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<title>Kausale Inferenz</title>
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<div class="pageContent band">
<div class="bandContent page">
<div class="topics">
<div id="section-vorbemerkung" class="section level2">
<h2>Vorbemerkung</h2>
<p>Dieses Tutorial orientiert sich am Projekt <a href="https://github.com/kfcaby/causalLab">Causal Inference in Introductory Statistics Courses</a> von <a href="https://westpoint.edu/mathematical-sciences/profile/kevin_cummiskey">LTC Kevin Cummiskey</a>. Siehe auch Cummiskey, K., Adams, B,. Pleuss, J., Turner, D., Clark, N. & Watts, K. (2020). <em>Causal Inference in Introductory Statistics Courses</em>, Journal of Statistics Education, <a href="https://doi.org/10.1080/10691898.2020.1713936">https://doi.org/10.1080/10691898.2020.1713936</a>.</p>
<p>Datengrundlage ist der Artikel von Kahn, M. (2005). <em>An exhalent problem for teaching statistics</em>. Journal of Statistics Education, 13(2), <a href="https://doi.org/10.1080/10691898.2005.11910559">https://doi.org/10.1080/10691898.2005.11910559</a>.</p>
</div>
<div id="section-rauchen-bei-kindern-und-jugendlichen" class="section level2">
<h2>Rauchen bei Kindern und Jugendlichen</h2>
<p>Mittlerweile sind wir ziemlich sicher, dass Rauchen der Gesundheit schadet. Aber das war nicht immer so, und eine naive Datenanalyse kann auch zu einem gegenteiligen Ergebnis kommen.</p>
<p>In einer Reihe von Papern (siehe z.B. <a href="https://doi.org/10.1080/10691898.2005.11910559">Kahn, 2005</a>) wurde der Frage nachgegangen inwieweit Rauchen das sogenannte <em>forcierte exspiratorische Volumen</em> – eine Kennzahl der Lungenfunktion – bei Heranwachsenden beeinflusst.</p>
<div id="section-section" class="section level3">
<h3></h3>
<div class="panel panel-default">
<div data-label="ethik" class="tutorial-question panel-body">
<div id="ethik-answer_container" class="shiny-html-output"></div>
<div id="ethik-message_container" class="shiny-html-output"></div>
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</div>
<div id="section-section-1" class="section level3">
<h3></h3>
<p>Der hier verwendete Datensatz <code>LV</code> hat folgende Struktur:</p>
<pre class="r"><code>str(LV)</code></pre>
<pre><code>## 'data.frame': 654 obs. of 5 variables:
## $ Alter : int 9 8 7 9 9 8 6 6 8 9 ...
## $ Lungenvolumen: num 1.71 1.72 1.72 1.56 1.9 ...
## $ Groesse : num 145 171 138 135 145 ...
## $ Geschlecht : Factor w/ 2 levels "m","w": 2 2 2 1 1 2 2 2 2 2 ...
## $ RaucherIn : Factor w/ 2 levels "nein","ja": 1 1 1 1 1 1 1 1 1 1 ...</code></pre>
<p>mit den Variablen</p>
<ul>
<li><code>Alter</code>: Alter in Jahren</li>
<li><code>Lungenvolumen</code>: forcierte exspiratorische Volumen in l</li>
<li><code>Groesse</code>: Größe in cm</li>
<li><code>Geschlecht</code>: <code>m</code> für männlich und <code>w</code> für weiblich</li>
<li><code>RaucherIn</code>: Hat die Person geraucht? <code>ja</code> oder <code>nein</code></li>
</ul>
<p>Übersicht der ersten Werte:</p>
<pre class="r"><code>head(LV)</code></pre>
<div data-pagedtable="false">
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<div class="panel panel-default">
<div data-label="skalennvieau" class="tutorial-question panel-body">
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</div>
<div id="section-section-2" class="section level3">
<h3></h3>
<p>Aus inhaltlichen Gründen wird dabei folgender Kausalzusammenhang angenommen:</p>
<p><img src="KausaleInferenz_files/figure-html/unnamed-chunk-1-1.png" width="624" /></p>
</div>
</div>
<div id="section-rauchen-und-lungenvolumen" class="section level2">
<h2>Rauchen und Lungenvolumen</h2>
<p>Ein Boxplot des Lungenvolumens in Abhängigkeit des Rauchverhaltens ergibt folgendes Ergebnis:</p>
<pre class="r"><code>gf_boxplot(Lungenvolumen ~ RaucherIn, data = LV)</code></pre>
<p><img src="KausaleInferenz_files/figure-html/b1-1.png" width="624" /></p>
<div id="section-section-3" class="section level3">
<h3></h3>
<div class="panel panel-default">
<div data-label="median" class="tutorial-question panel-body">
<div id="median-answer_container" class="shiny-html-output"></div>
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</div>
<div id="section-section-4" class="section level3">
<h3></h3>
<p>Sowohl Rauchen als auch Lungenvolumen hängen vom Geschlecht ab.</p>
<p>Erweitern Sie den Code, so dass Sie nach <code>Geschlecht</code> bedingen/ filtern.</p>
<div class="tutorial-exercise" data-label="bedingt" data-caption="Code" data-completion="1" data-diagnostics="1" data-startover="1" data-lines="0">
<pre class="text"><code>gf_boxplot(Lungenvolumen ~ RaucherIn, data = LV)</code></pre>
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</div>
<div class="tutorial-exercise-support" data-label="bedingt-solution" data-caption="Code" data-completion="1" data-diagnostics="1" data-startover="1" data-lines="0">
<pre class="text"><code>gf_boxplot(Lungenvolumen ~ RaucherIn | Geschlecht, data = LV)</code></pre>
</div>
</div>
<div id="section-section-5" class="section level3">
<h3></h3>
<p>Das Bild hat sich nicht geändert, Raucher*innen scheinen das größere Lungenvolumen zu haben.</p>
</div>
<div id="section-section-6" class="section level3">
<h3></h3>
<p>Woran könnte das liegen?</p>
</div>
</div>
<div id="section-das-alter" class="section level2">
<h2>Das Alter …</h2>
<p>Wie zu erwarten war, gibt es einen Zusammenhang zwischen Alter und Größe:</p>
<pre class="r"><code>gf_point(Groesse ~ Alter, data = LV) %>%
gf_smooth()</code></pre>
<pre><code>## `geom_smooth()` using method = 'loess'</code></pre>
<p><img src="KausaleInferenz_files/figure-html/unnamed-chunk-2-1.png" width="624" /></p>
<div id="section-section-7" class="section level3">
<h3></h3>
<p>Erweitern Sie den Code so, so dass Sie die Punkte gemäß der Variable <code>RaucherIn</code> farbig markieren:</p>
<div class="tutorial-exercise" data-label="color" data-caption="Code" data-completion="1" data-diagnostics="1" data-startover="1" data-lines="0">
<pre class="text"><code>gf_point(Groesse ~ Alter, data = LV) %>%
gf_smooth()</code></pre>
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</div>
<div class="tutorial-exercise-support" data-label="color-solution" data-caption="Code" data-completion="1" data-diagnostics="1" data-startover="1" data-lines="0">
<pre class="text"><code>gf_point(Groesse ~ Alter, color = ~ RaucherIn, data = LV) %>%
gf_smooth()</code></pre>
</div>
</div>
<div id="section-section-8" class="section level3">
<h3></h3>
<p>Klar: Bei Heranwachsenden sind die Raucher*innen älter als die Nichtraucher*innen – und damit auch größer.</p>
</div>
<div id="section-section-9" class="section level3">
<h3></h3>
<p>Und natürlich gibt es auch einen Zusammenhang zwischen der Größe und dem Lungenvolumen:</p>
<pre class="r"><code>gf_point(Lungenvolumen ~ Groesse, data = LV) %>%
gf_smooth()</code></pre>
<pre><code>## `geom_smooth()` using method = 'loess'</code></pre>
<p><img src="KausaleInferenz_files/figure-html/unnamed-chunk-3-1.png" width="624" /></p>
</div>
</div>
<div id="section-kausale-modellierung-rauchen-und-lungenvolumen" class="section level2">
<h2>Kausale Modellierung Rauchen und Lungenvolumen</h2>
<p>Hier noch einmal das angenommene Modell:</p>
<p><img src="KausaleInferenz_files/figure-html/p12-1.png" width="624" /></p>
<p>Eine naive Modellierung ergibt folgendes Ergebnis:</p>
<pre class="r"><code>lm(Lungenvolumen ~ RaucherIn, data = LV) %>%
summary()</code></pre>
<pre><code>##
## Call:
## lm(formula = Lungenvolumen ~ RaucherIn, data = LV)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7751 -0.6339 -0.1021 0.4804 3.2269
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.56614 0.03466 74.037 < 2e-16 ***
## RaucherInja 0.71072 0.10994 6.464 1.99e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8412 on 652 degrees of freedom
## Multiple R-squared: 0.06023, Adjusted R-squared: 0.05879
## F-statistic: 41.79 on 1 and 652 DF, p-value: 1.993e-10</code></pre>
<div id="section-section-10" class="section level3">
<h3></h3>
<p>Rauchen <em>scheint</em> das Lungenvolumen zu erhöhen.</p>
<p>Warum?</p>
</div>
<div id="section-section-11" class="section level3">
<h3></h3>
<p>Weil die nicht-kausalen Pfade durch die <em>Hintertür</em> (engl. backdoor, <em>Fork</em>) offen sind:</p>
<p><span class="math display">\[\text{RaucherIn} \leftarrow \text{Geschlecht} \rightarrow \text{Lungenvolumen}\]</span> bzw.</p>
<p><span class="math display">\[\text{RaucherIn} \leftarrow \text{Alter} \rightarrow \text{Lungenvolumen}\]</span> Diese Pfade sollten also z.B. durch Adjustierung <em>blockiert</em> werden.</p>
<div class="panel panel-default">
<div data-label="chain" class="tutorial-question panel-body">
<div id="chain-answer_container" class="shiny-html-output"></div>
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</div>
<div id="section-section-12" class="section level3">
<h3></h3>
<p>Geben Sie, unter der Annahme eines linearen Modells die Formel an, die den (totalen) kausalen Effekt des Rauchens auf das Lungenvolumen schätzt:</p>
<div class="tutorial-exercise" data-label="model" data-caption="Code" data-completion="1" data-diagnostics="1" data-startover="1" data-lines="0">
<pre class="text"><code>lm(Lungenvolumen ~ RaucherIn + ___ + ___, data = LV) %>%
summary()</code></pre>
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<div class="tutorial-exercise-support" data-label="model-solution" data-caption="Code" data-completion="1" data-diagnostics="1" data-startover="1" data-lines="0">
<pre class="text"><code>lm(Lungenvolumen ~ RaucherIn + Geschlecht + Alter, data = LV) %>%
summary()</code></pre>
</div>
</div>
<div id="section-section-13" class="section level3">
<h3></h3>
<div class="panel panel-default">
<div data-label="effekt" class="tutorial-question panel-body">
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<div id="section-section-14" class="section level3">
<h3></h3>
<div class="panel panel-default">
<div data-label="pwert" class="tutorial-question panel-body">
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<p><em>Hinweis</em>: Die Annahme eines linearen Modells ist aufgrund des nicht-linearen Zusammenhangs zwischen Alter und Größe sowie Größe und Lungenvolumen (siehe Abbildungen im Abschnitt <em>Das Alter …</em>) eher nur eine Näherung.</p>
</div>
</div>
<div id="section-ausblick" class="section level2">
<h2>Ausblick</h2>
Die Kausale Inferenz bietet viele weitere und fortgeschrittene Möglichkeiten der Analyse. Siehe z.B. als Einstieg: Pearl, J., Glymour, M., & Jewell, N. P. (2016). <em>Causal inference in statistics: A primer</em>. John Wiley & Sons, <a href="http://bayes.cs.ucla.edu/PRIMER/">http://bayes.cs.ucla.edu/PRIMER/</a>.
<script type="application/shiny-prerendered" data-context="server-start">
library(ggdag)
coordLV <- list(
x = c(Geschlecht = 0, Alter = 0, RaucherIn = 1, Groesse = 2, Lungenvolumen = 3),
y = c(Geschlecht = 1, Alter = 2, RaucherIn = 0, Groesse = 2, Lungenvolumen = 0))
dagLV <- dagify(Groesse ~ Geschlecht + Alter + RaucherIn,
RaucherIn ~ Geschlecht + Alter,
Lungenvolumen ~ Groesse + Geschlecht + Alter + RaucherIn,
coords = coordLV,
exposure = "RaucherIn",
outcome = "Lungenvolumen")
p1 <- ggdag(dagLV, text_col = "blue", node = FALSE, text_size = 5) + theme_dag_blank()
library(learnr)
library(mosaic)
load("LV.Rdata")
checker <- function(label, user_code, check_code, envir_result, evaluate_result, ...) {
list(message = check_code, correct = TRUE, location = "append")
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tutorial_options(exercise.timelimit = 60, exercise.checker = checker)
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