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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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<p>This section aims at providing some basic statistical tools to study the spatial distribution of epidemiological data.</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>
<p>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.</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>
<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></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</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>
<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>
<div class="cell-output-display">
<p><img src="07-basic_statistics_files/figure-html/cases_visualization-1.png" class="img-fluid" width="768"></p>
</div>
</div>
<p>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 district as the areal unit of the study.</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"># Aggregate cases over districts</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>district<span class="sc">$</span>cases <span class="ot"><-</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>
</div>
<p>The incidence (<span class="math inline">\(\frac{cases}{population}\)</span>) 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 <span class="math inline">\(SIR = \frac{Y_i}{E_i}\)</span> with <span class="math inline">\(Y_i\)</span>, the observed number of cases and <span class="math inline">\(E_i\)</span>, 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.</p>
<div class="cell" data-nm="true">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Compute incidence in each district (per 100 000 population)</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>district<span class="sc">$</span>incidence <span class="ot">=</span> district<span class="sc">$</span>cases<span class="sc">/</span>district<span class="sc">$</span>T_POP <span class="sc">*</span> <span class="dv">100000</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Compute the global risk</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>rate <span class="ot">=</span> <span class="fu">sum</span>(district<span class="sc">$</span>cases)<span class="sc">/</span><span class="fu">sum</span>(district<span class="sc">$</span>T_POP)</span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a><span class="co"># Compute expected number of cases </span></span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>district<span class="sc">$</span>expected <span class="ot">=</span> district<span class="sc">$</span>T_POP <span class="sc">*</span> rate</span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Compute SIR</span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a>district<span class="sc">$</span>SIR <span class="ot">=</span> district<span class="sc">$</span>cases <span class="sc">/</span> district<span class="sc">$</span>expected</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" data-nm="true">
<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><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">3</span>))</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot number of cases using proportional symbol </span></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> district) </span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(</span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> district, </span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> <span class="at">var =</span> <span class="st">"cases"</span>,</span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> <span class="at">val_max =</span> <span class="dv">50</span>,</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"prop"</span>,</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"#990000"</span>, </span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a> <span class="at">leg_title =</span> <span class="st">"Cases"</span>)</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_layout</span>(<span class="at">title =</span> <span class="st">"Number of cases of W Fever"</span>)</span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot incidence </span></span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> district,</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a> <span class="at">var =</span> <span class="st">"incidence"</span>,</span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"choro"</span>,</span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a> <span class="at">pal =</span> <span class="st">"Reds 3"</span>,</span>
<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a> <span class="at">leg_title =</span> <span class="st">"Incidence </span><span class="sc">\n</span><span class="st">(per 100 000)"</span>)</span>
<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_layout</span>(<span class="at">title =</span> <span class="st">"Incidence of W Fever"</span>)</span>
<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-21"><a href="#cb7-21" aria-hidden="true" tabindex="-1"></a><span class="co"># Plot SIRs</span></span>
<span id="cb7-22"><a href="#cb7-22" aria-hidden="true" tabindex="-1"></a><span class="co"># create breaks and associated color palette</span></span>
<span id="cb7-23"><a href="#cb7-23" aria-hidden="true" tabindex="-1"></a>break_SIR <span class="ot">=</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="fu">exp</span>(<span class="fu">mf_get_breaks</span>(<span class="fu">log</span>(district<span class="sc">$</span>SIR), <span class="at">nbreaks =</span> <span class="dv">8</span>, <span class="at">breaks =</span> <span class="st">"pretty"</span>)))</span>
<span id="cb7-24"><a href="#cb7-24" aria-hidden="true" tabindex="-1"></a>col_pal <span class="ot">=</span> <span class="fu">c</span>(<span class="st">"#273871"</span>, <span class="st">"#3267AD"</span>, <span class="st">"#6496C8"</span>, <span class="st">"#9BBFDD"</span>, <span class="st">"#CDE3F0"</span>, <span class="st">"#FFCEBC"</span>, <span class="st">"#FF967E"</span>, <span class="st">"#F64D41"</span>, <span class="st">"#B90E36"</span>)</span>
<span id="cb7-25"><a href="#cb7-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-26"><a href="#cb7-26" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> district,</span>
<span id="cb7-27"><a href="#cb7-27" aria-hidden="true" tabindex="-1"></a> <span class="at">var =</span> <span class="st">"SIR"</span>,</span>
<span id="cb7-28"><a href="#cb7-28" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"choro"</span>,</span>
<span id="cb7-29"><a href="#cb7-29" aria-hidden="true" tabindex="-1"></a> <span class="at">breaks =</span> break_SIR, </span>
<span id="cb7-30"><a href="#cb7-30" aria-hidden="true" tabindex="-1"></a> <span class="at">pal =</span> col_pal, </span>
<span id="cb7-31"><a href="#cb7-31" aria-hidden="true" tabindex="-1"></a> <span class="at">cex =</span> <span class="dv">2</span>,</span>
<span id="cb7-32"><a href="#cb7-32" aria-hidden="true" tabindex="-1"></a> <span class="at">leg_title =</span> <span class="st">"SIR"</span>)</span>
<span id="cb7-33"><a href="#cb7-33" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_layout</span>(<span class="at">title =</span> <span class="st">"Standardized Incidence Ratio of W Fever"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img src="07-basic_statistics_files/figure-html/inc_visualization-1.png" class="img-fluid" width="768"></p>
</div>
</div>
<p>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 :</p>
<ul>
<li><p>higher risk than average (SIR > 1) when standardized for population</p></li>
<li><p>lower risk than average (SIR < 1) when standardized for population</p></li>
<li><p>average risk (SIR ~ 1) when standardized for population</p></li>
</ul>
<p>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).</p>
</section>
<section id="cluster-analysis" class="level2" data-number="7.2">
<h2 data-number="7.2" class="anchored" data-anchor-id="cluster-analysis"><span class="header-section-number">7.2</span> Cluster analysis</h2>
<p>Since this W fever seems to have a heterogeneous distribution across Cambodia, it would be interesting to study where excess of cases appears, i.e. to identify clusters of the disease. The first question is to wonder if data are auto correlated or spatially independent, i.e. study if neighboring districts are likely to have similar incidence.</p>
<p>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.</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. This test tells us whether nearby units tend to exhibit similar incidences. It ranges from -1 to +1. A value of -1 denote 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>Here the statistics hypothesis are :</p>
<ul>
<li><p>H0 : the distribution of cases is spatially independant, i.e. Moran’s I value is 0.</p></li>
<li><p>H1: the distribution of cases is spatially autocorrelated, i.e. Moran’s I value is different than 0.</p></li>
</ul>
<p>We will compute the Moran’s statistics using <code>spdep</code> and <code>Dcluster</code> packages. <code>spdep</code> 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="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(spdep) <span class="co"># Functions for creating spatial weight, spatial analysis</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(DCluster) <span class="co"># Package with functions for spatial cluster analysis)</span></span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>qnb <span class="ot"><-</span> <span class="fu">poly2nb</span>(district)</span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>q_listw <span class="ot"><-</span> <span class="fu">nb2listw</span>(qnb, <span class="at">style =</span> <span class="st">'W'</span>) <span class="co"># row-standardized weights</span></span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a><span class="co"># Moran's I test</span></span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a><span class="fu">moranI.test</span>(cases <span class="sc">~</span> <span class="fu">offset</span>(<span class="fu">log</span>(expected)), </span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> district,</span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a> <span class="at">model =</span> <span class="st">'poisson'</span>,</span>
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a> <span class="at">R =</span> <span class="dv">499</span>,</span>
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a> <span class="at">listw =</span> q_listw,</span>
<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a> <span class="at">n =</span> <span class="dv">159</span>,</span>
<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a> <span class="at">S0 =</span> <span class="fu">Szero</span>(q_listw))</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>Moran's I test of spatial autocorrelation
Type of boots.: parametric
Model used when sampling: Poisson
Number of simulations: 499
Statistic: 0.1264291
p-value : 0.008 </code></pre>
</div>
</div>
</section>
<section id="spatial-scan-statistics" class="level3" data-number="7.2.2">
<h3 data-number="7.2.2" class="anchored" data-anchor-id="spatial-scan-statistics"><span class="header-section-number">7.2.2</span> Spatial scan statistics</h3>
<p>While Moran’s indice focuses on finding correlation between neighboring polygons, the spatial scan statistic compare the incidence level of a given windows of observation with the incidence level outside of this windows.</p>
<p>The package <code>SpatialEpi</code></p>
</section>
<section id="population-based-clusters-kulldorf-statistic" class="level3" data-number="7.2.3">
<h3 data-number="7.2.3" class="anchored" data-anchor-id="population-based-clusters-kulldorf-statistic"><span class="header-section-number">7.2.3</span> Population-based clusters (kulldorf statistic)</h3>
<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>
</section>
<section id="expectation-based-cluster" class="level3" data-number="7.2.4">
<h3 data-number="7.2.4" class="anchored" data-anchor-id="expectation-based-cluster"><span class="header-section-number">7.2.4</span> Expectation-based cluster</h3>
<p>In many case, population is not specific enough to</p>
</section>
<section id="to-go-further" class="level3" data-number="7.2.5">
<h3 data-number="7.2.5" class="anchored" data-anchor-id="to-go-further"><span class="header-section-number">7.2.5</span> To go further …</h3>
</section>
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