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<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><span class="fu">library</span>(tidyverse)</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>── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
✔ forcats 1.0.0 ✔ stringr 1.5.1
✔ lubridate 1.9.4 ✔ tibble 3.3.0
✔ purrr 1.1.0 ✔ tidyr 1.3.1
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (&lt;http://conflicted.r-lib.org/&gt;) to force all conflicts to become errors</code></pre>
</div>
<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">library</span>(survival)</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="co"># library(gtsummary)</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="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>dat <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="st">"./unos.txt"</span>, <span class="at">sep =</span> <span class="st">"</span><span class="sc">\t</span><span class="st">"</span>)</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(dat)</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> hlamat age age.1 cold_isc death year sex txtype fu
1 2 25 15 6 0 2002 0 1 0
2 1 42 10 11 1 1999 0 1 0
3 1 9 14 8 0 2002 1 1 0
4 0 35 12 26 0 2002 1 1 0
5 2 17 12 28 1 1997 1 1 0
6 3 44 13 1 0 2002 1 0 0</code></pre>
</div>
</div>
<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">names</span>(dat) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"hla.match"</span>, <span class="st">"age.donor"</span>, <span class="st">"age.rec"</span>, <span class="st">"cold.isc"</span>, <span class="st">"death"</span>,</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> <span class="st">"year"</span>, <span class="st">"sex"</span>, <span class="st">"tx.type"</span>, <span class="st">"follow.up"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<section id="exercise" class="level1" data-number="1">
<h1 data-number="1"><span class="header-section-number">1</span> Exercise</h1>
<section id="exercise-1" class="level2" data-number="1.1">
<h2 data-number="1.1" class="anchored" data-anchor-id="exercise-1"><span class="header-section-number">1.1</span> Exercise 1</h2>
<blockquote class="blockquote">
<p>Illustrate in a table the characteristics of the population (age, sex, race, donor, . . . ).</p>
</blockquote>
<div class="cell">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>g <span class="ot">&lt;-</span> <span class="fu">ggplot</span>(dat)</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="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>g <span class="sc">+</span> <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> follow.up, <span class="at">y =</span> death))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-5-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
<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>g <span class="sc">+</span> <span class="fu">geom_density</span>(<span class="fu">aes</span>(<span class="at">x =</span> follow.up))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-5-2.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
<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>g <span class="sc">+</span> <span class="fu">geom_density</span>(<span class="fu">aes</span>(<span class="at">x =</span> age.donor))</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: Removed 113 rows containing non-finite outside the scale range
(`stat_density()`).</code></pre>
</div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-5-3.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
<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>g <span class="sc">+</span> <span class="fu">geom_bar</span>(<span class="fu">aes</span>(<span class="at">x =</span> age.rec))</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: Removed 9 rows containing non-finite outside the scale range
(`stat_count()`).</code></pre>
</div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-5-4.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>g <span class="sc">+</span> <span class="fu">geom_boxplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> age.rec, <span class="at">y =</span> age.donor, <span class="at">group =</span> age.donor))</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: Removed 113 rows containing missing values or values outside the scale range
(`stat_boxplot()`).</code></pre>
</div>
<div class="cell-output cell-output-stderr">
<pre><code>Warning: Removed 7 rows containing non-finite outside the scale range
(`stat_boxplot()`).</code></pre>
</div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-5-5.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="co"># dat$age.1 |&gt; table()</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="exercise-2" class="level2" data-number="1.2">
<h2 data-number="1.2" class="anchored" data-anchor-id="exercise-2"><span class="header-section-number">1.2</span> Exercise 2</h2>
<p>Plot the Kaplan-Meier overall survival curve for pediatric kid- ney transplant recipients for the first 12 years after transplantation.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>km <span class="ot">&lt;-</span> <span class="fu">survfit</span>(<span class="fu">Surv</span>(follow.up, death) <span class="sc">~</span> <span class="dv">1</span>, <span class="at">data =</span> dat[dat<span class="sc">$</span>follow.up <span class="sc">&lt;=</span> <span class="dv">12</span>, ])</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(km)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-6-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
</section>
<section id="exercise-3" class="level2" data-number="1.3">
<h2 data-number="1.3" class="anchored" data-anchor-id="exercise-3"><span class="header-section-number">1.3</span> Exercise 3</h2>
<p>We are going to compare mortality rates (hazard functions) between children whose transplanted kidney was provided by a living donor (in general a family member) and those whose source was recently deceased (variable donor type: <code>txtype</code>). Use the life table method to calculate the death rates for the first 5 years for each group (take in the first year intervals of 4 months and then look at each year) and show the results in a table. Estimate the hazard ratio in each time interval as the ratio between the mortality rates in the two groups. What do you notice?</p>
<div class="cell">
<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>dat<span class="fl">.5</span> <span class="ot">&lt;-</span> dat[dat<span class="sc">$</span>follow.up <span class="sc">&lt;=</span> <span class="dv">5</span>, ]</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(dat<span class="fl">.5</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-stdout">
<pre><code> hla.match age.donor age.rec cold.isc death year sex tx.type follow.up
1 2 25 15 6 0 2002 0 1 0
2 1 42 10 11 1 1999 0 1 0
3 1 9 14 8 0 2002 1 1 0
4 0 35 12 26 0 2002 1 1 0
5 2 17 12 28 1 1997 1 1 0
6 3 44 13 1 0 2002 1 0 0</code></pre>
</div>
<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a>classify_time_interval <span class="ot">=</span> <span class="cf">function</span>(fu) {</span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> (fu <span class="sc">&lt;=</span> <span class="dv">1</span><span class="sc">/</span><span class="dv">3</span>) {</span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(<span class="dv">1</span><span class="sc">/</span><span class="dv">3</span>)</span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a> } <span class="cf">else</span> <span class="cf">if</span> (fu <span class="sc">&lt;=</span> <span class="dv">2</span><span class="sc">/</span><span class="dv">3</span>) {</span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(<span class="dv">2</span><span class="sc">/</span><span class="dv">3</span>)</span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a> } <span class="cf">else</span> <span class="cf">if</span> (fu <span class="sc">&lt;=</span> <span class="dv">1</span>) {</span>
<span id="cb21-7"><a href="#cb21-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(<span class="dv">1</span>)</span>
<span id="cb21-8"><a href="#cb21-8" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb21-9"><a href="#cb21-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">ceiling</span>(fu)</span>
<span id="cb21-10"><a href="#cb21-10" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb21-11"><a href="#cb21-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb21-12"><a href="#cb21-12" aria-hidden="true" tabindex="-1"></a>dat<span class="fl">.5</span><span class="sc">$</span>fu.interval <span class="ot">&lt;-</span> <span class="fu">sapply</span>(dat<span class="fl">.5</span><span class="sc">$</span>follow.up, classify_time_interval)</span>
<span id="cb21-13"><a href="#cb21-13" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(dat<span class="fl">.5</span><span class="sc">$</span>fu.interval)</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>
0.333333333333333 0.666666666666667 1 2
982 528 640 1226
3 4 5
1184 1093 950 </code></pre>
</div>
<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(dat<span class="fl">.5</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-stdout">
<pre><code> hla.match age.donor age.rec cold.isc death year sex tx.type follow.up
1 2 25 15 6 0 2002 0 1 0
2 1 42 10 11 1 1999 0 1 0
3 1 9 14 8 0 2002 1 1 0
4 0 35 12 26 0 2002 1 1 0
5 2 17 12 28 1 1997 1 1 0
6 3 44 13 1 0 2002 1 0 0
fu.interval
1 0.3333333
2 0.3333333
3 0.3333333
4 0.3333333
5 0.3333333
6 0.3333333</code></pre>
</div>
</div>
<div class="cell">
<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>dat.<span class="fl">5.</span>life <span class="ot">&lt;-</span> dat<span class="fl">.5</span> <span class="sc">|&gt;</span></span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(fu.interval) <span class="sc">|&gt;</span></span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">summarize</span>(</span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a> <span class="at">n.censored =</span> <span class="fu">sum</span>(death <span class="sc">==</span> <span class="dv">0</span>),</span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="at">n.event =</span> <span class="fu">sum</span>(death),</span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a> <span class="at">n.at.risk =</span> <span class="fu">nrow</span>(dat),</span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">2</span><span class="sc">:</span><span class="fu">nrow</span>(dat.<span class="fl">5.</span>life)) {</span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a> j <span class="ot">&lt;-</span> i <span class="sc">-</span> <span class="dv">1</span></span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a> n.censored.pre <span class="ot">&lt;-</span> dat.<span class="fl">5.</span>life<span class="sc">$</span>n.censored[j]</span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a> n.event.pre <span class="ot">&lt;-</span> dat.<span class="fl">5.</span>life<span class="sc">$</span>n.event[j]</span>
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a> n.at.risk.pre <span class="ot">&lt;-</span> dat.<span class="fl">5.</span>life<span class="sc">$</span>n.at.risk[j]</span>
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-16"><a href="#cb25-16" aria-hidden="true" tabindex="-1"></a> n.at.risk <span class="ot">&lt;-</span> n.at.risk.pre <span class="sc">-</span> n.event.pre <span class="sc">-</span> n.censored.pre</span>
<span id="cb25-17"><a href="#cb25-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-18"><a href="#cb25-18" aria-hidden="true" tabindex="-1"></a> dat.<span class="fl">5.</span>life<span class="sc">$</span>n.at.risk[i] <span class="ot">&lt;-</span> n.at.risk</span>
<span id="cb25-19"><a href="#cb25-19" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb25-20"><a href="#cb25-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-21"><a href="#cb25-21" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(<span class="fu">nrow</span>(dat))</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>[1] 9775</code></pre>
</div>
<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>dat.<span class="fl">5.</span>life</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># A tibble: 7 × 4
fu.interval n.censored n.event n.at.risk
&lt;dbl&gt; &lt;int&gt; &lt;int&gt; &lt;int&gt;
1 0.333 830 152 9775
2 0.667 491 37 8793
3 1 613 27 8265
4 2 1164 62 7625
5 3 1143 41 6399
6 4 1053 40 5215
7 5 919 31 4122</code></pre>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>dat.<span class="fl">5.</span>life <span class="ot">&lt;-</span> dat.<span class="fl">5.</span>life <span class="sc">|&gt;</span></span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a> <span class="at">hazard.rate =</span> n.event <span class="sc">/</span> n.at.risk</span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a> )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<hr>
<div class="cell">
<div class="sourceCode cell-code" id="cb30"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>get_life_table <span class="ot">=</span> <span class="cf">function</span>(dat) {</span>
<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a> dat <span class="ot">&lt;-</span> dat <span class="sc">|&gt;</span></span>
<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(fu.interval) <span class="sc">|&gt;</span></span>
<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">summarize</span>(</span>
<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a> <span class="at">n.censored =</span> <span class="fu">sum</span>(death <span class="sc">==</span> <span class="dv">0</span>),</span>
<span id="cb30-6"><a href="#cb30-6" aria-hidden="true" tabindex="-1"></a> <span class="at">n.event =</span> <span class="fu">sum</span>(death),</span>
<span id="cb30-7"><a href="#cb30-7" aria-hidden="true" tabindex="-1"></a> <span class="at">n.at.risk =</span> <span class="fu">nrow</span>(dat),</span>
<span id="cb30-8"><a href="#cb30-8" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb30-9"><a href="#cb30-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-10"><a href="#cb30-10" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">2</span><span class="sc">:</span><span class="fu">nrow</span>(dat)) {</span>
<span id="cb30-11"><a href="#cb30-11" aria-hidden="true" tabindex="-1"></a> j <span class="ot">&lt;-</span> i <span class="sc">-</span> <span class="dv">1</span></span>
<span id="cb30-12"><a href="#cb30-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-13"><a href="#cb30-13" aria-hidden="true" tabindex="-1"></a> n.censored.pre <span class="ot">&lt;-</span> dat<span class="sc">$</span>n.censored[j]</span>
<span id="cb30-14"><a href="#cb30-14" aria-hidden="true" tabindex="-1"></a> n.event.pre <span class="ot">&lt;-</span> dat<span class="sc">$</span>n.event[j]</span>
<span id="cb30-15"><a href="#cb30-15" aria-hidden="true" tabindex="-1"></a> n.at.risk.pre <span class="ot">&lt;-</span> dat<span class="sc">$</span>n.at.risk[j]</span>
<span id="cb30-16"><a href="#cb30-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-17"><a href="#cb30-17" aria-hidden="true" tabindex="-1"></a> n.at.risk <span class="ot">&lt;-</span> n.at.risk.pre <span class="sc">-</span> n.event.pre <span class="sc">-</span> n.censored.pre</span>
<span id="cb30-18"><a href="#cb30-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-19"><a href="#cb30-19" aria-hidden="true" tabindex="-1"></a> dat<span class="sc">$</span>n.at.risk[i] <span class="ot">&lt;-</span> n.at.risk</span>
<span id="cb30-20"><a href="#cb30-20" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb30-21"><a href="#cb30-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-22"><a href="#cb30-22" aria-hidden="true" tabindex="-1"></a> dat <span class="ot">&lt;-</span> dat <span class="sc">|&gt;</span></span>
<span id="cb30-23"><a href="#cb30-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span>
<span id="cb30-24"><a href="#cb30-24" aria-hidden="true" tabindex="-1"></a> <span class="at">hazard.rate =</span> n.event <span class="sc">/</span> n.at.risk</span>
<span id="cb30-25"><a href="#cb30-25" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb30-26"><a href="#cb30-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb30-27"><a href="#cb30-27" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(dat)</span>
<span id="cb30-28"><a href="#cb30-28" aria-hidden="true" tabindex="-1"></a>}</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="cb31"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a>dat.<span class="fl">5.</span>tx0 <span class="ot">=</span> dat<span class="fl">.5</span>[dat<span class="fl">.5</span><span class="sc">$</span>tx.type <span class="sc">==</span> <span class="dv">0</span>, ]</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>dat.<span class="fl">5.</span>tx1 <span class="ot">=</span> dat<span class="fl">.5</span>[dat<span class="fl">.5</span><span class="sc">$</span>tx.type <span class="sc">==</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>
<div class="cell">
<div class="sourceCode cell-code" id="cb32"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>tx0.life <span class="ot">&lt;-</span> <span class="fu">get_life_table</span>(dat.<span class="fl">5.</span>tx0)</span>
<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a>tx0.life</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># A tibble: 7 × 5
fu.interval n.censored n.event n.at.risk hazard.rate
&lt;dbl&gt; &lt;int&gt; &lt;int&gt; &lt;int&gt; &lt;dbl&gt;
1 0.333 463 49 3378 0.0145
2 0.667 253 13 2866 0.00454
3 1 340 11 2600 0.00423
4 2 591 24 2249 0.0107
5 3 568 17 1634 0.0104
6 4 521 16 1049 0.0153
7 5 501 11 512 0.0215 </code></pre>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb34"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a>tx1.life <span class="ot">&lt;-</span> <span class="fu">get_life_table</span>(dat.<span class="fl">5.</span>tx1)</span>
<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a>tx1.life</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># A tibble: 7 × 5
fu.interval n.censored n.event n.at.risk hazard.rate
&lt;dbl&gt; &lt;int&gt; &lt;int&gt; &lt;int&gt; &lt;dbl&gt;
1 0.333 367 103 3225 0.0319
2 0.667 238 24 2755 0.00871
3 1 273 16 2493 0.00642
4 2 573 38 2204 0.0172
5 3 575 24 1593 0.0151
6 4 532 24 994 0.0241
7 5 418 20 438 0.0457 </code></pre>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb36"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a>tx1.life<span class="sc">$</span>hazard.rate <span class="sc">/</span> tx0.life<span class="sc">$</span>hazard.rate</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>[1] 2.201766 1.920536 1.516975 1.615661 1.448100 1.582998 2.125363</code></pre>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb38"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a>hazard.df <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(</span>
<span id="cb38-2"><a href="#cb38-2" aria-hidden="true" tabindex="-1"></a> <span class="at">fu.interval =</span> tx1.life<span class="sc">$</span>fu.interval,</span>
<span id="cb38-3"><a href="#cb38-3" aria-hidden="true" tabindex="-1"></a> <span class="at">hazard.rate.0 =</span> tx0.life<span class="sc">$</span>hazard.rate,</span>
<span id="cb38-4"><a href="#cb38-4" aria-hidden="true" tabindex="-1"></a> <span class="at">hazard.rate.1 =</span> tx1.life<span class="sc">$</span>hazard.rate,</span>
<span id="cb38-5"><a href="#cb38-5" aria-hidden="true" tabindex="-1"></a> <span class="at">hazard.ratio =</span> tx1.life<span class="sc">$</span>hazard.rate <span class="sc">/</span> tx0.life<span class="sc">$</span>hazard.rate</span>
<span id="cb38-6"><a href="#cb38-6" aria-hidden="true" tabindex="-1"></a>) </span>
<span id="cb38-7"><a href="#cb38-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb38-8"><a href="#cb38-8" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(hazard.df, <span class="fu">aes</span>(<span class="at">x =</span> fu.interval)) <span class="sc">+</span></span>
<span id="cb38-9"><a href="#cb38-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>(<span class="fu">aes</span>(<span class="at">y =</span> hazard.rate<span class="fl">.0</span>), <span class="at">color =</span> <span class="st">"blue"</span>) <span class="sc">+</span> </span>
<span id="cb38-10"><a href="#cb38-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>(<span class="fu">aes</span>(<span class="at">y =</span> hazard.rate<span class="fl">.1</span>), <span class="at">color =</span> <span class="st">"orange"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-15-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
<div class="sourceCode cell-code" id="cb39"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(hazard.df, <span class="fu">aes</span>(<span class="at">x =</span> fu.interval)) <span class="sc">+</span></span>
<span id="cb39-2"><a href="#cb39-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>(<span class="fu">aes</span>(<span class="at">y =</span> hazard.ratio))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-15-2.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
</section>
<section id="exercise-4" class="level2" data-number="1.4">
<h2 data-number="1.4" class="anchored" data-anchor-id="exercise-4"><span class="header-section-number">1.4</span> Exercise 4</h2>
<p>Show a plot with Kaplan-Meier survival curves for the two donor types.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb40"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a>km.tx <span class="ot">&lt;-</span> <span class="fu">survfit</span>(<span class="fu">Surv</span>(follow.up, death) <span class="sc">~</span> tx.type, <span class="at">data =</span> dat[dat<span class="sc">$</span>follow.up <span class="sc">&lt;=</span> <span class="dv">12</span>, ])</span>
<span id="cb40-2"><a href="#cb40-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb40-3"><a href="#cb40-3" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(km.tx, <span class="at">col =</span> <span class="fu">c</span>(<span class="st">"blue"</span>, <span class="st">"orange"</span>))</span>
<span id="cb40-4"><a href="#cb40-4" aria-hidden="true" tabindex="-1"></a><span class="fu">legend</span>(<span class="at">legend =</span> <span class="fu">c</span>(<span class="st">"cadaveric"</span>, <span class="st">"living"</span>), <span class="st">"bottomleft"</span>, <span class="at">lwd =</span> <span class="dv">2</span>, <span class="at">col =</span> <span class="fu">c</span>(<span class="st">"blue"</span>, <span class="st">"orange"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div>
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-16-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
</section>
<section id="exercise-5" class="level2" data-number="1.5">
<h2 data-number="1.5" class="anchored" data-anchor-id="exercise-5"><span class="header-section-number">1.5</span> Exercise 5</h2>
<p>Fit a univariate Cox model with predictor donor type. Report the hazard ratio and 95% confidence interval and interpret the result obtained.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb41"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a>cox <span class="ot">&lt;-</span> <span class="fu">coxph</span>(<span class="fu">Surv</span>(follow.up, death) <span class="sc">~</span> tx.type, <span class="at">data =</span> dat)</span>
<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(cox)</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>Call:
coxph(formula = Surv(follow.up, death) ~ tx.type, data = dat)
n= 9775, number of events= 465
coef exp(coef) se(coef) z Pr(&gt;|z|)
tx.type 0.64469 1.90539 0.09558 6.745 1.53e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
tx.type 1.905 0.5248 1.58 2.298
Concordance= 0.586 (se = 0.012 )
Likelihood ratio test= 47.1 on 1 df, p=7e-12
Wald test = 45.5 on 1 df, p=2e-11
Score (logrank) test = 47.09 on 1 df, p=7e-12</code></pre>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb43"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a><span class="fl">1.90539</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-stdout">
<pre><code>[1] 1.90539</code></pre>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb45"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a><span class="fl">1.90539</span> <span class="sc">+</span> <span class="fl">1.96</span> <span class="sc">*</span> <span class="fu">exp</span>(<span class="fl">0.09558</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-stdout">
<pre><code>[1] 4.061972</code></pre>
</div>
<div class="sourceCode cell-code" id="cb47"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a>(<span class="fl">2.298</span> <span class="sc">-</span> <span class="fl">1.58</span>) <span class="sc">/</span> <span class="dv">2</span> <span class="sc">|&gt;</span> <span class="fu">exp</span>() <span class="sc">/</span> <span class="dv">2</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-stdout">
<pre><code>[1] 0.04858537</code></pre>
</div>
</div>
<p>Exercise 6 — Research shows that an important determinant of mortality after kidney transplant is the age of the recipient. Fit a Cox model with age as predictor and estimate the hazard ratio and its confidence interval. Consider age first as continuous variable and then divide into categories.</p>
<p>Exercise 7 — Fit a multivariate Cox model by using other predictors and describe your results.</p>
<p>Exercise 8 — Estimate the survival function for specific covariate patterns. Based on the previous results choose the best predictors.</p>
<p>Exercise 9 — Check the proportional hazards assumption. You may use the function cox.zph. Discuss the result and possible implications. Exercise 10 — Plot the Schoenfeld residuals and comment.</p>
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if (note) {
return note.innerHTML;
} else {
return "";
}
});
}
const xrefs = window.document.querySelectorAll('a.quarto-xref');
const processXRef = (id, note) => {
// Strip column container classes
const stripColumnClz = (el) => {
el.classList.remove("page-full", "page-columns");
if (el.children) {
for (const child of el.children) {
stripColumnClz(child);
}
}
}
stripColumnClz(note)
if (id === null || id.startsWith('sec-')) {
// Special case sections, only their first couple elements
const container = document.createElement("div");
if (note.children && note.children.length > 2) {
container.appendChild(note.children[0].cloneNode(true));
for (let i = 1; i < note.children.length; i++) {
const child = note.children[i];
if (child.tagName === "P" && child.innerText === "") {
continue;
} else {
container.appendChild(child.cloneNode(true));
break;
}
}
if (window.Quarto?.typesetMath) {
window.Quarto.typesetMath(container);
}
return container.innerHTML
} else {
if (window.Quarto?.typesetMath) {
window.Quarto.typesetMath(note);
}
return note.innerHTML;
}
} else {
// Remove any anchor links if they are present
const anchorLink = note.querySelector('a.anchorjs-link');
if (anchorLink) {
anchorLink.remove();
}
if (window.Quarto?.typesetMath) {
window.Quarto.typesetMath(note);
}
if (note.classList.contains("callout")) {
return note.outerHTML;
} else {
return note.innerHTML;
}
}
}
for (var i=0; i<xrefs.length; i++) {
const xref = xrefs[i];
tippyHover(xref, undefined, function(instance) {
instance.disable();
let url = xref.getAttribute('href');
let hash = undefined;
if (url.startsWith('#')) {
hash = url;
} else {
try { hash = new URL(url).hash; } catch {}
}
if (hash) {
const id = hash.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
if (note !== null) {
try {
const html = processXRef(id, note.cloneNode(true));
instance.setContent(html);
} finally {
instance.enable();
instance.show();
}
} else {
// See if we can fetch this
fetch(url.split('#')[0])
.then(res => res.text())
.then(html => {
const parser = new DOMParser();
const htmlDoc = parser.parseFromString(html, "text/html");
const note = htmlDoc.getElementById(id);
if (note !== null) {
const html = processXRef(id, note);
instance.setContent(html);
}
}).finally(() => {
instance.enable();
instance.show();
});
}
} else {
// See if we can fetch a full url (with no hash to target)
// This is a special case and we should probably do some content thinning / targeting
fetch(url)
.then(res => res.text())
.then(html => {
const parser = new DOMParser();
const htmlDoc = parser.parseFromString(html, "text/html");
const note = htmlDoc.querySelector('main.content');
if (note !== null) {
// This should only happen for chapter cross references
// (since there is no id in the URL)
// remove the first header
if (note.children.length > 0 && note.children[0].tagName === "HEADER") {
note.children[0].remove();
}
const html = processXRef(null, note);
instance.setContent(html);
}
}).finally(() => {
instance.enable();
instance.show();
});
}
}, function(instance) {
});
}
let selectedAnnoteEl;
const selectorForAnnotation = ( cell, annotation) => {
let cellAttr = 'data-code-cell="' + cell + '"';
let lineAttr = 'data-code-annotation="' + annotation + '"';
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
return selector;
}
const selectCodeLines = (annoteEl) => {
const doc = window.document;
const targetCell = annoteEl.getAttribute("data-target-cell");
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
const lineIds = lines.map((line) => {
return targetCell + "-" + line;
})
let top = null;
let height = null;
let parent = null;
if (lineIds.length > 0) {
//compute the position of the single el (top and bottom and make a div)
const el = window.document.getElementById(lineIds[0]);
top = el.offsetTop;
height = el.offsetHeight;
parent = el.parentElement.parentElement;
if (lineIds.length > 1) {
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
height = bottom - top;
}
if (top !== null && height !== null && parent !== null) {
// cook up a div (if necessary) and position it
let div = window.document.getElementById("code-annotation-line-highlight");
if (div === null) {
div = window.document.createElement("div");
div.setAttribute("id", "code-annotation-line-highlight");
div.style.position = 'absolute';
parent.appendChild(div);
}
div.style.top = top - 2 + "px";
div.style.height = height + 4 + "px";
div.style.left = 0;
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
if (gutterDiv === null) {
gutterDiv = window.document.createElement("div");
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
gutterDiv.style.position = 'absolute';
const codeCell = window.document.getElementById(targetCell);
const gutter = codeCell.querySelector('.code-annotation-gutter');
gutter.appendChild(gutterDiv);
}
gutterDiv.style.top = top - 2 + "px";
gutterDiv.style.height = height + 4 + "px";
}
selectedAnnoteEl = annoteEl;
}
};
const unselectCodeLines = () => {
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
elementsIds.forEach((elId) => {
const div = window.document.getElementById(elId);
if (div) {
div.remove();
}
});
selectedAnnoteEl = undefined;
};
// Handle positioning of the toggle
window.addEventListener(
"resize",
throttle(() => {
elRect = undefined;
if (selectedAnnoteEl) {
selectCodeLines(selectedAnnoteEl);
}
}, 10)
);
function throttle(fn, ms) {
let throttle = false;
let timer;
return (...args) => {
if(!throttle) { // first call gets through
fn.apply(this, args);
throttle = true;
} else { // all the others get throttled
if(timer) clearTimeout(timer); // cancel #2
timer = setTimeout(() => {
fn.apply(this, args);
timer = throttle = false;
}, ms);
}
};
}
// Attach click handler to the DT
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
for (const annoteDlNode of annoteDls) {
annoteDlNode.addEventListener('click', (event) => {
const clickedEl = event.target;
if (clickedEl !== selectedAnnoteEl) {
unselectCodeLines();
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
if (activeEl) {
activeEl.classList.remove('code-annotation-active');
}
selectCodeLines(clickedEl);
clickedEl.classList.add('code-annotation-active');
} else {
// Unselect the line
unselectCodeLines();
clickedEl.classList.remove('code-annotation-active');
}
});
}
const findCites = (el) => {
const parentEl = el.parentElement;
if (parentEl) {
const cites = parentEl.dataset.cites;
if (cites) {
return {
el,
cites: cites.split(' ')
};
} else {
return findCites(el.parentElement)
}
} else {
return undefined;
}
};
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const citeInfo = findCites(ref);
if (citeInfo) {
tippyHover(citeInfo.el, function() {
var popup = window.document.createElement('div');
citeInfo.cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
}
});
</script>
</div> <!-- /content -->
</body></html>