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<div id="header">
<h1 class="title toc-ignore">CompAREdesign: Binary endpoint</h1>
<h4 class="author">Marta Bofill Roig, Jordi Cortés Martínez and
Guadalupe Gómez Melis</h4>
<h4 class="date">2025-02-24</h4>
</div>
<div id="binary-endpoint-tuxedo-trial" class="section level2">
<h2>Binary endpoint: TUXEDO TRIAL</h2>
<p>This example is based on the data from the <a
href="https://doi.org/10.1056/nejmoa1510188">TUXEDO trial</a> [1].</p>
<p>The Taxus Element versus Xience Prime in a Diabetic Population
(TUXEDO)–India study is an investigator-initiated, multicenter,
randomized clinical trial. The trial protocol is available with the full
text of this article at NEJM.org. The trial was funded by Boston
Scientific, the manufacturer of the paclitaxeleluting stent (Taxus
Element).</p>
<div id="input-parameters" class="section level3">
<h3>Input Parameters</h3>
<p>To use the functions in CompAREdesign, we first of all need to
include the information for the components of the composite
endpoint.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="do">## Probabilities of observing the event in control arm at the end of follow-up</span></span>
<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a>p0_e1 <span class="ot"><-</span> <span class="fl">0.059</span> <span class="co"># Ischemia-driven target-lesion revascularization </span></span>
<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a>p0_e2 <span class="ot"><-</span> <span class="fl">0.032</span> <span class="co"># Cardiac death or target-vessel MI </span></span>
<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a></span>
<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a><span class="do">## Effect size (absolute reduction) for each endpoint</span></span>
<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a>AR_e1 <span class="ot"><-</span> <span class="sc">-</span><span class="fl">0.0196</span> <span class="co"># Ischemia-driven target-lesion revascularization </span></span>
<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a>AR_e2 <span class="ot"><-</span> <span class="sc">-</span><span class="fl">0.0098</span> <span class="co"># Cardiac death or target-vessel MI</span></span>
<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a></span>
<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a><span class="do">## Correlation</span></span>
<span id="cb1-10"><a href="#cb1-10" tabindex="-1"></a>rho <span class="ot"><-</span> <span class="fl">0.4</span></span></code></pre></div>
</div>
<div id="are-asymptotic-relatively-efficiency" class="section level3">
<h3>ARE: Asymptotic Relatively Efficiency</h3>
<p>Aiming to compare the gain in power of using the composite endpoint
over the most relevant of its components. One can use the function ARE.
As the ARE is greater than 1, we can state that the design using the
composite endpoint is more efficient.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">ARE_cbe</span>(<span class="at">p0_e1 =</span> p0_e1 , <span class="at">p0_e2 =</span> p0_e2, </span>
<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a> <span class="at">eff_e1 =</span> AR_e1 , <span class="at">eff_e2 =</span> AR_e2, </span>
<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a> <span class="at">effm_e1 =</span> <span class="st">"diff"</span> , <span class="at">effm_e2 =</span> <span class="st">"diff"</span>, <span class="at">effm_ce =</span> <span class="st">"or"</span>,</span>
<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a> <span class="at">rho =</span> rho) </span></code></pre></div>
<pre><code>## [1] 1.139515</code></pre>
</div>
<div id="effect-size-of-the-composite-endpoint" class="section level3">
<h3>Effect size of the Composite Endpoint</h3>
<p>If we can anticipate the baseline information of the composite
components and expected effect sizes together with the correlation
between the components, we can obtain the expected treatment effect on
the composite endpoint (odds ratio, <em>OR</em>).</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a><span class="fu">effectsize_cbe</span>(<span class="at">p0_e1 =</span> p0_e1 , <span class="at">p0_e2 =</span> p0_e2, </span>
<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a> <span class="at">eff_e1 =</span> AR_e1 , <span class="at">eff_e2 =</span> AR_e2, </span>
<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a> <span class="at">effm_e1 =</span> <span class="st">"diff"</span> , <span class="at">effm_e2 =</span> <span class="st">"diff"</span>, <span class="at">effm_ce =</span> <span class="st">"or"</span>,</span>
<span id="cb4-4"><a href="#cb4-4" tabindex="-1"></a> <span class="at">rho =</span> rho) </span></code></pre></div>
<pre><code>## Effect E1 Effect E2 Effect CE
## 1 0.6541709 0.6867969 0.662605</code></pre>
</div>
<div id="sample-size" class="section level3">
<h3>Sample size</h3>
<p>Lastly, we can compute the required sample size for the design using
the composite endpoint, in this case obtaining
<strong>2644</strong>.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="fu">samplesize_cbe</span>(<span class="at">p0_e1 =</span> p0_e1 , <span class="at">p0_e2 =</span> p0_e2, </span>
<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a> <span class="at">eff_e1 =</span> AR_e1 , <span class="at">eff_e2 =</span> AR_e2, </span>
<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a> <span class="at">effm_e1 =</span> <span class="st">"diff"</span> , <span class="at">effm_e2 =</span> <span class="st">"diff"</span>, <span class="at">effm_ce =</span> <span class="st">"or"</span>,</span>
<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a> <span class="at">rho =</span> rho,</span>
<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a> <span class="at">alpha =</span> <span class="fl">0.05</span>, <span class="at">beta =</span> <span class="fl">0.2</span>) </span></code></pre></div>
<pre><code>## [1] 2643.829</code></pre>
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<div id="references" class="section level2">
<h2>References</h2>
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<li>Kaul U, Bangalore S, Seth A, Priyadarshini A, Rajpal KA, Tejas MP et
al. Paclitaxel-Eluting versus EverolimusEluting Coronary Stents in
Diabetes. N Engl J Med. 2015;373(18):1709-19.</li>
</ol>
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