+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<meta charset="utf-8">
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<title>White and Pagano: Utilizing the Serial Distribution • Rnaught</title>
+<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
+<script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet">
+<link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet">
+<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="White and Pagano: Utilizing the Serial Distribution">
+</head>
+<body>
+ <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
+
+
+ <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
+
+ <a class="navbar-brand me-2" href="../index.html">Rnaught</a>
+
+ <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.1.0</small>
+
+
+ <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
+ <span class="navbar-toggler-icon"></span>
+ </button>
+
+ <div id="navbar" class="collapse navbar-collapse ms-3">
+ <ul class="navbar-nav me-auto">
+<li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
+<li class="active nav-item dropdown">
+ <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button>
+ <ul class="dropdown-menu" aria-labelledby="dropdown-articles">
+<li><a class="dropdown-item" href="../articles/seq_bayes_post.html">Sequential Bayes: Utilizing the Posterior Distribution</a></li>
+ <li><a class="dropdown-item" href="../articles/wp_serial.html">White and Pagano: Utilizing the Serial Distribution</a></li>
+ </ul>
+</li>
+ </ul>
+<ul class="navbar-nav">
+<li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
+</form></li>
+<li class="nav-item"><a class="external-link nav-link" href="https://github.com/MI2YorkU/Rnaught/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+ </ul>
+</div>
+
+
+ </div>
+</nav><div class="container template-article">
+
+
+
+
+<div class="row">
+ <main id="main" class="col-md-9"><div class="page-header">
+ <img src="../logo.svg" class="logo" alt=""><h1>White and Pagano: Utilizing the Serial Distribution</h1>
+
+
+ <small class="dont-index">Source: <a href="https://github.com/MI2YorkU/Rnaught/blob/master/vignettes/wp_serial.Rmd" class="external-link"><code>vignettes/wp_serial.Rmd</code></a></small>
+ <div class="d-none name"><code>wp_serial.Rmd</code></div>
+ </div>
+
+
+
+<p>The serial distribution of an infectious disease is the distribution
+of the time from when an infectious individual – the infector – becomes
+symptomatic, to when another individual who is infected by the infector
+becomes symptomatic. The serial interval refers to a range of likely
+values from this distribution, although it is typically reported as the
+mean.</p>
+<p>In the White and Pagano method, the serial distribution is assumed to
+be a discretized, finite version of a gamma distribution. Setting the
+parameter <code>serial</code> to <code>TRUE</code> causes this
+discretized distribution to be returned in addition to the estimate of
+R0. Furthermore, the method can be used whether or not the serial
+interval (specified as the parameter <code>mu</code>) is known. When
+<code>mu</code> is specified, it is taken to be the mean of a continuous
+gamma distribution (i.e., before the discretization). As such, the mean
+computed from the returned serial distribution may differ slightly from
+<code>mu</code>:</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Case counts.</span></span>
+<span><span class="va">cases</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span>, <span class="fl">4</span>, <span class="fl">10</span>, <span class="fl">5</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">19</span>, <span class="fl">3</span>, <span class="fl">3</span>, <span class="fl">14</span>, <span class="fl">4</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">estimate</span> <span class="op"><-</span> <span class="fu"><a href="../reference/wp.html">wp</a></span><span class="op">(</span><span class="va">cases</span>, mu <span class="op">=</span> <span class="fl">3.333</span>, serial <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># `supp` is the support of the distribution, and `pmf` is its probability mass</span></span>
+<span><span class="co"># function.</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">estimate</span><span class="op">$</span><span class="va">supp</span> <span class="op">*</span> <span class="va">estimate</span><span class="op">$</span><span class="va">pmf</span><span class="op">)</span></span>
+<span><span class="co">#> [1] 3.840047</span></span></code></pre></div>
+<p>When <code>mu</code> is unspecified (left to its default value of
+<code>NA</code>), the method performs a maximum likelihood estimation
+over all (discretized) gamma distributions via a grid search, whose
+range of parameters are specified via <code>grid_length</code>,
+<code>max_shape</code> and <code>max_scale</code> (see <code><a href="../reference/wp.html">?wp</a></code>
+for more details). It is useful to return the estimated serial
+distribution in this case, as it can provide estimates of the serial
+interval when it is unknown:</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># The grid search parameters specified below are the default values.</span></span>
+<span><span class="va">estimate</span> <span class="op"><-</span> <span class="fu"><a href="../reference/wp.html">wp</a></span><span class="op">(</span><span class="va">cases</span>, serial <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span> grid_length <span class="op">=</span> <span class="fl">100</span>, max_shape <span class="op">=</span> <span class="fl">10</span>, max_scale <span class="op">=</span> <span class="fl">10</span></span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">serial_mean</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">estimate</span><span class="op">$</span><span class="va">supp</span> <span class="op">*</span> <span class="va">estimate</span><span class="op">$</span><span class="va">pmf</span><span class="op">)</span></span>
+<span><span class="va">serial_mean</span></span>
+<span><span class="co">#> [1] 3.564191</span></span>
+<span></span>
+<span><span class="co"># Compute the (discrete) median for an alternative estimate of the serial</span></span>
+<span><span class="co"># interval.</span></span>
+<span><span class="va">cdf</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cumsum.html" class="external-link">cumsum</a></span><span class="op">(</span><span class="va">estimate</span><span class="op">$</span><span class="va">pmf</span><span class="op">)</span></span>
+<span><span class="va">serial_med</span> <span class="op"><-</span> <span class="va">estimate</span><span class="op">$</span><span class="va">supp</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/which.html" class="external-link">which</a></span><span class="op">(</span><span class="va">cdf</span> <span class="op">>=</span> <span class="fl">0.5</span> <span class="op">&</span> <span class="va">estimate</span><span class="op">$</span><span class="va">pmf</span> <span class="op">-</span> <span class="va">cdf</span> <span class="op">+</span> <span class="fl">1</span> <span class="op">>=</span> <span class="fl">0.5</span><span class="op">)</span><span class="op">]</span></span>
+<span><span class="va">serial_med</span></span>
+<span><span class="co">#> [1] 2</span></span></code></pre></div>
+<p>Below is a graph of the above results, containing the serial
+distribution as well as its mean and median, which could be used as
+estimates of the serial interval:</p>
+<p><img src="wp_serial_files/figure-html/unnamed-chunk-4-1.png" width="1400"></p>
+ </main>
+</div>
+
+
+
+ <footer><div class="pkgdown-footer-left">
+ <p>Developed by Sawitree Boonpatcharanon, Jane Heffernan, Hanna Jankowski, Naeem Model.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+ <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
+</div>
+
+ </footer>
+</div>
+
+
+
+
+
+ </body>
+</html>
git.nmode.ca / Rnaught / blobdiff
