Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
<meta charset="utf-8">
<meta name="generator" content="quarto-1.1.189">
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
<title>Mapping and spatial analyses in R for One Health studies - 7 Basic statistics for spatial analysis</title>
<style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
div.columns{display: flex; gap: min(4vw, 1.5em);}
div.column{flex: auto; overflow-x: auto;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
ul.task-list li input[type="checkbox"] {
width: 0.8em;
margin: 0 0.8em 0.2em -1.6em;
vertical-align: middle;
}
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { color: #008000; } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { color: #008000; font-weight: bold; } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
</style>
<script src="site_libs/quarto-nav/quarto-nav.js"></script>
<script src="site_libs/quarto-nav/headroom.min.js"></script>
<script src="site_libs/clipboard/clipboard.min.js"></script>
<script src="site_libs/quarto-search/autocomplete.umd.js"></script>
<script src="site_libs/quarto-search/fuse.min.js"></script>
<script src="site_libs/quarto-search/quarto-search.js"></script>
<meta name="quarto:offset" content="./">
<link href="./references.html" rel="next">
<link href="./06-advanced_spatial_analysis.html" rel="prev">
<script src="site_libs/quarto-html/quarto.js"></script>
<script src="site_libs/quarto-html/popper.min.js"></script>
<script src="site_libs/quarto-html/tippy.umd.min.js"></script>
<script src="site_libs/quarto-html/anchor.min.js"></script>
<link href="site_libs/quarto-html/tippy.css" rel="stylesheet">
<link href="site_libs/quarto-html/quarto-syntax-highlighting.css" rel="stylesheet" id="quarto-text-highlighting-styles">
<script src="site_libs/bootstrap/bootstrap.min.js"></script>
<link href="site_libs/bootstrap/bootstrap-icons.css" rel="stylesheet">
<link href="site_libs/bootstrap/bootstrap.min.css" rel="stylesheet" id="quarto-bootstrap" data-mode="light">
<script id="quarto-search-options" type="application/json">{
"location": "sidebar",
"copy-button": false,
"collapse-after": 3,
"panel-placement": "start",
"type": "textbox",
"limit": 20,
"language": {
"search-no-results-text": "No results",
"search-matching-documents-text": "matching documents",
"search-copy-link-title": "Copy link to search",
"search-hide-matches-text": "Hide additional matches",
"search-more-match-text": "more match in this document",
"search-more-matches-text": "more matches in this document",
"search-clear-button-title": "Clear",
"search-detached-cancel-button-title": "Cancel",
"search-submit-button-title": "Submit"
}
}</script>
<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml-full.js" type="text/javascript"></script>
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
<link rel="stylesheet" href="styles.css">
</head>
<body class="nav-sidebar floating">
<div id="quarto-search-results"></div>
<header id="quarto-header" class="headroom fixed-top">
<nav class="quarto-secondary-nav" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
<div class="container-fluid d-flex justify-content-between">
<h1 class="quarto-secondary-nav-title"><span class="chapter-number">7</span> <span class="chapter-title">Basic statistics for spatial analysis</span></h1>
<button type="button" class="quarto-btn-toggle btn" aria-label="Show secondary navigation">
<i class="bi bi-chevron-right"></i>
</button>
</div>
</nav>
</header>
<!-- content -->
<div id="quarto-content" class="quarto-container page-columns page-rows-contents page-layout-article">
<!-- sidebar -->
<nav id="quarto-sidebar" class="sidebar collapse sidebar-navigation floating overflow-auto">
<div class="pt-lg-2 mt-2 text-left sidebar-header">
<div class="sidebar-title mb-0 py-0">
<a href="./">Mapping and spatial analyses in R for One Health studies</a>
<div class="sidebar-tools-main">
<a href="https://forge.ird.fr/espace-dev/personnels/longour/geohealth/documentation/rspatial-for-onehealth" title="Source Code" class="sidebar-tool px-1"><i class="bi bi-git"></i></a>
</div>
</div>
</div>
<div class="mt-2 flex-shrink-0 align-items-center">
<div class="sidebar-search">
<div id="quarto-search" class="" title="Search"></div>
</div>
</div>
<div class="sidebar-menu-container">
<ul class="list-unstyled mt-1">
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./index.html" class="sidebar-item-text sidebar-link">Preface</a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./01-introduction.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">1</span> <span class="chapter-title">Introduction</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./02-data_acquisition.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">2</span> <span class="chapter-title">Data Acquisition</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./03-vector_data.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">3</span> <span class="chapter-title">Vector Data</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./04-raster_data.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">4</span> <span class="chapter-title">Work with Raster Data</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./05-mapping_with_r.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">5</span> <span class="chapter-title">Mapping With R</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./06-advanced_spatial_analysis.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">6</span> <span class="chapter-title">Advanced Spatial Analysis</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./07-basic_statistics.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">7</span> <span class="chapter-title">Basic statistics for spatial analysis</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./references.html" class="sidebar-item-text sidebar-link">References</a>
</div>
</li>
</ul>
</div>
</nav>
<!-- margin-sidebar -->
<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
<nav id="TOC" role="doc-toc" class="toc-active">
<h2 id="toc-title">Table of contents</h2>
<ul>
<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>
<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>
<ul class="collapse">
<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>
</ul></li>
<li><a href="#cluster-analysis" id="toc-cluster-analysis" class="nav-link" data-scroll-target="#cluster-analysis"><span class="toc-section-number">7.3</span> Cluster analysis</a>
<ul class="collapse">
<li><a href="#population-based-clusters-kulldorf-statistic" id="toc-population-based-clusters-kulldorf-statistic" class="nav-link" data-scroll-target="#population-based-clusters-kulldorf-statistic"><span class="toc-section-number">7.3.1</span> Population-based clusters (kulldorf statistic)</a></li>
<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>
<li><a href="#to-go-further" id="toc-to-go-further" class="nav-link" data-scroll-target="#to-go-further"><span class="toc-section-number">7.3.3</span> To go further …</a></li>
</ul></li>
</ul>
</nav>
</div>
<!-- main -->
<main class="content" id="quarto-document-content">
<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title d-none d-lg-block"><span class="chapter-number">7</span> <span class="chapter-title">Basic statistics for spatial analysis</span></h1>
</div>
<div class="quarto-title-meta">
</div>
</header>
<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>
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
<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 aggreagation 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>
</div>
<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>
<span id="cb7-23"><a href="#cb7-23" aria-hidden="true" tabindex="-1"></a><span class="co"># create breaks and associated color palette</span></span>
<span id="cb7-24"><a href="#cb7-24" 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="cb7-25"><a href="#cb7-25" 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="cb7-26"><a href="#cb7-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-27"><a href="#cb7-27" aria-hidden="true" tabindex="-1"></a><span class="fu">mf_map</span>(<span class="at">x =</span> district,</span>
<span id="cb7-28"><a href="#cb7-28" aria-hidden="true" tabindex="-1"></a> <span class="at">var =</span> <span class="st">"SIR"</span>,</span>
<span id="cb7-29"><a href="#cb7-29" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"choro"</span>,</span>
<span id="cb7-30"><a href="#cb7-30" aria-hidden="true" tabindex="-1"></a> <span class="at">breaks =</span> break_SIR, </span>
<span id="cb7-31"><a href="#cb7-31" aria-hidden="true" tabindex="-1"></a> <span class="at">pal =</span> col_pal, </span>
<span id="cb7-32"><a href="#cb7-32" aria-hidden="true" tabindex="-1"></a> <span class="at">cex =</span> <span class="dv">2</span>,</span>
<span id="cb7-33"><a href="#cb7-33" aria-hidden="true" tabindex="-1"></a> <span class="at">leg_title =</span> <span class="st">"SIR"</span>)</span>
<span id="cb7-34"><a href="#cb7-34" 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 in Cambodia"</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. Howerver, this case does not apply for all disease and for all observed events (e.g. the number of childhood illness and death outcomes 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="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>
<p>The problem is 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>
<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. <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="co"># Plot the incidence histogramm</span></span>
<span id="cb8-2"><a href="#cb8-2" 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>
<div class="cell-output-display">
<p><img src="07-basic_statistics_files/figure-html/MoransI-1.png" class="img-fluid" width="768"></p>
</div>
</div>
</section>
</section>
<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>
<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="7.3.2">
<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>
</section>
<section id="to-go-further" class="level3" data-number="7.3.3">
<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>
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
</section>
</section>
</main> <!-- /main -->
<script id="quarto-html-after-body" type="application/javascript">
window.document.addEventListener("DOMContentLoaded", function (event) {
const toggleBodyColorMode = (bsSheetEl) => {
const mode = bsSheetEl.getAttribute("data-mode");
const bodyEl = window.document.querySelector("body");
if (mode === "dark") {
bodyEl.classList.add("quarto-dark");
bodyEl.classList.remove("quarto-light");
} else {
bodyEl.classList.add("quarto-light");
bodyEl.classList.remove("quarto-dark");
}
}
const toggleBodyColorPrimary = () => {
const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
if (bsSheetEl) {
toggleBodyColorMode(bsSheetEl);
}
}
toggleBodyColorPrimary();
const icon = "";
const anchorJS = new window.AnchorJS();
anchorJS.options = {
placement: 'right',
icon: icon
};
anchorJS.add('.anchored');
const clipboard = new window.ClipboardJS('.code-copy-button', {
target: function(trigger) {
return trigger.previousElementSibling;
}
});
clipboard.on('success', function(e) {
// button target
const button = e.trigger;
// don't keep focus
button.blur();
// flash "checked"
button.classList.add('code-copy-button-checked');
var currentTitle = button.getAttribute("title");
button.setAttribute("title", "Copied!");
setTimeout(function() {
button.setAttribute("title", currentTitle);
button.classList.remove('code-copy-button-checked');
}, 1000);
// clear code selection
e.clearSelection();
});
function tippyHover(el, contentFn) {
const config = {
allowHTML: true,
content: contentFn,
maxWidth: 500,
delay: 100,
arrow: false,
appendTo: function(el) {
return el.parentElement;
},
interactive: true,
interactiveBorder: 10,
theme: 'quarto',
placement: 'bottom-start'
};
window.tippy(el, config);
}
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
for (var i=0; i<noterefs.length; i++) {
const ref = noterefs[i];
tippyHover(ref, function() {
// use id or data attribute instead here
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
try { href = new URL(href).hash; } catch {}
const id = href.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
return note.innerHTML;
});
}
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const cites = ref.parentNode.getAttribute('data-cites').split(' ');
tippyHover(ref, function() {
var popup = window.document.createElement('div');
cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
var filterRegex = new RegExp('/' + window.location.host + '/');
var isInternal = (href) => {
return filterRegex.test(href) || localhostRegex.test(href);
}
// Inspect non-navigation links and adorn them if external
var links = window.document.querySelectorAll('a:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external)');
for (var i=0; i<links.length; i++) {
const link = links[i];
if (!isInternal(link.href)) {
// target, if specified
link.setAttribute("target", "_blank");
}
}
});
</script>
<nav class="page-navigation">
<div class="nav-page nav-page-previous">
<a href="./06-advanced_spatial_analysis.html" class="pagination-link">
<i class="bi bi-arrow-left-short"></i> <span class="nav-page-text"><span class="chapter-number">6</span> <span class="chapter-title">Advanced Spatial Analysis</span></span>
</a>
</div>
<div class="nav-page nav-page-next">
<a href="./references.html" class="pagination-link">
<span class="nav-page-text">References</span> <i class="bi bi-arrow-right-short"></i>
</a>
</div>
</nav>
</div> <!-- /content -->
<footer class="footer">
<div class="nav-footer">
<div class="nav-footer-left">UMR 228 ESPACE-DEV</div>
<div class="nav-footer-right"><img src="img/ird_footer.png" height="50"></div>
</div>
</footer>
</body></html>