT ((280036.2 12841...
2  1 W fever MULTIPOINT ((451859.5 11790...
3  2 W fever  MULTIPOINT ((255891 1467441))
4  5 W fever MULTIPOINT ((506647.4 12322...
5  6 W fever  MULTIPOINT ((440668 1197958))
6  7 W fever MULTIPOINT ((481594.5 12714...</code></pre>
</div>
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Map the cases</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(mapsf)</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> district, <span class="at">border =</span> <span class="st">"white"</span>)</span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> country,<span class="at">lwd =</span> <span class="dv">2</span>, <span class="at">col =</span> <span class="cn">NA</span>, <span class="at">add =</span> <span class="cn">TRUE</span>)</span>
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<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> cases, <span class="at">lwd =</span> .<span class="dv">5</span>, <span class="at">col =</span> <span class="st">"#990000"</span>, <span class="at">pch =</span> <span class="dv">20</span>, <span class="at">add =</span> <span class="cn">TRUE</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="cell-output-display">
<p><img src="07-basic_statistics_files/figure-html/cases_visualization-1.png" class="img-fluid" width="768"></p>
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<section id="basics-statistics" class="level2" data-number="7.2">
<h2 data-number="7.2" class="anchored" data-anchor-id="basics-statistics"><span class="header-section-number">7.2</span> Basics statistics</h2>
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<p>The problem is usually expressed by defining two hypothesis : the null hypothesis (H0), i.e.&nbsp;an a priori hypothesis of the studied phenomenon (e.g.&nbsp;the situation is a random) and the alternative hypothesis (HA), e.g.&nbsp;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.</p>
<p>The statistical analysis performed relies on the type of data.</p>
<section id="spatial-autocorrelation-morans-i-test" class="level3" data-number="7.2.1">
<h3 data-number="7.2.1" class="anchored" data-anchor-id="spatial-autocorrelation-morans-i-test"><span class="header-section-number">7.2.1</span> Spatial autocorrelation (Moran’s I test)</h3>
<p>A popular test for spatial autocorrelation is the Moran’s test.</p>
<p>Moran’s I test tells us whether nearby units tend to exhibit similar rates. It ranges from -1 to +1, whith a value of -1 denoting that units with low rates are located near other units with high rates, while a Moran’s I value of +1 indicates a concentration of spatial units exhibiting similar rates.</p>
<p>We will compute the Moran’s statistics using <code>spdep</code> and <code>Dcluster</code> packages. This package provides a collection of functions to analyze spatial correlations of polygons and works with sp objects. <code>Dcluster</code> package provides a set of functions for the detection of spatial clusters of disease using count data.</p>
<div class="cell" data-nm="true">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Compte incidence in each district (per 100 000 population)</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>district<span class="sc">$</span>incidence <span class="ot">&lt;-</span> district<span class="sc">$</span>cases<span class="sc">/</span>district<span class="sc">$</span>T_POP <span class="sc">*</span> <span class="dv">100000</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot the incidence histogramm</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(<span class="fu">log</span>(district<span class="sc">$</span>incidence))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</section>
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<section id="cluster-analysis" class="level2" data-number="7.3">
<h2 data-number="7.3" class="anchored" data-anchor-id="cluster-analysis"><span class="header-section-number">7.3</span> Cluster analysis</h2>
<p>In epidemiology, the definition of a cluster</p>
<section id="population-based-clusters-kulldorf-statistic" class="level3" data-number="7.3.1">
<h3 data-number="7.3.1" class="anchored" data-anchor-id="population-based-clusters-kulldorf-statistic"><span class="header-section-number">7.3.1</span> Population-based clusters (kulldorf statistic)</h3>
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<p>Kulldorff ’s spatial scan statistic identifies the most likely disease clusters maximizing the likelihood that disease cases are located within a set of concentric circles that are moved across the study area.</p>
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<h3 data-number="7.3.2" class="anchored" data-anchor-id="expectation-based-cluster"><span class="header-section-number">7.3.2</span> Expectation-based cluster</h3>
<p>In many case, population is not specific enough to</p>
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<h3 data-number="7.3.3" class="anchored" data-anchor-id="to-go-further"><span class="header-section-number">7.3.3</span> To go further …</h3>
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