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<!DOCTYPE html>
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<title>Chapter 10 Estimation using different methods | Understanding Propensity Score Matching</title>
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<meta name="author" content="Ehsan Karim" />
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<div class="book without-animation with-summary font-size-2 font-family-1" data-basepath=".">
<div class="book-summary">
<nav role="navigation">
<ul class="summary">
<li><a href="./">Understanding Propensity Score Matching</a></li>
<li class="divider"></li>
<li><a href="index.html#preamble">Preamble<span></span></a>
<ul>
<li><a href="index.html#description">Description<span></span></a></li>
<li><a href="index.html#main-references">Main references<span></span></a></li>
<li><a href="index.html#version-history">Version history<span></span></a></li>
<li><a href="index.html#prerequisites">Prerequisites<span></span></a>
<ul>
<li><a href="index.html#license">License<span></span></a></li>
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<li><a href="index.html#comments">Comments<span></span></a></li>
</ul></li>
<li class="chapter" data-level="1" data-path="terms.html"><a href="terms.html"><i class="fa fa-check"></i><b>1</b> Defining Parameter<span></span></a>
<ul>
<li class="chapter" data-level="1.1" data-path="terms.html"><a href="terms.html#potential-outcome"><i class="fa fa-check"></i><b>1.1</b> Potential outcome<span></span></a></li>
<li class="chapter" data-level="1.2" data-path="terms.html"><a href="terms.html#parameters-of-interest"><i class="fa fa-check"></i><b>1.2</b> Parameters of interest<span></span></a>
<ul>
<li class="chapter" data-level="1.2.1" data-path="terms.html"><a href="terms.html#te"><i class="fa fa-check"></i><b>1.2.1</b> TE<span></span></a></li>
<li class="chapter" data-level="1.2.2" data-path="terms.html"><a href="terms.html#ate"><i class="fa fa-check"></i><b>1.2.2</b> ATE<span></span></a></li>
<li class="chapter" data-level="1.2.3" data-path="terms.html"><a href="terms.html#interpretation-of-ate"><i class="fa fa-check"></i><b>1.2.3</b> Interpretation of ATE<span></span></a></li>
<li class="chapter" data-level="1.2.4" data-path="terms.html"><a href="terms.html#identifiability-assumptions"><i class="fa fa-check"></i><b>1.2.4</b> Identifiability Assumptions<span></span></a></li>
<li class="chapter" data-level="1.2.5" data-path="terms.html"><a href="terms.html#att"><i class="fa fa-check"></i><b>1.2.5</b> ATT<span></span></a></li>
<li class="chapter" data-level="1.2.6" data-path="terms.html"><a href="terms.html#interpretation-of-att"><i class="fa fa-check"></i><b>1.2.6</b> Interpretation of ATT<span></span></a></li>
<li class="chapter" data-level="1.2.7" data-path="terms.html"><a href="terms.html#att-vs.-ate"><i class="fa fa-check"></i><b>1.2.7</b> ATT vs. ATE<span></span></a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="2" data-path="balance.html"><a href="balance.html"><i class="fa fa-check"></i><b>2</b> Balance and Overlap<span></span></a>
<ul>
<li class="chapter" data-level="2.1" data-path="balance.html"><a href="balance.html#balance-1"><i class="fa fa-check"></i><b>2.1</b> Balance<span></span></a>
<ul>
<li class="chapter" data-level="2.1.1" data-path="balance.html"><a href="balance.html#measures-of-balance"><i class="fa fa-check"></i><b>2.1.1</b> Measures of Balance<span></span></a></li>
</ul></li>
<li class="chapter" data-level="2.2" data-path="balance.html"><a href="balance.html#adjustment"><i class="fa fa-check"></i><b>2.2</b> Adjustment<span></span></a>
<ul>
<li class="chapter" data-level="2.2.1" data-path="balance.html"><a href="balance.html#why-adjust"><i class="fa fa-check"></i><b>2.2.1</b> Why adjust?<span></span></a></li>
<li class="chapter" data-level="2.2.2" data-path="balance.html"><a href="balance.html#adjustment-methods"><i class="fa fa-check"></i><b>2.2.2</b> Adjustment Methods<span></span></a></li>
</ul></li>
<li class="chapter" data-level="2.3" data-path="balance.html"><a href="balance.html#lack-of-overlap"><i class="fa fa-check"></i><b>2.3</b> Lack of overlap<span></span></a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="ps.html"><a href="ps.html"><i class="fa fa-check"></i><b>3</b> Propensity score<span></span></a>
<ul>
<li class="chapter" data-level="3.1" data-path="ps.html"><a href="ps.html#motivating-problem"><i class="fa fa-check"></i><b>3.1</b> Motivating problem<span></span></a></li>
<li class="chapter" data-level="3.2" data-path="ps.html"><a href="ps.html#defining-propensity-score"><i class="fa fa-check"></i><b>3.2</b> Defining Propensity score<span></span></a>
<ul>
<li class="chapter" data-level="3.2.1" data-path="ps.html"><a href="ps.html#theoretical-result"><i class="fa fa-check"></i><b>3.2.1</b> Theoretical result<span></span></a></li>
<li class="chapter" data-level="3.2.2" data-path="ps.html"><a href="ps.html#assumptions"><i class="fa fa-check"></i><b>3.2.2</b> Assumptions<span></span></a></li>
<li class="chapter" data-level="3.2.3" data-path="ps.html"><a href="ps.html#ways-to-use-ps"><i class="fa fa-check"></i><b>3.2.3</b> Ways to use PS<span></span></a></li>
</ul></li>
<li class="chapter" data-level="3.3" data-path="ps.html"><a href="ps.html#ps-matching-steps"><i class="fa fa-check"></i><b>3.3</b> PS Matching Steps<span></span></a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="s1.html"><a href="s1.html"><i class="fa fa-check"></i><b>4</b> Step 1: Exposure modelling<span></span></a>
<ul>
<li class="chapter" data-level="4.1" data-path="s1.html"><a href="s1.html#model-specification"><i class="fa fa-check"></i><b>4.1</b> Model specification<span></span></a>
<ul>
<li class="chapter" data-level="4.1.1" data-path="s1.html"><a href="s1.html#updating-model-specification"><i class="fa fa-check"></i><b>4.1.1</b> Updating model specification<span></span></a></li>
<li class="chapter" data-level="4.1.2" data-path="s1.html"><a href="s1.html#stability-of-ps"><i class="fa fa-check"></i><b>4.1.2</b> Stability of PS<span></span></a></li>
</ul></li>
<li class="chapter" data-level="4.2" data-path="s1.html"><a href="s1.html#variables-to-adjust"><i class="fa fa-check"></i><b>4.2</b> Variables to adjust<span></span></a>
<ul>
<li class="chapter" data-level="4.2.1" data-path="s1.html"><a href="s1.html#best-approach"><i class="fa fa-check"></i><b>4.2.1</b> Best approach<span></span></a></li>
<li class="chapter" data-level="4.2.2" data-path="s1.html"><a href="s1.html#general-guideline-of-type-of-variables"><i class="fa fa-check"></i><b>4.2.2</b> General guideline of type of variables<span></span></a></li>
<li class="chapter" data-level="4.2.3" data-path="s1.html"><a href="s1.html#what-not-to-include"><i class="fa fa-check"></i><b>4.2.3</b> What NOT to include<span></span></a></li>
<li class="chapter" data-level="4.2.4" data-path="s1.html"><a href="s1.html#mediators"><i class="fa fa-check"></i><b>4.2.4</b> Mediators<span></span></a></li>
<li class="chapter" data-level="4.2.5" data-path="s1.html"><a href="s1.html#unmeasured-confounding"><i class="fa fa-check"></i><b>4.2.5</b> Unmeasured confounding<span></span></a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="s1.html"><a href="s1.html#model-selection-not-encouraged"><i class="fa fa-check"></i><b>4.3</b> Model selection (Not encouraged!)<span></span></a>
<ul>
<li class="chapter" data-level="4.3.1" data-path="s1.html"><a href="s1.html#based-on-association-with-outcome"><i class="fa fa-check"></i><b>4.3.1</b> Based on association with outcome<span></span></a></li>
<li class="chapter" data-level="4.3.2" data-path="s1.html"><a href="s1.html#based-on-association-with-exposure"><i class="fa fa-check"></i><b>4.3.2</b> Based on association with exposure<span></span></a></li>
</ul></li>
<li class="chapter" data-level="4.4" data-path="s1.html"><a href="s1.html#alternative-modelling-strategies"><i class="fa fa-check"></i><b>4.4</b> Alternative modelling strategies<span></span></a></li>
<li class="chapter" data-level="4.5" data-path="s1.html"><a href="s1.html#ps-estimation"><i class="fa fa-check"></i><b>4.5</b> PS estimation<span></span></a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="s2.html"><a href="s2.html"><i class="fa fa-check"></i><b>5</b> Step 2: Propensity score Matching<span></span></a>
<ul>
<li class="chapter" data-level="5.1" data-path="s2.html"><a href="s2.html#matching-method-nn"><i class="fa fa-check"></i><b>5.1</b> Matching method NN<span></span></a></li>
<li class="chapter" data-level="5.2" data-path="s2.html"><a href="s2.html#initial-fit"><i class="fa fa-check"></i><b>5.2</b> Initial fit<span></span></a></li>
<li class="chapter" data-level="5.3" data-path="s2.html"><a href="s2.html#fine-tuning-add-caliper"><i class="fa fa-check"></i><b>5.3</b> Fine tuning: add caliper<span></span></a></li>
<li class="chapter" data-level="5.4" data-path="s2.html"><a href="s2.html#things-to-keep-track-of"><i class="fa fa-check"></i><b>5.4</b> Things to keep track of<span></span></a></li>
<li class="chapter" data-level="5.5" data-path="s2.html"><a href="s2.html#matches"><i class="fa fa-check"></i><b>5.5</b> Matches<span></span></a></li>
<li class="chapter" data-level="5.6" data-path="s2.html"><a href="s2.html#other-matching-algorithms"><i class="fa fa-check"></i><b>5.6</b> Other matching algorithms<span></span></a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="s3.html"><a href="s3.html"><i class="fa fa-check"></i><b>6</b> Step 3: Balance and overlap<span></span></a>
<ul>
<li class="chapter" data-level="6.1" data-path="s3.html"><a href="s3.html#assessment-of-balance-by-smd"><i class="fa fa-check"></i><b>6.1</b> Assessment of Balance by SMD<span></span></a></li>
<li class="chapter" data-level="6.2" data-path="s3.html"><a href="s3.html#smd-vs.-p-values"><i class="fa fa-check"></i><b>6.2</b> SMD vs. P-values<span></span></a></li>
<li class="chapter" data-level="6.3" data-path="s3.html"><a href="s3.html#vizualization-for-overlap"><i class="fa fa-check"></i><b>6.3</b> Vizualization for Overlap<span></span></a></li>
<li class="chapter" data-level="6.4" data-path="s3.html"><a href="s3.html#variance-ratio-1"><i class="fa fa-check"></i><b>6.4</b> Variance ratio<span></span></a></li>
<li class="chapter" data-level="6.5" data-path="s3.html"><a href="s3.html#close-inspection-of-boundaries"><i class="fa fa-check"></i><b>6.5</b> Close inspection of boundaries<span></span></a></li>
<li class="chapter" data-level="6.6" data-path="s3.html"><a href="s3.html#unsatirfactory-balance"><i class="fa fa-check"></i><b>6.6</b> Unsatirfactory balance<span></span></a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="s4.html"><a href="s4.html"><i class="fa fa-check"></i><b>7</b> Step 4: Outcome modelling<span></span></a>
<ul>
<li class="chapter" data-level="7.1" data-path="s4.html"><a href="s4.html#crude-outcome-model"><i class="fa fa-check"></i><b>7.1</b> Crude outcome model<span></span></a></li>
<li class="chapter" data-level="7.2" data-path="s4.html"><a href="s4.html#double-adjustment"><i class="fa fa-check"></i><b>7.2</b> Double-adjustment<span></span></a></li>
<li class="chapter" data-level="7.3" data-path="s4.html"><a href="s4.html#adjusted-outcome-model"><i class="fa fa-check"></i><b>7.3</b> Adjusted outcome model<span></span></a></li>
<li class="chapter" data-level="7.4" data-path="s4.html"><a href="s4.html#variance-considerations"><i class="fa fa-check"></i><b>7.4</b> Variance considerations<span></span></a>
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<li class="chapter" data-level="7.4.1" data-path="s4.html"><a href="s4.html#cluster-option"><i class="fa fa-check"></i><b>7.4.1</b> Cluster option<span></span></a></li>
<li class="chapter" data-level="7.4.2" data-path="s4.html"><a href="s4.html#bootstrap"><i class="fa fa-check"></i><b>7.4.2</b> Bootstrap<span></span></a></li>
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<li class="chapter" data-level="7.5" data-path="s4.html"><a href="s4.html#estimate-obtained"><i class="fa fa-check"></i><b>7.5</b> Estimate obtained<span></span></a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="compare.html"><a href="compare.html"><i class="fa fa-check"></i><b>8</b> PS vs. Regression<span></span></a>
<ul>
<li class="chapter" data-level="8.1" data-path="compare.html"><a href="compare.html#data-simulation"><i class="fa fa-check"></i><b>8.1</b> Data Simulation<span></span></a></li>
<li class="chapter" data-level="8.2" data-path="compare.html"><a href="compare.html#treatment-effect-from-counterfactuals"><i class="fa fa-check"></i><b>8.2</b> Treatment effect from counterfactuals<span></span></a></li>
<li class="chapter" data-level="8.3" data-path="compare.html"><a href="compare.html#treatment-effect-from-regression"><i class="fa fa-check"></i><b>8.3</b> Treatment effect from Regression<span></span></a></li>
<li class="chapter" data-level="8.4" data-path="compare.html"><a href="compare.html#treatment-effect-from-ps"><i class="fa fa-check"></i><b>8.4</b> Treatment effect from PS<span></span></a></li>
<li class="chapter" data-level="8.5" data-path="compare.html"><a href="compare.html#non-linear-model"><i class="fa fa-check"></i><b>8.5</b> Non-linear Model<span></span></a>
<ul>
<li class="chapter" data-level="8.5.1" data-path="compare.html"><a href="compare.html#data-generation"><i class="fa fa-check"></i><b>8.5.1</b> Data generation<span></span></a></li>
<li class="chapter" data-level="8.5.2" data-path="compare.html"><a href="compare.html#regression"><i class="fa fa-check"></i><b>8.5.2</b> Regression<span></span></a></li>
<li class="chapter" data-level="8.5.3" data-path="compare.html"><a href="compare.html#ps-1"><i class="fa fa-check"></i><b>8.5.3</b> PS<span></span></a></li>
<li class="chapter" data-level="8.5.4" data-path="compare.html"><a href="compare.html#machine-learning"><i class="fa fa-check"></i><b>8.5.4</b> Machine learning<span></span></a></li>
<li class="chapter" data-level="8.5.5" data-path="compare.html"><a href="compare.html#regression-is-doomed"><i class="fa fa-check"></i><b>8.5.5</b> Regression is doomed?<span></span></a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="9" data-path="misspecify.html"><a href="misspecify.html"><i class="fa fa-check"></i><b>9</b> Model-misspecification<span></span></a>
<ul>
<li class="chapter" data-level="9.1" data-path="misspecify.html"><a href="misspecify.html#complex-data-simulation"><i class="fa fa-check"></i><b>9.1</b> Complex Data Simulation<span></span></a>
<ul>
<li><a href="misspecify.html#true-exposure-model">True Exposure Model<span></span></a></li>
<li><a href="misspecify.html#true-outcome-model">True Outcome Model<span></span></a></li>
<li><a href="misspecify.html#assumption">Assumption<span></span></a></li>
<li><a href="misspecify.html#outcomes-and-exposures-are-complex-functions-of-measured-covariates">Outcomes and exposures are complex functions of measured covariates<span></span></a></li>
</ul></li>
<li class="chapter" data-level="9.2" data-path="misspecify.html"><a href="misspecify.html#generate-data"><i class="fa fa-check"></i><b>9.2</b> Generate data<span></span></a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="estimation-using-different-methods.html"><a href="estimation-using-different-methods.html"><i class="fa fa-check"></i><b>10</b> Estimation using different methods<span></span></a>
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<li class="chapter" data-level="10.1" data-path="estimation-using-different-methods.html"><a href="estimation-using-different-methods.html#regression-1"><i class="fa fa-check"></i><b>10.1</b> Regression<span></span></a></li>
<li class="chapter" data-level="10.2" data-path="estimation-using-different-methods.html"><a href="estimation-using-different-methods.html#propensity-score"><i class="fa fa-check"></i><b>10.2</b> Propensity score<span></span></a>
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<li class="chapter" data-level="10.2.1" data-path="estimation-using-different-methods.html"><a href="estimation-using-different-methods.html#tmle-with-superlearner"><i class="fa fa-check"></i><b>10.2.1</b> TMLE with superlearner<span></span></a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="11" data-path="guide.html"><a href="guide.html"><i class="fa fa-check"></i><b>11</b> Reporting Guidelines<span></span></a>
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<li class="chapter" data-level="11.1" data-path="guide.html"><a href="guide.html#discipline-specific-reviews"><i class="fa fa-check"></i><b>11.1</b> Discipline-specific Reviews<span></span></a></li>
<li class="chapter" data-level="11.2" data-path="guide.html"><a href="guide.html#suggested-guidelines"><i class="fa fa-check"></i><b>11.2</b> Suggested Guidelines<span></span></a></li>
<li class="chapter" data-level="11.3" data-path="guide.html"><a href="guide.html#additional-topics"><i class="fa fa-check"></i><b>11.3</b> Additional topics<span></span></a></li>
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<li class="chapter" data-level="12" data-path="final.html"><a href="final.html"><i class="fa fa-check"></i><b>12</b> Final Words<span></span></a>
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<li class="chapter" data-level="12.1" data-path="final.html"><a href="final.html#common-misconception"><i class="fa fa-check"></i><b>12.1</b> Common misconception<span></span></a></li>
<li class="chapter" data-level="12.2" data-path="final.html"><a href="final.html#understanding-sources-of-bias-is-important"><i class="fa fa-check"></i><b>12.2</b> Understanding sources of bias is important<span></span></a></li>
<li class="chapter" data-level="12.3" data-path="final.html"><a href="final.html#benifits-of-ps"><i class="fa fa-check"></i><b>12.3</b> Benifits of PS<span></span></a></li>
<li class="chapter" data-level="12.4" data-path="final.html"><a href="final.html#limitations-of-ps"><i class="fa fa-check"></i><b>12.4</b> Limitations of PS<span></span></a></li>
<li class="chapter" data-level="12.5" data-path="final.html"><a href="final.html#sensitivity-analysis"><i class="fa fa-check"></i><b>12.5</b> Sensitivity analysis<span></span></a></li>
<li class="chapter" data-level="12.6" data-path="final.html"><a href="final.html#software"><i class="fa fa-check"></i><b>12.6</b> Software<span></span></a></li>
<li class="chapter" data-level="12.7" data-path="final.html"><a href="final.html#further-resources"><i class="fa fa-check"></i><b>12.7</b> Further Resources<span></span></a></li>
</ul></li>
<li><a href="references.html#references">References<span></span></a></li>
<li class="divider"></li>
<li><a href="https://ehsank.com/" target="blank">Ehsan Karim</a></li>
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<h1>
<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Understanding Propensity Score Matching</a>
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<div id="estimation-using-different-methods" class="section level1 hasAnchor" number="10">
<h1><span class="header-section-number">Chapter 10</span> Estimation using different methods<a href="estimation-using-different-methods.html#estimation-using-different-methods" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<div id="regression-1" class="section level2 hasAnchor" number="10.1">
<h2><span class="header-section-number">10.1</span> Regression<a href="estimation-using-different-methods.html#regression-1" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="estimation-using-different-methods.html#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">round</span>(<span class="fu">coef</span>(<span class="fu">glm</span>(Y <span class="sc">~</span> A <span class="sc">+</span> L1 <span class="sc">+</span> L2 <span class="sc">+</span> L3 <span class="sc">+</span> L4, <span class="at">family=</span><span class="st">"gaussian"</span>, </span>
<span id="cb4-2"><a href="estimation-using-different-methods.html#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data=</span>result.data<span class="sc">$</span>observed)),<span class="dv">2</span>)</span></code></pre></div>
<pre><code>## (Intercept) A L1 L2 L3 L4
## 86.32 7.59 4.42 -0.06 -2.90 0.07</code></pre>
</div>
<div id="propensity-score" class="section level2 hasAnchor" number="10.2">
<h2><span class="header-section-number">10.2</span> Propensity score<a href="estimation-using-different-methods.html#propensity-score" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Propensity score model fitting:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="estimation-using-different-methods.html#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">require</span>(MatchIt)</span></code></pre></div>
<pre><code>## Loading required package: MatchIt</code></pre>
<pre><code>## Warning: package 'MatchIt' was built under R version 4.1.3</code></pre>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="estimation-using-different-methods.html#cb9-1" aria-hidden="true" tabindex="-1"></a>match.obj <span class="ot"><-</span> <span class="fu">matchit</span>(A <span class="sc">~</span> L1 <span class="sc">+</span> L2 <span class="sc">+</span> L3 <span class="sc">+</span> L4, <span class="at">method =</span> <span class="st">"nearest"</span>, </span>
<span id="cb9-2"><a href="estimation-using-different-methods.html#cb9-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> result.data<span class="sc">$</span>observed,</span>
<span id="cb9-3"><a href="estimation-using-different-methods.html#cb9-3" aria-hidden="true" tabindex="-1"></a> <span class="at">distance =</span> <span class="st">'logit'</span>, </span>
<span id="cb9-4"><a href="estimation-using-different-methods.html#cb9-4" aria-hidden="true" tabindex="-1"></a> <span class="at">caliper =</span> <span class="fl">0.2</span>,</span>
<span id="cb9-5"><a href="estimation-using-different-methods.html#cb9-5" aria-hidden="true" tabindex="-1"></a> <span class="at">replace =</span> <span class="cn">FALSE</span>, </span>
<span id="cb9-6"><a href="estimation-using-different-methods.html#cb9-6" aria-hidden="true" tabindex="-1"></a> <span class="at">ratio =</span> <span class="dv">1</span>)</span>
<span id="cb9-7"><a href="estimation-using-different-methods.html#cb9-7" aria-hidden="true" tabindex="-1"></a>match.obj</span></code></pre></div>
<pre><code>## A matchit object
## - method: 1:1 nearest neighbor matching without replacement
## - distance: Propensity score [caliper]
## - estimated with logistic regression
## - caliper: <distance> (0.035)
## - number of obs.: 10000 (original), 5800 (matched)
## - target estimand: ATT
## - covariates: L1, L2, L3, L4</code></pre>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="estimation-using-different-methods.html#cb11-1" aria-hidden="true" tabindex="-1"></a>matched.data <span class="ot"><-</span> <span class="fu">match.data</span>(match.obj)</span></code></pre></div>
<p>Results from step 4: crude and adjusted</p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="estimation-using-different-methods.html#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">round</span>(<span class="fu">coef</span>(<span class="fu">glm</span>(Y <span class="sc">~</span> A, </span>
<span id="cb12-2"><a href="estimation-using-different-methods.html#cb12-2" aria-hidden="true" tabindex="-1"></a> <span class="at">family=</span><span class="st">"gaussian"</span>, </span>
<span id="cb12-3"><a href="estimation-using-different-methods.html#cb12-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data=</span>matched.data)),<span class="dv">2</span>)</span></code></pre></div>
<pre><code>## (Intercept) A
## 121.28 7.89</code></pre>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="estimation-using-different-methods.html#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">round</span>(<span class="fu">coef</span>(<span class="fu">glm</span>(Y <span class="sc">~</span> A <span class="sc">+</span> L1 <span class="sc">+</span> L2 <span class="sc">+</span> L3 <span class="sc">+</span> L4, </span>
<span id="cb14-2"><a href="estimation-using-different-methods.html#cb14-2" aria-hidden="true" tabindex="-1"></a> <span class="at">family=</span><span class="st">"gaussian"</span>, </span>
<span id="cb14-3"><a href="estimation-using-different-methods.html#cb14-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data=</span>matched.data)),<span class="dv">2</span>)</span></code></pre></div>
<pre><code>## (Intercept) A L1 L2 L3 L4
## 83.64 7.63 4.39 -0.02 11.43 0.07</code></pre>
<div id="tmle-with-superlearner" class="section level3 hasAnchor" number="10.2.1">
<h3><span class="header-section-number">10.2.1</span> TMLE with superlearner<a href="estimation-using-different-methods.html#tmle-with-superlearner" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="estimation-using-different-methods.html#cb16-1" aria-hidden="true" tabindex="-1"></a>tmle.res <span class="ot"><-</span> <span class="fu">ltmle</span>(<span class="at">data=</span>result.data<span class="sc">$</span>observed, <span class="at">Anodes=</span><span class="st">'A'</span>, <span class="at">Ynodes=</span><span class="st">'Y'</span>, <span class="at">abar=</span><span class="fu">list</span>(<span class="dv">1</span>,<span class="dv">0</span>), </span>
<span id="cb16-2"><a href="estimation-using-different-methods.html#cb16-2" aria-hidden="true" tabindex="-1"></a> <span class="at">SL.library=</span><span class="fu">c</span>(<span class="st">'SL.glm'</span>, <span class="st">'SL.step.interaction'</span>, <span class="st">'SL.earth'</span>, <span class="st">'SL.mean'</span>), </span>
<span id="cb16-3"><a href="estimation-using-different-methods.html#cb16-3" aria-hidden="true" tabindex="-1"></a> <span class="at">estimate.time=</span>F,</span>
<span id="cb16-4"><a href="estimation-using-different-methods.html#cb16-4" aria-hidden="true" tabindex="-1"></a> <span class="at">SL.cvControl=</span><span class="fu">list</span>(<span class="at">V=</span><span class="dv">10</span>),</span>
<span id="cb16-5"><a href="estimation-using-different-methods.html#cb16-5" aria-hidden="true" tabindex="-1"></a> <span class="at">gbounds=</span><span class="fu">c</span>(<span class="fl">0.025</span>, <span class="fl">0.975</span>))</span></code></pre></div>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="estimation-using-different-methods.html#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(tmle.res)</span></code></pre></div>
<pre><code>## Estimator: tmle
## Call:
## ltmle(data = result.data$observed, Anodes = "A", Ynodes = "Y",
## abar = list(1, 0), gbounds = c(0.025, 0.975), SL.library = c("SL.glm",
## "SL.step.interaction", "SL.earth", "SL.mean"), SL.cvControl = list(V = 10),
## estimate.time = F)
##
## Treatment Estimate:
## Parameter Estimate: 126.01
## Estimated Std Err: 0.16692
## p-value: <2e-16
## 95% Conf Interval: (125.69, 126.34)
##
## Control Estimate:
## Parameter Estimate: 119.84
## Estimated Std Err: 0.098537
## p-value: <2e-16
## 95% Conf Interval: (119.64, 120.03)
##
## Additive Treatment Effect:
## Parameter Estimate: 6.1786
## Estimated Std Err: 0.17483
## p-value: <2e-16
## 95% Conf Interval: (5.8359, 6.5213)</code></pre>
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