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<img src="../logo.svg" class="logo" alt=""><h1>Estimating Empirical Coverage with WISCA</h1>
<small class="dont-index">Source: <a href="https://github.com/msberends/AMR/blob/main/vignettes/WISCA.Rmd" class="external-link"><code>vignettes/WISCA.Rmd</code></a></small>
<div class="d-none name"><code>WISCA.Rmd</code></div>
</div>
<div class="section level2">
<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
</h2>
<p>Clinical guidelines for empirical antimicrobial therapy require
<em>probabilistic reasoning</em>: what is the chance that a regimen will
cover the likely infecting organisms, before culture results are
available?</p>
<p>This is the purpose of <strong>WISCA</strong>, or:</p>
<blockquote>
<p><strong>Weighted-Incidence Syndromic Combination
Antibiogram</strong></p>
</blockquote>
<p>WISCA is a Bayesian approach that integrates: - <strong>Pathogen
prevalence</strong> (how often each species causes the syndrome), -
<strong>Regimen susceptibility</strong> (how often a regimen works
<em>if</em> the pathogen is known),</p>
<p>to estimate the <strong>overall empirical coverage</strong> of
antimicrobial regimens — with quantified uncertainty.</p>
<p>This vignette explains how WISCA works, why it is useful, and how to
apply it in <strong>AMR</strong>.</p>
<hr>
</div>
<div class="section level2">
<h2 id="why-traditional-antibiograms-fall-short">Why traditional antibiograms fall short<a class="anchor" aria-label="anchor" href="#why-traditional-antibiograms-fall-short"></a>
</h2>
<p>A standard antibiogram gives you:</p>
<p>``` Species → Antibiotic → Susceptibility %</p>
<p>But clinicians don’t know the species <em>a priori</em>. They need to
choose a regimen that covers the <strong>likely pathogens</strong> —
without knowing which one is present.</p>
<p>Traditional antibiograms: - Fragment information by organism, - Do
not weight by real-world prevalence, - Do not account for combination
therapy or sample size, - Do not provide uncertainty.</p>
<hr>
</div>
<div class="section level2">
<h2 id="the-idea-of-wisca">The idea of WISCA<a class="anchor" aria-label="anchor" href="#the-idea-of-wisca"></a>
</h2>
<p>WISCA asks:</p>
<blockquote>
<p>“What is the <strong>probability</strong> that this regimen
<strong>will cover</strong> the pathogen, given the syndrome?”</p>
</blockquote>
<p>This means combining two things: - <strong>Incidence</strong> of each
pathogen in the syndrome, - <strong>Susceptibility</strong> of each
pathogen to the regimen.</p>
<p>We can write this as:</p>
<p>``` coverage = ∑ (pathogen incidence × susceptibility)</p>
<p>For example, suppose: - E. coli causes 60% of cases, and 90% of
<em>E. coli</em> are susceptible to a drug. - Klebsiella causes 40% of
cases, and 70% of <em>Klebsiella</em> are susceptible.</p>
<p>Then:</p>
<p>``` coverage = (0.6 × 0.9) + (0.4 × 0.7) = 0.82</p>
<p>But in real data, incidence and susceptibility are <strong>estimated
from samples</strong> — so they carry uncertainty. WISCA models this
<strong>probabilistically</strong>, using conjugate Bayesian
distributions.</p>
<hr>
</div>
<div class="section level2">
<h2 id="the-bayesian-engine-behind-wisca">The Bayesian engine behind WISCA<a class="anchor" aria-label="anchor" href="#the-bayesian-engine-behind-wisca"></a>
</h2>
<div class="section level3">
<h3 id="pathogen-incidence">Pathogen incidence<a class="anchor" aria-label="anchor" href="#pathogen-incidence"></a>
</h3>
<p>Let: - K be the number of pathogens, -
<code>α = (1, 1, ..., 1) be a **Dirichlet** prior (uniform), -</code> n
= (n₁, …, nₖ) be the observed counts per species.</p>
<p>Then the posterior incidence follows:</p>
<p>``` incidence ∼ Dirichlet(α + n)</p>
<p>In simulations, we draw from this posterior using:</p>
<p>``` xᵢ ∼ Gamma(αᵢ + nᵢ, 1)</p>
<p>``` incidenceᵢ = xᵢ / ∑ xⱼ</p>
<hr>
</div>
<div class="section level3">
<h3 id="susceptibility">Susceptibility<a class="anchor" aria-label="anchor" href="#susceptibility"></a>
</h3>
<p>Each pathogen–regimen pair has: - <code>prior: Beta(1, 1) -</code>
data: S susceptible out of N tested</p>
<p>Then:</p>
<p>``` susceptibility ∼ Beta(1 + S, 1 + (N - S))</p>
<p>In each simulation, we draw random susceptibility per species from
this Beta distribution.</p>
<hr>
</div>
<div class="section level3">
<h3 id="final-coverage-estimate">Final coverage estimate<a class="anchor" aria-label="anchor" href="#final-coverage-estimate"></a>
</h3>
<p>Putting it together:</p>
<p>``` For each simulation: - Draw incidence ∼ Dirichlet - Draw
susceptibility ∼ Beta - Multiply → coverage estimate</p>
<p>We repeat this (e.g. 1000×) and summarise: - <strong>Mean</strong>:
expected coverage - <strong>Quantiles</strong>: credible interval
(default 95%)</p>
<hr>
</div>
</div>
<div class="section level2">
<h2 id="practical-use-in-amr">Practical use in AMR<a class="anchor" aria-label="anchor" href="#practical-use-in-amr"></a>
</h2>
<div class="section level3">
<h3 id="simulate-a-synthetic-syndrome">Simulate a synthetic syndrome<a class="anchor" aria-label="anchor" href="#simulate-a-synthetic-syndrome"></a>
</h3>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://amr-for-r.org">AMR</a></span><span class="op">)</span></span>
<span><span class="va">data</span> <span class="op">&lt;-</span> <span class="va">example_isolates</span></span>
<span></span>
<span><span class="co"># Add a fake syndrome column for stratification</span></span>
<span><span class="va">data</span><span class="op">$</span><span class="va">syndrome</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/ifelse.html" class="external-link">ifelse</a></span><span class="op">(</span><span class="va">data</span><span class="op">$</span><span class="va">mo</span> <span class="op"><a href="../reference/like.html">%like%</a></span> <span class="st">"coli"</span>, <span class="st">"UTI"</span>, <span class="st">"Other"</span><span class="op">)</span></span></code></pre></div>
</div>
<div class="section level3">
<h3 id="basic-wisca-antibiogram">Basic WISCA antibiogram<a class="anchor" aria-label="anchor" href="#basic-wisca-antibiogram"></a>
</h3>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../reference/antibiogram.html">antibiogram</a></span><span class="op">(</span><span class="va">data</span>,</span>
<span> wisca <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<table class="table">
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</colgroup>
<thead><tr class="header">
<th align="left">Amikacin</th>
<th align="left">Amoxicillin</th>
<th align="left">Amoxicillin/clavulanic acid</th>
<th align="left">Ampicillin</th>
<th align="left">Azithromycin</th>
<th align="left">Benzylpenicillin</th>
<th align="left">Cefazolin</th>
<th align="left">Cefepime</th>
<th align="left">Cefotaxime</th>
<th align="left">Cefoxitin</th>
<th align="left">Ceftazidime</th>
<th align="left">Ceftriaxone</th>
<th align="left">Cefuroxime</th>
<th align="left">Chloramphenicol</th>
<th align="left">Ciprofloxacin</th>
<th align="left">Clindamycin</th>
<th align="left">Colistin</th>
<th align="left">Doxycycline</th>
<th align="left">Erythromycin</th>
<th align="left">Flucloxacillin</th>
<th align="left">Fosfomycin</th>
<th align="left">Gentamicin</th>
<th align="left">Imipenem</th>
<th align="left">Kanamycin</th>
<th align="left">Linezolid</th>
<th align="left">Meropenem</th>
<th align="left">Metronidazole</th>
<th align="left">Moxifloxacin</th>
<th align="left">Mupirocin</th>
<th align="left">Nitrofurantoin</th>
<th align="left">Oxacillin</th>
<th align="left">Piperacillin/tazobactam</th>
<th align="left">Rifampicin</th>
<th align="left">Teicoplanin</th>
<th align="left">Tetracycline</th>
<th align="left">Tigecycline</th>
<th align="left">Tobramycin</th>
<th align="left">Trimethoprim</th>
<th align="left">Trimethoprim/sulfamethoxazole</th>
<th align="left">Vancomycin</th>
</tr></thead>
<tbody><tr class="odd">
<td align="left">41.7% (37.2-47.5%)</td>
<td align="left">35.7% (33.3-38.2%)</td>
<td align="left">73.7% (71.7-75.8%)</td>
<td align="left">35.8% (33.6-38.1%)</td>
<td align="left">43.8% (41.5-46%)</td>
<td align="left">28.2% (25.8-30.8%)</td>
<td align="left">69.3% (64.9-73.8%)</td>
<td align="left">74.8% (70.5-78.8%)</td>
<td align="left">73.3% (69.2-77.3%)</td>
<td align="left">69.6% (65.5-73.7%)</td>
<td align="left">35.9% (33.6-38.2%)</td>
<td align="left">73.3% (68.9-77.2%)</td>
<td align="left">71.9% (69.8-74%)</td>
<td align="left">64.9% (51.7-78.5%)</td>
<td align="left">77% (74.5-79.6%)</td>
<td align="left">47.3% (44.7-49.6%)</td>
<td align="left">33% (30.8-35.1%)</td>
<td align="left">63.6% (52.1-74.9%)</td>
<td align="left">43.7% (41.6-46%)</td>
<td align="left">59.3% (47-71%)</td>
<td align="left">60.5% (55.5-65.8%)</td>
<td align="left">72.7% (70.7-74.8%)</td>
<td align="left">78.2% (74-82.2%)</td>
<td align="left">25.6% (13.5-37.7%)</td>
<td align="left">54.9% (50.4-59%)</td>
<td align="left">77.1% (72.8-81.2%)</td>
<td align="left">56.1% (39.5-70.7%)</td>
<td align="left">49.6% (43.6-55.6%)</td>
<td align="left">65.2% (52.7-78.1%)</td>
<td align="left">76.5% (69.4-82.3%)</td>
<td align="left">57.8% (45.4-69.6%)</td>
<td align="left">69.4% (64.2-74.2%)</td>
<td align="left">52.4% (47.6-56.8%)</td>
<td align="left">48.1% (43.4-52.9%)</td>
<td align="left">61.4% (53.6-70.5%)</td>
<td align="left">81.9% (78.1-85.5%)</td>
<td align="left">60.7% (57.8-63.5%)</td>
<td align="left">61% (58.8-63.5%)</td>
<td align="left">76.5% (74.5-78.5%)</td>
<td align="left">61.9% (59.8-64.2%)</td>
</tr></tbody>
</table>
</div>
<div class="section level3">
<h3 id="stratify-by-syndrome">Stratify by syndrome<a class="anchor" aria-label="anchor" href="#stratify-by-syndrome"></a>
</h3>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../reference/antibiogram.html">antibiogram</a></span><span class="op">(</span><span class="va">data</span>,</span>
<span> syndromic_group <span class="op">=</span> <span class="st">"syndrome"</span>,</span>
<span> wisca <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
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<thead><tr class="header">
<th align="left">Syndromic Group</th>
<th align="left">Amikacin</th>
<th align="left">Amoxicillin</th>
<th align="left">Amoxicillin/clavulanic acid</th>
<th align="left">Ampicillin</th>
<th align="left">Azithromycin</th>
<th align="left">Benzylpenicillin</th>
<th align="left">Cefazolin</th>
<th align="left">Cefepime</th>
<th align="left">Cefotaxime</th>
<th align="left">Cefoxitin</th>
<th align="left">Ceftazidime</th>
<th align="left">Ceftriaxone</th>
<th align="left">Cefuroxime</th>
<th align="left">Chloramphenicol</th>
<th align="left">Ciprofloxacin</th>
<th align="left">Clindamycin</th>
<th align="left">Colistin</th>
<th align="left">Doxycycline</th>
<th align="left">Erythromycin</th>
<th align="left">Flucloxacillin</th>
<th align="left">Fosfomycin</th>
<th align="left">Gentamicin</th>
<th align="left">Imipenem</th>
<th align="left">Kanamycin</th>
<th align="left">Linezolid</th>
<th align="left">Meropenem</th>
<th align="left">Metronidazole</th>
<th align="left">Moxifloxacin</th>
<th align="left">Mupirocin</th>
<th align="left">Nitrofurantoin</th>
<th align="left">Oxacillin</th>
<th align="left">Piperacillin/tazobactam</th>
<th align="left">Rifampicin</th>
<th align="left">Teicoplanin</th>
<th align="left">Tetracycline</th>
<th align="left">Tigecycline</th>
<th align="left">Tobramycin</th>
<th align="left">Trimethoprim</th>
<th align="left">Trimethoprim/sulfamethoxazole</th>
<th align="left">Vancomycin</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">Other</td>
<td align="left">25% (20.2-31.7%)</td>
<td align="left">31.6% (28.7-34%)</td>
<td align="left">70.1% (67.7-72.4%)</td>
<td align="left">31.6% (29.1-34.1%)</td>
<td align="left">56.4% (53.8-58.8%)</td>
<td align="left">36.3% (33.1-39.4%)</td>
<td align="left">61.5% (55.7-66.5%)</td>
<td align="left">68.5% (63.4-73.8%)</td>
<td align="left">66.7% (61.4-71.9%)</td>
<td align="left">63% (57.7-68.6%)</td>
<td align="left">18.3% (15.9-20.8%)</td>
<td align="left">66.6% (61.4-71.5%)</td>
<td align="left">65.5% (62.7-68%)</td>
<td align="left">69.6% (60-77.2%)</td>
<td align="left">74% (70.8-77.2%)</td>
<td align="left">60.9% (58.1-63.6%)</td>
<td align="left">13.9% (11.8-15.8%)</td>
<td align="left">67.4% (63.7-70.9%)</td>
<td align="left">56.4% (54-58.9%)</td>
<td align="left">61.4% (56-67.6%)</td>
<td align="left">49.6% (43.2-56.3%)</td>
<td align="left">65.6% (62.8-68.1%)</td>
<td align="left">71.8% (66.7-77%)</td>
<td align="left">18.6% (13.1-25.9%)</td>
<td align="left">70.8% (65.1-75.8%)</td>
<td align="left">70.6% (65.1-75.7%)</td>
<td align="left">49.8% (34.2-66.6%)</td>
<td align="left">63.3% (56.2-70.3%)</td>
<td align="left">69.8% (62.6-76.4%)</td>
<td align="left">70.5% (61.2-77.5%)</td>
<td align="left">60% (54.4-65.4%)</td>
<td align="left">62.4% (56.4-68.6%)</td>
<td align="left">67.6% (61.9-73.2%)</td>
<td align="left">61.9% (55.4-67.6%)</td>
<td align="left">67.8% (64.8-70.6%)</td>
<td align="left">77% (72.3-81.8%)</td>
<td align="left">50.1% (46.7-53.6%)</td>
<td align="left">61.1% (58.4-64%)</td>
<td align="left">78.8% (76.4-80.9%)</td>
<td align="left">79.6% (77.4-81.8%)</td>
</tr>
<tr class="even">
<td align="left">UTI</td>
<td align="left">91.5% (88.8-93.5%)</td>
<td align="left">50% (45.5-54.6%)</td>
<td align="left">80.9% (77.8-84%)</td>
<td align="left">49.9% (45.6-54.3%)</td>
<td align="left">8.2% (6.4-10.5%)</td>
<td align="left">8.2% (6.3-10.3%)</td>
<td align="left">88.9% (84.2-92.3%)</td>
<td align="left">89.4% (86.5-91.8%)</td>
<td align="left">89.9% (87.4-92.1%)</td>
<td align="left">86.1% (82.9-88.9%)</td>
<td align="left">89.8% (87.2-91.9%)</td>
<td align="left">89.8% (87.1-92.1%)</td>
<td align="left">87.4% (84.5-89.8%)</td>
<td align="left">NA</td>
<td align="left">81.4% (78.3-84.3%)</td>
<td align="left">8.2% (6.3-10.4%)</td>
<td align="left">91.7% (89.6-93.8%)</td>
<td align="left">NA</td>
<td align="left">8.1% (6.3-10.4%)</td>
<td align="left">NA</td>
<td align="left">90.6% (86.5-93.3%)</td>
<td align="left">90.2% (87.9-92.2%)</td>
<td align="left">91.8% (89.7-93.8%)</td>
<td align="left">NA</td>
<td align="left">8.1% (6.1-10.2%)</td>
<td align="left">91.8% (89.6-93.8%)</td>
<td align="left">71.4% (31.8-91.6%)</td>
<td align="left">9.3% (6.7-13.3%)</td>
<td align="left">NA</td>
<td align="left">89.4% (86.9-91.7%)</td>
<td align="left">NA</td>
<td align="left">87.2% (84.4-89.6%)</td>
<td align="left">8.2% (6.3-10.4%)</td>
<td align="left">8.2% (6.3-10.3%)</td>
<td align="left">41.2% (14.3-74.4%)</td>
<td align="left">90.9% (87.7-93.3%)</td>
<td align="left">89.6% (87.1-91.8%)</td>
<td align="left">59.1% (54.7-63.4%)</td>
<td align="left">65.3% (61.3-69.2%)</td>
<td align="left">8.2% (6.2-10.3%)</td>
</tr>
</tbody>
</table>
</div>
<div class="section level3">
<h3 id="use-combination-regimens">Use combination regimens<a class="anchor" aria-label="anchor" href="#use-combination-regimens"></a>
</h3>
<p>The <code><a href="../reference/antibiogram.html">antibiogram()</a></code> function supports combination
regimens:</p>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../reference/antibiogram.html">antibiogram</a></span><span class="op">(</span><span class="va">data</span>,</span>
<span> antimicrobials <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="st">"AMC"</span>, <span class="st">"GEN"</span>, <span class="st">"AMC + GEN"</span>, <span class="st">"CIP"</span><span class="op">)</span>,</span>
<span> wisca <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<colgroup>
<col width="26%">
<col width="39%">
<col width="16%">
<col width="18%">
</colgroup>
<thead><tr class="header">
<th align="left">Amoxicillin/clavulanic acid</th>
<th align="left">Amoxicillin/clavulanic acid + Gentamicin</th>
<th align="left">Ciprofloxacin</th>
<th align="left">Gentamicin</th>
</tr></thead>
<tbody><tr class="odd">
<td align="left">73.8% (71.7-75.8%)</td>
<td align="left">89.7% (88.2-91.2%)</td>
<td align="left">77% (74.3-79.6%)</td>
<td align="left">72.8% (70.6-74.9%)</td>
</tr></tbody>
</table>
<hr>
</div>
</div>
<div class="section level2">
<h2 id="interpretation">Interpretation<a class="anchor" aria-label="anchor" href="#interpretation"></a>
</h2>
<p>Suppose you get this output:</p>
<table class="table">
<thead><tr class="header">
<th>Regimen</th>
<th>Coverage</th>
<th>Lower_CI</th>
<th>Upper_CI</th>
</tr></thead>
<tbody>
<tr class="odd">
<td>AMC</td>
<td>0.72</td>
<td>0.65</td>
<td>0.78</td>
</tr>
<tr class="even">
<td>AMC + GEN</td>
<td>0.88</td>
<td>0.83</td>
<td>0.93</td>
</tr>
</tbody>
</table>
<p>Interpretation:</p>
<blockquote>
<p><em>“AMC + GEN covers 88% of expected pathogens for this syndrome,
with 95% certainty that the true coverage lies between 83% and
93%.”</em></p>
</blockquote>
<p>Regimens with few tested isolates will show <strong>wider
intervals</strong>.</p>
<hr>
</div>
<div class="section level2">
<h2 id="sensible-defaults-but-you-can-customise">Sensible defaults, but you can customise<a class="anchor" aria-label="anchor" href="#sensible-defaults-but-you-can-customise"></a>
</h2>
<ul>
<li>
<code>minimum = 30</code>: exclude regimens with &lt;30 isolates
tested.</li>
<li>
<code>simulations = 1000</code>: number of Monte Carlo samples.</li>
<li>
<code>conf_interval = 0.95</code>: coverage interval width.</li>
<li>
<code>combine_SI = TRUE</code>: count “I”/“SDD” as susceptible.</li>
</ul>
<hr>
</div>
<div class="section level2">
<h2 id="limitations">Limitations<a class="anchor" aria-label="anchor" href="#limitations"></a>
</h2>
<ul>
<li>WISCA does not model time trends or temporal resistance shifts.</li>
<li>It assumes data are representative of current clinical
practice.</li>
<li>It does not account for patient-level covariates (yet).</li>
<li>Species-specific data are abstracted into syndrome-level
estimates.</li>
</ul>
<hr>
</div>
<div class="section level2">
<h2 id="reference">Reference<a class="anchor" aria-label="anchor" href="#reference"></a>
</h2>
<p>Bielicki JA et al. (2016).<br><em>Weighted-incidence syndromic combination antibiograms to guide
empiric treatment in pediatric bloodstream infections.</em><br><strong>J Antimicrob Chemother</strong>, 71(2):529–536. <a href="doi:10.1093/jac/dkv397" class="uri">doi:10.1093/jac/dkv397</a></p>
<hr>
</div>
<div class="section level2">
<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a>
</h2>
<p>WISCA shifts empirical therapy from simple percent susceptible toward
<strong>probabilistic, syndrome-based decision support</strong>. It is a
statistically principled, clinically intuitive method to guide regimen
selection — and easy to use via the <code><a href="../reference/antibiogram.html">antibiogram()</a></code> function
in the <strong>AMR</strong> package.</p>
<p>For antimicrobial stewardship teams, it enables
<strong>disease-specific, reproducible, and data-driven
guidance</strong> — even in the face of sparse data.</p>
</div>
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