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<h2 id="toc-title">Table of contents</h2>
<ul>
<li><a href="#introduction" id="toc-introduction" class="nav-link active" data-scroll-target="#introduction">Introduction</a></li>
<li><a href="#data-heart-failure-clinical-records" id="toc-data-heart-failure-clinical-records" class="nav-link" data-scroll-target="#data-heart-failure-clinical-records">Data: <em>Heart failure clinical records</em></a></li>
<li><a href="#creating-synthetic-data" id="toc-creating-synthetic-data" class="nav-link" data-scroll-target="#creating-synthetic-data">Creating synthetic data</a></li>
<li><a href="#synthetic-data-utility" id="toc-synthetic-data-utility" class="nav-link" data-scroll-target="#synthetic-data-utility">Synthetic data utility</a>
<ul class="collapse">
<li><a href="#univariate-data-utility" id="toc-univariate-data-utility" class="nav-link" data-scroll-target="#univariate-data-utility">Univariate data utility</a></li>
<li><a href="#multivariate-data-utility" id="toc-multivariate-data-utility" class="nav-link" data-scroll-target="#multivariate-data-utility">Multivariate data utility</a>
<ul class="collapse">
<li><a href="#general-utility-measures" id="toc-general-utility-measures" class="nav-link" data-scroll-target="#general-utility-measures">General utility measures</a></li>
<li><a href="#specific-utility-measures" id="toc-specific-utility-measures" class="nav-link" data-scroll-target="#specific-utility-measures">Specific utility measures</a></li>
</ul></li>
</ul></li>
<li><a href="#statistical-disclosure-control" id="toc-statistical-disclosure-control" class="nav-link" data-scroll-target="#statistical-disclosure-control">Statistical disclosure control</a></li>
<li><a href="#inferences-from-synthetic-data" id="toc-inferences-from-synthetic-data" class="nav-link" data-scroll-target="#inferences-from-synthetic-data">Inferences from synthetic data</a></li>
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<main class="content" id="quarto-document-content">
<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title">Synthetic data in <code>R</code>: Generating synthetic data with high utility using <code>mice</code></h1>
</div>
<div class="quarto-title-meta">
<div>
<div class="quarto-title-meta-heading">Author</div>
<div class="quarto-title-meta-contents">
<p>Thom Volker & Gerko Vink </p>
</div>
</div>
</div>
</header>
<section id="introduction" class="level1">
<h1>Introduction</h1>
<p>In this workshop, you will learn how to create and evaluate synthetic data in <code>R</code>. In the practical, we will work with the <code>R</code> package <code>mice</code> <span class="citation" data-cites="mice">(<a href="#ref-mice" role="doc-biblioref">van Buuren and Groothuis-Oudshoorn 2011</a>)</span>. <code>mice</code> was originally developed to impute missing data, but, as you will experience, can also be used to impute synthetic data <span class="citation" data-cites="volker_vink_synthetic_mice_2021">(see <a href="#ref-volker_vink_synthetic_mice_2021" role="doc-biblioref">Volker and Vink 2021</a>)</span>. Other alternatives to create synthetic data are, for example, the R-package <code>synthpop</code> <span class="citation" data-cites="synthpop">(<a href="#ref-synthpop" role="doc-biblioref">Nowok, Raab, and Dibben 2016</a>)</span>, or the stand-alone software <code>IVEware</code> <span class="citation" data-cites="iveware">(<a href="#ref-iveware" role="doc-biblioref"><span>“<span>IVE</span>ware: Imputation and Variance Estimation Software,”</span> n.d.</a>)</span>.</p>
<p>In this workshop, you will (at least) use the packages <code>mice</code> <span class="citation" data-cites="mice">(<a href="#ref-mice" role="doc-biblioref">van Buuren and Groothuis-Oudshoorn 2011</a>)</span>, <code>ggmice</code> <span class="citation" data-cites="ggmice">(make sure to download the latest version from GitHub, <a href="#ref-ggmice" role="doc-biblioref">Oberman 2022</a>)</span>, <code>ggplot2</code> <span class="citation" data-cites="ggplot2">(<a href="#ref-ggplot2" role="doc-biblioref">Wickham 2016</a>)</span>, <code>patchwork</code> <span class="citation" data-cites="patchwork">(<a href="#ref-patchwork" role="doc-biblioref">Pedersen 2022</a>)</span>, <code>psych</code> <span class="citation" data-cites="psych">(<a href="#ref-psych" role="doc-biblioref">Revelle 2022</a>)</span>, <code>purrr</code> <span class="citation" data-cites="purrr">(<a href="#ref-purrr" role="doc-biblioref">Henry and Wickham 2022</a>)</span> and <code>synthpop</code> <span class="citation" data-cites="synthpop">(<a href="#ref-synthpop" role="doc-biblioref">Nowok, Raab, and Dibben 2016</a>)</span>. Make sure to load them (in case you haven’t installed them already, install them first, using <code>install.packages("package.name")</code>).</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>remotes<span class="sc">::</span><span class="fu">install_github</span>(<span class="st">"amices/mice"</span>)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>remotes<span class="sc">::</span><span class="fu">install_github</span>(<span class="st">"amices/ggmice"</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"ggplot2"</span>)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"patchwork"</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"psych"</span>)</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"purrr"</span>)</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"synthpop"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(mice) <span class="co"># to create the synthetic data</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggmice) <span class="co"># to make visualizations of the synthetic data</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2) <span class="co"># required when using ggmice</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(patchwork) <span class="co"># to stitch multiple figures together</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(psych) <span class="co"># to obtain descriptive statistics</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(purrr) <span class="co"># to work with multiply imputed synthetic datasets</span></span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(synthpop) <span class="co"># to assess the utility of our synthetic data</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Additionally, make sure to set a seed, so that your results can be compared with our results.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">1</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<hr>
</section>
<section id="data-heart-failure-clinical-records" class="level1">
<h1>Data: <em>Heart failure clinical records</em></h1>
<p>The <em>Heart failure clinical records</em> data set is a medical data set from the UCI Machine Learning Repository (<a href="archive.ics.uci.edu/ml/datasets/Heart+failure+clinical+records">click here for the source</a>), originally collected by <span class="citation" data-cites="tanvir_heart_failure_2017">Ahmad (<a href="#ref-tanvir_heart_failure_2017" role="doc-biblioref">2017</a>)</span> from the Government College University, Faisalabad, Pakistan, and adapted and uploaded to the UCI MLR by <span class="citation" data-cites="chicco_ml_2020">Chicco and Jurman (<a href="#ref-chicco_ml_2020" role="doc-biblioref">2020</a>)</span>. This data set contains medical information of 299 individuals on 13 variables, and is typically used to predict whether or not a patient will survive during the follow-up period, using several biomedical predictors.</p>
<p>If you have <code>R Studio</code> installed on your own machine, you can download the <em>cleaned</em> version of the <em>Heart failure clinical records</em> data set from my GitHub and load it as <code>heart_failure</code>, by running the following line of code.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>heart_failure <span class="ot"><-</span> <span class="fu">readRDS</span>(<span class="fu">url</span>(<span class="st">"https://thomvolker.github.io/UMCUSynthetic/data/heart_failure.RDS"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>The <em>Heart failure clinical records</em> data consists of the following variables:</p>
<ul>
<li><code>age</code>: Age in years</li>
<li><code>anaemia</code>: Whether the patient has a decrease of red blood cells (No/Yes)</li>
<li><code>hypertension</code>: Whether the patient has high blood pressure (No/Yes)</li>
<li><code>creatinine_phosphokinase</code>: Level of the creatinine phosphokinase enzyme in the blood (mcg/L)</li>
<li><code>diabetes</code>: Whether the patient has diabetes (No/Yes)</li>
<li><code>ejection_fraction</code>: Percentage of blood leaving the heart at each contraction</li>
<li><code>platelets</code>: Platelets in de blood (kiloplatelets/mL)</li>
<li><code>sex</code>: Sex (Female/Male)</li>
<li><code>serum_creatinine</code>: Level of serum creatinine in the blood (mg/dL)</li>
<li><code>serum_sodium</code>: Level of serum sodium in the blood (mg/dL)</li>
<li><code>smoking</code>: Whether the patient smokes (No/Yes)</li>
<li><code>follow_up</code>: Follow-up period (days)</li>
<li><code>deceased</code>: Whether the patient deceased during the follow-up period</li>
</ul>
<p>After loading the data, it is always wise to first inspect the data, so that you have an idea what to expect.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(heart_failure)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="cell-output-display">
<div style="border: 1px solid #ddd; padding: 5px; overflow-x: scroll; width:100%; "><table class="table table-striped table-hover" style="margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:right;"> age </th>
<th style="text-align:left;"> anaemia </th>
<th style="text-align:right;"> creatinine_phosphokinase </th>
<th style="text-align:left;"> diabetes </th>
<th style="text-align:right;"> ejection_fraction </th>
<th style="text-align:right;"> platelets </th>
<th style="text-align:right;"> serum_creatinine </th>
<th style="text-align:right;"> serum_sodium </th>
<th style="text-align:left;"> sex </th>
<th style="text-align:left;"> smoking </th>
<th style="text-align:left;"> hypertension </th>
<th style="text-align:left;"> deceased </th>
<th style="text-align:right;"> follow_up </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 75 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 582 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 265000 </td>
<td style="text-align:right;"> 1.9 </td>
<td style="text-align:right;"> 130 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 4 </td>
</tr>
<tr>
<td style="text-align:right;"> 55 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 7861 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 38 </td>
<td style="text-align:right;"> 263358 </td>
<td style="text-align:right;"> 1.1 </td>
<td style="text-align:right;"> 136 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 6 </td>
</tr>
<tr>
<td style="text-align:right;"> 65 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 146 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 162000 </td>
<td style="text-align:right;"> 1.3 </td>
<td style="text-align:right;"> 129 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 7 </td>
</tr>
<tr>
<td style="text-align:right;"> 50 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 111 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 210000 </td>
<td style="text-align:right;"> 1.9 </td>
<td style="text-align:right;"> 137 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 7 </td>
</tr>
<tr>
<td style="text-align:right;"> 65 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 160 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 327000 </td>
<td style="text-align:right;"> 2.7 </td>
<td style="text-align:right;"> 116 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 8 </td>
</tr>
<tr>
<td style="text-align:right;"> 90 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 47 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 40 </td>
<td style="text-align:right;"> 204000 </td>
<td style="text-align:right;"> 2.1 </td>
<td style="text-align:right;"> 132 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 8 </td>
</tr>
</tbody>
</table></div>
</div>
</div>
<p>Additionally, we can ask for a summary of all variables, or use <code>describe()</code> from the <code>psych</code>-package to provide descriptive statistics of all variables.</p>
<p><em>Note.</em> Make sure to install <code>psych</code> if you haven’t done so in the past.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(heart_failure)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> age anaemia creatinine_phosphokinase diabetes ejection_fraction
Min. :40.00 No :170 Min. : 23.0 No :174 Min. :14.00
1st Qu.:51.00 Yes:129 1st Qu.: 116.5 Yes:125 1st Qu.:30.00
Median :60.00 Median : 250.0 Median :38.00
Mean :60.83 Mean : 581.8 Mean :38.08
3rd Qu.:70.00 3rd Qu.: 582.0 3rd Qu.:45.00
Max. :95.00 Max. :7861.0 Max. :80.00
platelets serum_creatinine serum_sodium sex smoking
Min. : 25100 Min. :0.500 Min. :113.0 Female:105 No :203
1st Qu.:212500 1st Qu.:0.900 1st Qu.:134.0 Male :194 Yes: 96
Median :262000 Median :1.100 Median :137.0
Mean :263358 Mean :1.394 Mean :136.6
3rd Qu.:303500 3rd Qu.:1.400 3rd Qu.:140.0
Max. :850000 Max. :9.400 Max. :148.0
hypertension deceased follow_up
No :194 No :203 Min. : 4.0
Yes:105 Yes: 96 1st Qu.: 73.0
Median :115.0
Mean :130.3
3rd Qu.:203.0
Max. :285.0 </code></pre>
</div>
</div>
<p>This gives a good impression about the measurement levels of all variables, as well as the range of the possible values each variable can have.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">describe</span>(heart_failure)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="cell-output-display">
<div style="border: 1px solid #ddd; padding: 5px; overflow-x: scroll; width:100%; "><table class="table table-striped table-hover" style="margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:left;"> </th>
<th style="text-align:right;"> vars </th>
<th style="text-align:right;"> n </th>
<th style="text-align:right;"> mean </th>
<th style="text-align:right;"> sd </th>
<th style="text-align:right;"> median </th>
<th style="text-align:right;"> trimmed </th>
<th style="text-align:right;"> mad </th>
<th style="text-align:right;"> min </th>
<th style="text-align:right;"> max </th>
<th style="text-align:right;"> range </th>
<th style="text-align:right;"> skew </th>
<th style="text-align:right;"> kurtosis </th>
<th style="text-align:right;"> se </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;"> age </td>
<td style="text-align:right;"> 1 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 6.083389e+01 </td>
<td style="text-align:right;"> 1.189481e+01 </td>
<td style="text-align:right;"> 60.0 </td>
<td style="text-align:right;"> 6.021715e+01 </td>
<td style="text-align:right;"> 14.82600 </td>
<td style="text-align:right;"> 40.0 </td>
<td style="text-align:right;"> 95.0 </td>
<td style="text-align:right;"> 55.0 </td>
<td style="text-align:right;"> 0.4188266 </td>
<td style="text-align:right;"> -0.2204793 </td>
<td style="text-align:right;"> 0.6878946 </td>
</tr>
<tr>
<td style="text-align:left;"> anaemia* </td>
<td style="text-align:right;"> 2 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.431438e+00 </td>
<td style="text-align:right;"> 4.961073e-01 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 1.414938e+00 </td>
<td style="text-align:right;"> 0.00000 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 0.2754750 </td>
<td style="text-align:right;"> -1.9305367 </td>
<td style="text-align:right;"> 0.0286906 </td>
</tr>
<tr>
<td style="text-align:left;"> creatinine_phosphokinase </td>
<td style="text-align:right;"> 3 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 5.818395e+02 </td>
<td style="text-align:right;"> 9.702879e+02 </td>
<td style="text-align:right;"> 250.0 </td>
<td style="text-align:right;"> 3.654938e+02 </td>
<td style="text-align:right;"> 269.83320 </td>
<td style="text-align:right;"> 23.0 </td>
<td style="text-align:right;"> 7861.0 </td>
<td style="text-align:right;"> 7838.0 </td>
<td style="text-align:right;"> 4.4184296 </td>
<td style="text-align:right;"> 24.5254138 </td>
<td style="text-align:right;"> 56.1131970 </td>
</tr>
<tr>
<td style="text-align:left;"> diabetes* </td>
<td style="text-align:right;"> 4 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.418060e+00 </td>
<td style="text-align:right;"> 4.940671e-01 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 1.398340e+00 </td>
<td style="text-align:right;"> 0.00000 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 0.3305857 </td>
<td style="text-align:right;"> -1.8970241 </td>
<td style="text-align:right;"> 0.0285726 </td>
</tr>
<tr>
<td style="text-align:left;"> ejection_fraction </td>
<td style="text-align:right;"> 5 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 3.808361e+01 </td>
<td style="text-align:right;"> 1.183484e+01 </td>
<td style="text-align:right;"> 38.0 </td>
<td style="text-align:right;"> 3.742739e+01 </td>
<td style="text-align:right;"> 11.86080 </td>
<td style="text-align:right;"> 14.0 </td>
<td style="text-align:right;"> 80.0 </td>
<td style="text-align:right;"> 66.0 </td>
<td style="text-align:right;"> 0.5498228 </td>
<td style="text-align:right;"> 0.0005484 </td>
<td style="text-align:right;"> 0.6844265 </td>
</tr>
<tr>
<td style="text-align:left;"> platelets </td>
<td style="text-align:right;"> 6 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 2.633580e+05 </td>
<td style="text-align:right;"> 9.780424e+04 </td>
<td style="text-align:right;"> 262000.0 </td>
<td style="text-align:right;"> 2.567301e+05 </td>
<td style="text-align:right;"> 65234.40000 </td>
<td style="text-align:right;"> 25100.0 </td>
<td style="text-align:right;"> 850000.0 </td>
<td style="text-align:right;"> 824900.0 </td>
<td style="text-align:right;"> 1.4476814 </td>
<td style="text-align:right;"> 6.0252322 </td>
<td style="text-align:right;"> 5656.1650591 </td>
</tr>
<tr>
<td style="text-align:left;"> serum_creatinine </td>
<td style="text-align:right;"> 7 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.393880e+00 </td>
<td style="text-align:right;"> 1.034510e+00 </td>
<td style="text-align:right;"> 1.1 </td>
<td style="text-align:right;"> 1.189295e+00 </td>
<td style="text-align:right;"> 0.29652 </td>
<td style="text-align:right;"> 0.5 </td>
<td style="text-align:right;"> 9.4 </td>
<td style="text-align:right;"> 8.9 </td>
<td style="text-align:right;"> 4.4113866 </td>
<td style="text-align:right;"> 25.1888415 </td>
<td style="text-align:right;"> 0.0598273 </td>
</tr>
<tr>
<td style="text-align:left;"> serum_sodium </td>
<td style="text-align:right;"> 8 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.366254e+02 </td>
<td style="text-align:right;"> 4.412477e+00 </td>
<td style="text-align:right;"> 137.0 </td>
<td style="text-align:right;"> 1.368216e+02 </td>
<td style="text-align:right;"> 4.44780 </td>
<td style="text-align:right;"> 113.0 </td>
<td style="text-align:right;"> 148.0 </td>
<td style="text-align:right;"> 35.0 </td>
<td style="text-align:right;"> -1.0376430 </td>
<td style="text-align:right;"> 3.9841899 </td>
<td style="text-align:right;"> 0.2551802 </td>
</tr>
<tr>
<td style="text-align:left;"> sex* </td>
<td style="text-align:right;"> 9 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.648829e+00 </td>
<td style="text-align:right;"> 4.781364e-01 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.684647e+00 </td>
<td style="text-align:right;"> 0.00000 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> -0.6204576 </td>
<td style="text-align:right;"> -1.6204183 </td>
<td style="text-align:right;"> 0.0276513 </td>
</tr>
<tr>
<td style="text-align:left;"> smoking* </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.321070e+00 </td>
<td style="text-align:right;"> 4.676704e-01 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 1.278008e+00 </td>
<td style="text-align:right;"> 0.00000 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 0.7626368 </td>
<td style="text-align:right;"> -1.4231112 </td>
<td style="text-align:right;"> 0.0270461 </td>
</tr>
<tr>
<td style="text-align:left;"> hypertension* </td>
<td style="text-align:right;"> 11 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.351171e+00 </td>
<td style="text-align:right;"> 4.781364e-01 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 1.315353e+00 </td>
<td style="text-align:right;"> 0.00000 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 0.6204576 </td>
<td style="text-align:right;"> -1.6204183 </td>
<td style="text-align:right;"> 0.0276513 </td>
</tr>
<tr>
<td style="text-align:left;"> deceased* </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.321070e+00 </td>
<td style="text-align:right;"> 4.676704e-01 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 1.278008e+00 </td>
<td style="text-align:right;"> 0.00000 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 2.0 </td>
<td style="text-align:right;"> 1.0 </td>
<td style="text-align:right;"> 0.7626368 </td>
<td style="text-align:right;"> -1.4231112 </td>
<td style="text-align:right;"> 0.0270461 </td>
</tr>
<tr>
<td style="text-align:left;"> follow_up </td>
<td style="text-align:right;"> 13 </td>
<td style="text-align:right;"> 299 </td>
<td style="text-align:right;"> 1.302609e+02 </td>
<td style="text-align:right;"> 7.761421e+01 </td>
<td style="text-align:right;"> 115.0 </td>
<td style="text-align:right;"> 1.292780e+02 </td>
<td style="text-align:right;"> 105.26460 </td>
<td style="text-align:right;"> 4.0 </td>
<td style="text-align:right;"> 285.0 </td>
<td style="text-align:right;"> 281.0 </td>
<td style="text-align:right;"> 0.1265232 </td>
<td style="text-align:right;"> -1.2238150 </td>
<td style="text-align:right;"> 4.4885455 </td>
</tr>
</tbody>
</table></div>
</div>
</div>
<p>The <code>describe()</code> function gives more distributional information about all variables.</p>
<hr>
</section>
<section id="creating-synthetic-data" class="level1">
<h1>Creating synthetic data</h1>
<p>Broadly speaking, two methods for creating synthetic data can be distinguished. The first one is based on parametric imputation models, which assumes that the structure of the data is fixed, and draws synthetic values from a pre-specified probability distribution. That is, after estimating a statistical model, the synthetic data are generated from a probability distribution, without making any further use of the observed data. In general, this procedure is less likely to result in an accidental release of disclosive information. However, these parametric methods are often less capable of capturing the complex nature of real-world data sets.</p>
<p>The subtleties of real-world data are often better reproduced with non-parametric imputation models. Using this approach, a non-parametric model is estimated, resulting in a donor pool out of which a single observation per observation and per variable is drawn. These models thus reuse the observed data to serve as synthetic data. Accordingly, much of the values that were in the observed data end up in the synthetic data. However, these observed data are generally combined in unique ways, it is generally not possible to link this information to the original respondents. The non-parametric procedures often yield better inferences, while still being able to prevent disclosure risk (although more research into measures to qualify the remaining risks is required). Therefore, this practical will showcase how to generate synthetic data using one such non-parametric method: classification and regression trees [CART; <span class="citation" data-cites="breiman_cart_1984">Breiman et al. (<a href="#ref-breiman_cart_1984" role="doc-biblioref">1984</a>)</span>].</p>
<hr>
<p>Now you have a feeling of what the data looks like, we will use these two different ways to create synthetic data: a fully parametric approach, in which the data are synthesized using either linear or logistic regression, and a fully non-parametric approach, in which we synthesize all data using CART.</p>
<p>In general, <code>mice</code> proceeds as follows: from first to the last column in your data set, the given variable is synthesized based on all other variables in the data. Specifically, a model is trained on the observed data, and new values for variable <span class="math inline">\(X_j\)</span> are imputed on the basis of all other variables <span class="math inline">\(X_{-j}\)</span>. This procedure is repeated sequentially, until all variables are synthesized. In this way, the relationships between the variables are generally preserved.</p>
<p>However, before we can use <code>mice</code> to generate synthetic data, we have to take care of some issues, because <code>mice</code> was not initially developed to create synthetic data. Specifically, we have to do two things: specify which values we want to overimpute and specify which method we want to use for the imputations.</p>
<hr>
<p><strong>1. Create a matrix of the same dimensions as the original data called <code>where</code>, specifying all cells as the logical operator <code>TRUE</code>.</strong></p>
<p><em>Hint:</em> You can use the <code>mice</code> function <code>make.where()</code>.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>where <span class="ot"><-</span> <span class="fu">make.where</span>(heart_failure, <span class="st">"all"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<hr>
<p><strong>2. Create a vector of length 13 called <code>method</code>, indicating which (parametric) method to use to synthesize each variable.</strong></p>
<p><em>Hint:</em> You can use <code>make.method()</code> to create an initial vector with imputation methods, and replace each cell with <code>"pmm"</code> with <code>"norm"</code>.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>method <span class="ot"><-</span> <span class="fu">make.method</span>(heart_failure, <span class="at">where =</span> where)</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>method[method <span class="sc">==</span> <span class="st">"pmm"</span>] <span class="ot"><-</span> <span class="st">"norm"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<hr>
<p>Now we have specified which values ought to be synthetic, and which method to use to create the synthetic values, we can actually create the synthetic data.</p>
<hr>
<p><strong>3. Use <code>mice()</code> to create <code>m = 10</code> synthetic data sets in an object called <code>syn_param</code>, using the previously specified <code>method</code> vector and <code>where</code>-matrix.</strong></p>
<p><em>Hint:</em> When creating synthetic data, a single iteration is sufficient when there is no missing data, so we can set <code>maxit = 1</code>.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>syn_param <span class="ot"><-</span> <span class="fu">mice</span>(heart_failure, </span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a> <span class="at">m =</span> <span class="dv">10</span>, </span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a> <span class="at">maxit =</span> <span class="dv">1</span>,</span>
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a> <span class="at">method =</span> method,</span>
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a> <span class="at">where =</span> where,</span>
<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a> <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>
<hr>
<p>Creating the synthetic data is a piece of cake. However, after creating the synthetic data, we must assess its quality in terms of data utility and disclosure risk. Quality control is conveniently performed using visual methods, and can be done using the package <code>ggmice</code> <span class="citation" data-cites="ggmice">(<a href="#ref-ggmice" role="doc-biblioref">Oberman 2022</a>)</span>.</p>
<hr>
</section>
<section id="synthetic-data-utility" class="level1">
<h1>Synthetic data utility</h1>
<p>The quality of synthetic data sets can be assessed on multiple levels and in multiple different ways. Starting on a univariate level, the distributions of the synthetic data sets can be compared with the distribution of the observed data. For the continuous variables, this can be done by comparing the densities of the synthetic data sets with the observed data sets. Later on, we also look at the utility of the synthetic data on a multivariate level.</p>
<hr>
<section id="univariate-data-utility" class="level2">
<h2 class="anchored" data-anchor-id="univariate-data-utility">Univariate data utility</h2>
<p><strong>4. To get an idea of whether creating the synthetic data went accordingly, compare the 10 rows of the fourth synthetic data set with the first 10 rows of the original data.</strong></p>
<p><em>Hint:</em> You can use <code>complete(syn_param, 4)</code> to extract the fourth synthetic data set from the <code>syn_param</code> object.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">complete</span>(syn_param, <span class="dv">4</span>) <span class="sc">|></span> </span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">head</span>(<span class="dv">10</span>)</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>heart_failure <span class="sc">|></span> </span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">head</span>(<span class="dv">10</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="cell-output-display">
<div style="border: 1px solid #ddd; padding: 5px; overflow-x: scroll; width:100%; "><table class="table table-striped table-hover" style="margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:right;"> age </th>
<th style="text-align:left;"> anaemia </th>
<th style="text-align:right;"> creatinine_phosphokinase </th>
<th style="text-align:left;"> diabetes </th>
<th style="text-align:right;"> ejection_fraction </th>
<th style="text-align:right;"> platelets </th>
<th style="text-align:right;"> serum_creatinine </th>
<th style="text-align:right;"> serum_sodium </th>
<th style="text-align:left;"> sex </th>
<th style="text-align:left;"> smoking </th>
<th style="text-align:left;"> hypertension </th>
<th style="text-align:left;"> deceased </th>
<th style="text-align:right;"> follow_up </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 75.11100 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 2060.89571 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 46.38556 </td>
<td style="text-align:right;"> 187131.3 </td>
<td style="text-align:right;"> 2.5139107 </td>
<td style="text-align:right;"> 130.2098 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 31.41877 </td>
</tr>
<tr>
<td style="text-align:right;"> 58.99690 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> -32.50274 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 51.22575 </td>
<td style="text-align:right;"> 305181.1 </td>
<td style="text-align:right;"> 2.1044455 </td>
<td style="text-align:right;"> 143.7124 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 170.42709 </td>
</tr>
<tr>
<td style="text-align:right;"> 80.99417 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 318.24894 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 17.98667 </td>
<td style="text-align:right;"> 211219.0 </td>
<td style="text-align:right;"> 1.1220858 </td>
<td style="text-align:right;"> 139.9554 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> -59.47753 </td>
</tr>
<tr>
<td style="text-align:right;"> 51.43676 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 86.26985 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 50.91203 </td>
<td style="text-align:right;"> 146552.4 </td>
<td style="text-align:right;"> 2.0270056 </td>
<td style="text-align:right;"> 136.2363 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 125.68678 </td>
</tr>
<tr>
<td style="text-align:right;"> 70.93176 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> -111.81437 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 32.73975 </td>
<td style="text-align:right;"> 190398.2 </td>
<td style="text-align:right;"> 2.9693363 </td>
<td style="text-align:right;"> 143.2878 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 52.52242 </td>
</tr>
<tr>
<td style="text-align:right;"> 79.29488 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> -1567.74208 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 40.78996 </td>
<td style="text-align:right;"> 321876.9 </td>
<td style="text-align:right;"> 1.7963209 </td>
<td style="text-align:right;"> 132.4501 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 24.25108 </td>
</tr>
<tr>
<td style="text-align:right;"> 73.92658 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 2270.81420 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 40.16377 </td>
<td style="text-align:right;"> 154892.2 </td>
<td style="text-align:right;"> 2.7336876 </td>
<td style="text-align:right;"> 130.2880 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 51.66466 </td>
</tr>
<tr>
<td style="text-align:right;"> 68.99649 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> -732.59574 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 57.68586 </td>
<td style="text-align:right;"> 236312.4 </td>
<td style="text-align:right;"> 3.4349341 </td>
<td style="text-align:right;"> 135.9754 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> -39.48097 </td>
</tr>
<tr>
<td style="text-align:right;"> 52.72441 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 984.08018 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 46.42904 </td>
<td style="text-align:right;"> 269673.5 </td>
<td style="text-align:right;"> 1.9509181 </td>
<td style="text-align:right;"> 136.2238 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 86.93647 </td>
</tr>
<tr>
<td style="text-align:right;"> 77.71020 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 200.34505 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 31.18680 </td>
<td style="text-align:right;"> 119468.1 </td>
<td style="text-align:right;"> 0.5534818 </td>
<td style="text-align:right;"> 133.4264 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 43.17234 </td>
</tr>
</tbody>
</table></div>
</div>
<div class="cell-output-display">
<div style="border: 1px solid #ddd; padding: 5px; overflow-x: scroll; width:100%; "><table class="table table-striped table-hover" style="margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:right;"> age </th>
<th style="text-align:left;"> anaemia </th>
<th style="text-align:right;"> creatinine_phosphokinase </th>
<th style="text-align:left;"> diabetes </th>
<th style="text-align:right;"> ejection_fraction </th>
<th style="text-align:right;"> platelets </th>
<th style="text-align:right;"> serum_creatinine </th>
<th style="text-align:right;"> serum_sodium </th>
<th style="text-align:left;"> sex </th>
<th style="text-align:left;"> smoking </th>
<th style="text-align:left;"> hypertension </th>
<th style="text-align:left;"> deceased </th>
<th style="text-align:right;"> follow_up </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 75 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 582 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 265000 </td>
<td style="text-align:right;"> 1.9 </td>
<td style="text-align:right;"> 130 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 4 </td>
</tr>
<tr>
<td style="text-align:right;"> 55 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 7861 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 38 </td>
<td style="text-align:right;"> 263358 </td>
<td style="text-align:right;"> 1.1 </td>
<td style="text-align:right;"> 136 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 6 </td>
</tr>
<tr>
<td style="text-align:right;"> 65 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 146 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 162000 </td>
<td style="text-align:right;"> 1.3 </td>
<td style="text-align:right;"> 129 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 7 </td>
</tr>
<tr>
<td style="text-align:right;"> 50 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 111 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 210000 </td>
<td style="text-align:right;"> 1.9 </td>
<td style="text-align:right;"> 137 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 7 </td>
</tr>
<tr>
<td style="text-align:right;"> 65 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 160 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 20 </td>
<td style="text-align:right;"> 327000 </td>
<td style="text-align:right;"> 2.7 </td>
<td style="text-align:right;"> 116 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 8 </td>
</tr>
<tr>
<td style="text-align:right;"> 90 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 47 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 40 </td>
<td style="text-align:right;"> 204000 </td>
<td style="text-align:right;"> 2.1 </td>
<td style="text-align:right;"> 132 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 8 </td>
</tr>
<tr>
<td style="text-align:right;"> 75 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 246 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 15 </td>
<td style="text-align:right;"> 127000 </td>
<td style="text-align:right;"> 1.2 </td>
<td style="text-align:right;"> 137 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 10 </td>
</tr>
<tr>
<td style="text-align:right;"> 60 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 315 </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 60 </td>
<td style="text-align:right;"> 454000 </td>
<td style="text-align:right;"> 1.1 </td>
<td style="text-align:right;"> 131 </td>
<td style="text-align:left;"> Male </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 10 </td>
</tr>
<tr>
<td style="text-align:right;"> 65 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 157 </td>
<td style="text-align:left;"> No </td>
<td style="text-align:right;"> 65 </td>
<td style="text-align:right;"> 263358 </td>
<td style="text-align:right;"> 1.5 </td>
<td style="text-align:right;"> 138 </td>
<td style="text-align:left;"> Female </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> No </td>
<td style="text-align:left;"> Yes </td>
<td style="text-align:right;"> 10 </td>
</tr>
<tr>
<td style="text-align:right;"> 80 </td>
<td style="text-align:left;"> Yes </td>