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<h3 id="author" class="author">
<strong>Filippo Gambarota</strong><sup> 1</sup><br>
<a class="twitter" href="https://mobile.twitter.com/fgambarota"><i class="fab fa-twitter"></i> @fgambarota</a><br>
<a class='envelope'><i class="fas fa-envelope"></i></a> <a href="mailto:[email protected]" class="email">[email protected]</a> <br>
</h3>
<h5 id="author_extra", class="author_extra">
Anna Vesely<sup>2</sup>
Livio Finos<sup>3</sup>
Gianmarco Altoè<sup>1</sup>
</h5>
<p id="affiliation" class="affiliation">
<sup>1</sup> Department of Developmental and Social Psychology, University of Padova<br> <sup>2</sup> Institute for Statistics, University of Bremen<br> <sup>3</sup> Department of Statistics, University of Padova
</p>
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<div id="the-multiverse-problem" class="section level1">
<h1>The Multiverse problem</h1>
<p><img src="img/big-picture.svg" width="80%" style="display: block; margin: auto;" /></p>
<p><strong>As example, we used the dataset by <a href="https://pubmed.ncbi.nlm.nih.gov/34545236/">Daros et al. (2021)</a></strong> with a multivariate meta-analysis of RCTs designs with multiple measure for the same outcome. <strong>We considered a total of 162 plausible scenarios</strong>.</p>
</div>
<div id="the-proposed-workflow" class="section level1">
<h1>The Proposed Workflow</h1>
<p><img src="img/workflow.svg" width="100%" style="display: block; margin: auto;" /></p>
<p>We <strong>simulated a plausible multiverse</strong> sampling from a multivariate normal distribution with a vector of means (i.e., the meta-analysis results) and a variance-covariance matrix for the relationship between different scenarios.</p>
<p></br></p>
</div>
<div id="multiverse-summary" class="section level1">
<h1>Multiverse Summary</h1>
<p>The multiverse is a associated with an <strong>overall p-value <span class="math inline">\(< 0.001\)</span></strong>, an <strong>average effect of <span class="math inline">\(0.403\)</span> (<span class="math inline">\(SD = 0.112\)</span>)</strong> and an <strong>average correlation of <span class="math inline">\(0.620\)</span> (<span class="math inline">\(SD = 0.102\)</span>)</strong>.</p>
<p><img src="sips-2023_files/figure-html/unnamed-chunk-5-1.png" width="80%" style="display: block; margin: auto;" /></p>
<p><img src="sips-2023_files/figure-html/unnamed-chunk-6-1.png" width="80%" style="display: block; margin: auto;" /></p>
</div>
<div id="multiverse-post-hoc-p-values" class="section level1">
<h1>Multiverse post-hoc p-values</h1>
<p><img src="sips-2023_files/figure-html/unnamed-chunk-7-1.png" width="80%" style="display: block; margin: auto;" /></p>
</div>
<div id="conclusions-and-next-steps" class="section level1">
<h1>Conclusions and Next Steps</h1>
<ul>
<li><strong>Corrected p-values for valid post-hoc inference</strong> on specific scenarios</li>
<li>The method <strong>control the Family-wise Error Rate (FWER)</strong> across the multiverse</li>
<li><strong>Fast meta-analysis via permutations</strong> using the <code>flip</code> package</li>
<li>Implementing multilevel and multivariate meta-analysis</li>
</ul>
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<p><strong>joinmeta</strong> - controlling the type-1 error in multiverse meta-analysis</p>
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