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<li><a href="#load-and-visualize-data" id="toc-load-and-visualize-data" class="nav-link active" data-scroll-target="#load-and-visualize-data"><span class="toc-section-number">7.1</span> Load and visualize data</a></li>
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<li><a href="#autocorrelation" id="toc-autocorrelation" class="nav-link" data-scroll-target="#autocorrelation"><span class="toc-section-number">7.2.1</span> Autocorrelation</a></li>
<li><a href="#morans-test" id="toc-morans-test" class="nav-link" data-scroll-target="#morans-test"><span class="toc-section-number">7.2.2</span> Moran’s test</a></li>
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<li><a href="#expectation-based-cluster" id="toc-expectation-based-cluster" class="nav-link" data-scroll-target="#expectation-based-cluster"><span class="toc-section-number">7.3.2</span> Expectation-based cluster</a></li>
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<section id="load-and-visualize-data" class="level2" data-number="7.1">
<h2 data-number="7.1" class="anchored" data-anchor-id="load-and-visualize-data"><span class="header-section-number">7.1</span> Load and visualize data</h2>
<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>
<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></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<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>
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<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>
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<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>
<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> <span class="fu">subset</span>(cases, Disease <span class="sc">==</span> <span class="st">"W fever"</span>), <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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<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>
<section id="autocorrelation" class="level3" data-number="7.2.1">
<h3 data-number="7.2.1" class="anchored" data-anchor-id="autocorrelation"><span class="header-section-number">7.2.1</span> Autocorrelation</h3>
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<section id="morans-test" class="level3" data-number="7.2.2">
<h3 data-number="7.2.2" class="anchored" data-anchor-id="morans-test"><span class="header-section-number">7.2.2</span> Moran’s test</h3>
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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>
</section>
<section id="expectation-based-cluster" class="level3" data-number="7.3.2">
<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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