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Expand Up @@ -227,6 +227,7 @@ <h2 id="toc-title">Table of contents</h2>
<li><a href="#heterogeneous-treatment-effect" id="toc-heterogeneous-treatment-effect" class="nav-link" data-scroll-target="#heterogeneous-treatment-effect"><span class="header-section-number">5.4</span> Heterogeneous Treatment Effect</a>
<ul class="collapse">
<li><a href="#methods-for-dealing-with-missing-data" id="toc-methods-for-dealing-with-missing-data" class="nav-link" data-scroll-target="#methods-for-dealing-with-missing-data"><span class="header-section-number">5.4.1</span> Methods for Dealing with Missing Data</a></li>
<li><a href="#results-1" id="toc-results-1" class="nav-link" data-scroll-target="#results-1"><span class="header-section-number">5.4.2</span> Results</a></li>
</ul></li>
<li><a href="#version-info" id="toc-version-info" class="nav-link" data-scroll-target="#version-info">Version info</a></li>
<li><a href="#references" id="toc-references" class="nav-link" data-scroll-target="#references">References</a></li>
Expand Down Expand Up @@ -802,6 +803,75 @@ <h4 data-number="5.4.1.3" class="anchored" data-anchor-id="parametric-multiple-i
<span id="cb24-5"><a href="#cb24-5" aria-hidden="true" tabindex="-1"></a> <span class="at">maxit =</span> <span class="dv">10</span>, <span class="at">printFlag =</span> <span class="cn">FALSE</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="non-parametric-multiple-imputation" class="level4" data-number="5.4.1.4">
<h4 data-number="5.4.1.4" class="anchored" data-anchor-id="non-parametric-multiple-imputation"><span class="header-section-number">5.4.1.4</span> Non-parametric Multiple Imputation</h4>
<p>Another option is to use imputation methods based on non-parametric approaches such as random forest, which are robust to the inclusion of interaction and quadratic terms. Here we use the “rf” method included in mice, but there are other available options as discussed by .</p>
<div class="cell" data-hash="chapter_09_cache/html/het rf_98ef4be494838edfed94a7770fdaea14">
<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>imp_rf <span class="ot">&lt;-</span> <span class="fu">mice</span>(impdata_het, <span class="at">method =</span> <span class="st">"rf"</span>, <span class="at">m =</span> <span class="dv">10</span>, <span class="at">maxit =</span> <span class="dv">10</span>, </span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a> <span class="at">ntree =</span> <span class="dv">10</span>, <span class="at">printFlag =</span> <span class="cn">FALSE</span>)</span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a><span class="co">#plot(imp_rf)</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>It has also been proposed a new method based on XGBoost that seems also an option for data with interaction terms . Here it is required to calibrate the parameters to be included in the function and do an extra job to put it in the mice package format.</p>
<div class="cell" data-hash="chapter_09_cache/html/het gb_e5820af4c1d0278627d7c049066dfc07">
<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(mixgb)</span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a>params <span class="ot">&lt;-</span> <span class="fu">list</span>(<span class="at">max_depth =</span> <span class="dv">3</span>, <span class="at">subsample =</span> <span class="fl">0.7</span>, <span class="at">nthread =</span> <span class="dv">2</span>)</span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a>cv.results <span class="ot">&lt;-</span> <span class="fu">mixgb_cv</span>(<span class="at">data =</span> impdata_het, <span class="at">nrounds =</span> <span class="dv">100</span>,</span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a> <span class="at">xgb.params =</span> params, <span class="at">verbose =</span> <span class="cn">FALSE</span>)</span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a>imp_gb <span class="ot">&lt;-</span> <span class="fu">mixgb</span>(<span class="at">data =</span> impdata_het, <span class="at">m =</span> <span class="dv">10</span>, <span class="at">maxit =</span> <span class="dv">10</span>, <span class="at">nrounds =</span> cv.results<span class="sc">$</span>best.nrounds)</span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a>data_gb <span class="ot">&lt;-</span> <span class="fu">bind_rows</span>(impdata_het,imp_gb, <span class="at">.id =</span> <span class="st">'.imp'</span>)</span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a>data_gb<span class="sc">$</span><span class="st">'.imp'</span> <span class="ot">&lt;-</span> <span class="fu">as.numeric</span>(data_gb<span class="sc">$</span><span class="st">'.imp'</span>) <span class="sc">-</span> <span class="dv">1</span></span>
<span id="cb26-9"><a href="#cb26-9" aria-hidden="true" tabindex="-1"></a>imp_gb <span class="ot">&lt;-</span> mice<span class="sc">::</span><span class="fu">as.mids</span>(data_gb)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>After checking the convergence of all the imputation methods,via traceplots, we proceed to estimate the treatment effect with the <strong>ATE_estimation()</strong> function, were it is required to specify the variable <em>Iscore</em> to evaluate the treatment effect on each group.</p>
<div class="cell" data-hash="chapter_09_cache/html/het all_5f50fc928acecd16c79c321f2f06abd9">
<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>imp_datasets <span class="ot">&lt;-</span> <span class="fu">list</span>(imp_sep,imp_y,imp_iy,imp_rf,imp_gb)</span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a>n_analysis <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"MICE (separated)"</span>,<span class="st">"MICE (no interaction)"</span>, <span class="st">"MICE (interaction)"</span>, <span class="st">"Random forest"</span>, <span class="st">"MixGb"</span>)</span>
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a>response_imp <span class="ot">&lt;-</span> <span class="fu">lapply</span>(<span class="fu">seq_along</span>(imp_datasets), \(i) </span>
<span id="cb27-4"><a href="#cb27-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">ATE_estimation</span>( <span class="at">data =</span> imp_datasets[[i]],</span>
<span id="cb27-5"><a href="#cb27-5" aria-hidden="true" tabindex="-1"></a> <span class="at">model =</span> het.model,</span>
<span id="cb27-6"><a href="#cb27-6" aria-hidden="true" tabindex="-1"></a> <span class="at">approach =</span> <span class="st">"within"</span>,</span>
<span id="cb27-7"><a href="#cb27-7" aria-hidden="true" tabindex="-1"></a> <span class="at">variable =</span> <span class="st">"Iscore"</span>,</span>
<span id="cb27-8"><a href="#cb27-8" aria-hidden="true" tabindex="-1"></a> <span class="at">analysis =</span> n_analysis[[i]])<span class="sc">$</span>ATE_var)</span>
<span id="cb27-9"><a href="#cb27-9" aria-hidden="true" tabindex="-1"></a>response_imp <span class="ot">&lt;-</span> <span class="fu">do.call</span>(rbind,response_imp)</span>
<span id="cb27-10"><a href="#cb27-10" aria-hidden="true" tabindex="-1"></a>result_het <span class="ot">&lt;-</span> <span class="fu">bind_rows</span>(result_het,response_imp)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
</section>
<section id="results-1" class="level3" data-number="5.4.2">
<h3 data-number="5.4.2" class="anchored" data-anchor-id="results-1"><span class="header-section-number">5.4.2</span> Results</h3>
<div class="cell" data-hash="chapter_09_cache/html/het plot_30e69ed1b7df0b2cd633d34928b76252">
<div class="sourceCode cell-code" id="cb28"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a>result_het<span class="sc">$</span>Iscore <span class="ot">&lt;-</span> <span class="fu">as.factor</span>(result_het<span class="sc">$</span>Iscore)</span>
<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a><span class="fu">levels</span>(result_het<span class="sc">$</span>Iscore) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"High DMF"</span>,<span class="st">"Moderate DMF"</span>, <span class="st">"Neutral"</span>, </span>
<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a> <span class="st">"Moderate TERI"</span>, <span class="st">"High TERI"</span>)</span>
<span id="cb28-5"><a href="#cb28-5" aria-hidden="true" tabindex="-1"></a>result_het<span class="sc">$</span>analysis <span class="ot">=</span> <span class="fu">factor</span>(result_het<span class="sc">$</span>analysis,</span>
<span id="cb28-6"><a href="#cb28-6" aria-hidden="true" tabindex="-1"></a> <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Full data"</span>,</span>
<span id="cb28-7"><a href="#cb28-7" aria-hidden="true" tabindex="-1"></a> <span class="st">"Complete Case Analysis"</span>,</span>
<span id="cb28-8"><a href="#cb28-8" aria-hidden="true" tabindex="-1"></a> <span class="st">"MICE (separated)"</span>,</span>
<span id="cb28-9"><a href="#cb28-9" aria-hidden="true" tabindex="-1"></a> <span class="st">"MICE (no interaction)"</span>,</span>
<span id="cb28-10"><a href="#cb28-10" aria-hidden="true" tabindex="-1"></a> <span class="st">"MICE (interaction)"</span>,</span>
<span id="cb28-11"><a href="#cb28-11" aria-hidden="true" tabindex="-1"></a> <span class="st">"Random forest"</span>,</span>
<span id="cb28-12"><a href="#cb28-12" aria-hidden="true" tabindex="-1"></a> <span class="st">"MixGb"</span>))</span>
<span id="cb28-13"><a href="#cb28-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-14"><a href="#cb28-14" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(result_het,<span class="fu">aes</span>(<span class="at">x =</span> analysis, <span class="at">y =</span> estimate, <span class="at">col =</span> analysis)) <span class="sc">+</span></span>
<span id="cb28-15"><a href="#cb28-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_point</span>(<span class="at">shape =</span> <span class="dv">1</span>,</span>
<span id="cb28-16"><a href="#cb28-16" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb28-17"><a href="#cb28-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_errorbar</span>(<span class="fu">aes</span>(<span class="at">ymin =</span> conf.low,</span>
<span id="cb28-18"><a href="#cb28-18" aria-hidden="true" tabindex="-1"></a> <span class="at">ymax =</span> conf.high),</span>
<span id="cb28-19"><a href="#cb28-19" aria-hidden="true" tabindex="-1"></a> <span class="at">width =</span> <span class="fl">0.2</span>,</span>
<span id="cb28-20"><a href="#cb28-20" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.5</span>) <span class="sc">+</span></span>
<span id="cb28-21"><a href="#cb28-21" aria-hidden="true" tabindex="-1"></a> see<span class="sc">::</span><span class="fu">scale_color_flat</span>() <span class="sc">+</span> <span class="fu">theme_light</span>() <span class="sc">+</span> </span>
<span id="cb28-22"><a href="#cb28-22" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">axis.title.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb28-23"><a href="#cb28-23" aria-hidden="true" tabindex="-1"></a> <span class="at">axis.text.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb28-24"><a href="#cb28-24" aria-hidden="true" tabindex="-1"></a> <span class="at">axis.ticks.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb28-25"><a href="#cb28-25" aria-hidden="true" tabindex="-1"></a> <span class="at">legend.position =</span> <span class="st">"bottom"</span>) <span class="sc">+</span></span>
<span id="cb28-26"><a href="#cb28-26" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_wrap</span>(<span class="st">"Iscore"</span>,<span class="at">ncol =</span> <span class="dv">2</span>, <span class="at">scales =</span> <span class="st">"free"</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="chapter_09_files/figure-html/het plot-1.png" class="img-fluid" width="672"></p>
</div>
</div>
<p>We found that except for the complete case analysis, all the methods lead to unbiased results of the treatment effect across all the Iscore groups. However, it seems that the estimation of the MixGb method leads to estimations closer to the Full dataset ones.</p>
</section>
</section>
<section id="version-info" class="level2 unnumbered">
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4 changes: 2 additions & 2 deletions docs/chapter_10.html
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Expand Up @@ -1021,7 +1021,7 @@ <h3 data-number="6.3.2" class="anchored" data-anchor-id="pharmacologic-treatment

</div>
</div>
<div class="cell" data-hash="chapter_10_cache/html/unnamed-chunk-25_8d275b4401059182df05b01028f9d1b1">
<div class="cell" data-hash="chapter_10_cache/html/unnamed-chunk-25_c333d66e193fd29e5b1d0e796e742cbd">
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>Baker <span class="ot">&lt;-</span> <span class="fu">pairwise</span>(<span class="at">treat =</span> treatment,</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a> <span class="at">event =</span> exac,</span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a> <span class="at">n =</span> total,</span>
Expand All @@ -1030,7 +1030,7 @@ <h3 data-number="6.3.2" class="anchored" data-anchor-id="pharmacologic-treatment
<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> Baker2009)</span>
<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a>NMA.COPD <span class="ot">&lt;-</span> <span class="fu">netmeta</span>(<span class="at">TE =</span> TE, <span class="at">seTE =</span> seTE, <span class="at">treat1 =</span> treat1, <span class="at">treat2 =</span> treat2,</span>
<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a> <span class="at">studlab =</span> studlab, <span class="at">data =</span> Baker, <span class="at">sm=</span><span class="st">"OR"</span>, <span class="at">ref =</span> <span class="st">"Placebo"</span>,</span>
<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a> <span class="at">studlab =</span> studlab, <span class="at">data =</span> Baker, <span class="at">sm =</span> <span class="st">"OR"</span>, <span class="at">ref =</span> <span class="st">"Placebo"</span>,</span>
<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a> <span class="at">comb.random =</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 cell-output-stderr">
<pre><code>Warning: Comparisons with missing TE / seTE or zero seTE not considered in
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