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<!DOCTYPE html>
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<title>Chapter 5 Step 2: Propensity score Matching | Understanding Propensity Score Matching</title>
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<meta name="twitter:title" content="Chapter 5 Step 2: Propensity score Matching | Understanding Propensity Score Matching" />
<meta name="twitter:description" content="Chapter 5 Step 2: Propensity score Matching | Understanding Propensity Score Matching." />
<meta name="author" content="Ehsan Karim" />
<meta name="date" content="2023-03-19" />
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<div class="book-summary">
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<ul class="summary">
<li><a href="./">Understanding Propensity Score Matching</a></li>
<li class="divider"></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Preamble</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#description"><i class="fa fa-check"></i>Description</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#main-references"><i class="fa fa-check"></i>Main references</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#version-history"><i class="fa fa-check"></i>Version history</a></li>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html#prerequisites"><i class="fa fa-check"></i>Prerequisites</a>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html#license"><i class="fa fa-check"></i>License</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#comments"><i class="fa fa-check"></i>Comments</a></li>
</ul></li>
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<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</a>
<ul>
<li class="chapter" data-level="1.1" data-path="terms.html"><a href="terms.html#epidemiological-research-goals"><i class="fa fa-check"></i><b>1.1</b> Epidemiological research goals</a></li>
<li class="chapter" data-level="1.2" data-path="terms.html"><a href="terms.html#potential-outcome"><i class="fa fa-check"></i><b>1.2</b> Potential outcome</a></li>
<li class="chapter" data-level="1.3" data-path="terms.html"><a href="terms.html#parameters-of-interest"><i class="fa fa-check"></i><b>1.3</b> Parameters of interest</a>
<ul>
<li class="chapter" data-level="1.3.1" data-path="terms.html"><a href="terms.html#te"><i class="fa fa-check"></i><b>1.3.1</b> TE</a></li>
<li class="chapter" data-level="1.3.2" data-path="terms.html"><a href="terms.html#ate"><i class="fa fa-check"></i><b>1.3.2</b> ATE</a></li>
<li class="chapter" data-level="1.3.3" data-path="terms.html"><a href="terms.html#interpretation-of-ate"><i class="fa fa-check"></i><b>1.3.3</b> Interpretation of ATE</a></li>
<li class="chapter" data-level="1.3.4" data-path="terms.html"><a href="terms.html#identifiability-assumptions"><i class="fa fa-check"></i><b>1.3.4</b> Identifiability Assumptions</a></li>
<li class="chapter" data-level="1.3.5" data-path="terms.html"><a href="terms.html#att"><i class="fa fa-check"></i><b>1.3.5</b> ATT</a></li>
<li class="chapter" data-level="1.3.6" data-path="terms.html"><a href="terms.html#interpretation-of-att"><i class="fa fa-check"></i><b>1.3.6</b> Interpretation of ATT</a></li>
<li class="chapter" data-level="1.3.7" data-path="terms.html"><a href="terms.html#att-vs.-ate"><i class="fa fa-check"></i><b>1.3.7</b> ATT vs. ATE</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</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</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</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</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?</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="s1.html"><a href="s1.html#model-selection"><i class="fa fa-check"></i><b>4.3</b> Model selection</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</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</a>
<ul>
<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</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</a></li>
</ul></li>
<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</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</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</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</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</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</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</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</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</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</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</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?</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> PS vs. Double robust methods</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</a>
<ul>
<li class="chapter" data-level="" data-path="misspecify.html"><a href="misspecify.html#true-exposure-model"><i class="fa fa-check"></i>True Exposure Model</a></li>
<li class="chapter" data-level="" data-path="misspecify.html"><a href="misspecify.html#true-outcome-model"><i class="fa fa-check"></i>True Outcome Model</a></li>
<li class="chapter" data-level="" data-path="misspecify.html"><a href="misspecify.html#outcomes-and-exposures-are-complex-functions-of-measured-covariates"><i class="fa fa-check"></i>Outcomes and exposures are complex functions of measured covariates</a></li>
</ul></li>
<li class="chapter" data-level="9.2" data-path="misspecify.html"><a href="misspecify.html#understanding-finite-sample-bias"><i class="fa fa-check"></i><b>9.2</b> Understanding finite sample bias</a></li>
<li class="chapter" data-level="9.3" data-path="misspecify.html"><a href="misspecify.html#estimation-using-different-methods"><i class="fa fa-check"></i><b>9.3</b> Estimation using different methods</a>
<ul>
<li class="chapter" data-level="9.3.1" data-path="misspecify.html"><a href="misspecify.html#regression-1"><i class="fa fa-check"></i><b>9.3.1</b> Regression</a></li>
<li class="chapter" data-level="9.3.2" data-path="misspecify.html"><a href="misspecify.html#propensity-score"><i class="fa fa-check"></i><b>9.3.2</b> Propensity score</a></li>
<li class="chapter" data-level="9.3.3" data-path="misspecify.html"><a href="misspecify.html#double-machine-learning-method"><i class="fa fa-check"></i><b>9.3.3</b> Double machine learning method</a></li>
<li class="chapter" data-level="9.3.4" data-path="misspecify.html"><a href="misspecify.html#augmented-inverse-probability-weighting"><i class="fa fa-check"></i><b>9.3.4</b> Augmented Inverse probability weighting</a></li>
<li class="chapter" data-level="9.3.5" data-path="misspecify.html"><a href="misspecify.html#double-robust-method-tmle"><i class="fa fa-check"></i><b>9.3.5</b> Double robust method (TMLE)</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="10" data-path="guide.html"><a href="guide.html"><i class="fa fa-check"></i><b>10</b> Reporting Guidelines</a>
<ul>
<li class="chapter" data-level="10.1" data-path="guide.html"><a href="guide.html#discipline-specific-reviews"><i class="fa fa-check"></i><b>10.1</b> Discipline-specific Reviews</a></li>
<li class="chapter" data-level="10.2" data-path="guide.html"><a href="guide.html#suggested-guidelines"><i class="fa fa-check"></i><b>10.2</b> Suggested Guidelines</a></li>
<li class="chapter" data-level="10.3" data-path="guide.html"><a href="guide.html#additional-topics"><i class="fa fa-check"></i><b>10.3</b> Additional topics</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="final.html"><a href="final.html"><i class="fa fa-check"></i><b>11</b> Final Words</a>
<ul>
<li class="chapter" data-level="11.1" data-path="final.html"><a href="final.html#common-misconception"><i class="fa fa-check"></i><b>11.1</b> Common misconception</a></li>
<li class="chapter" data-level="11.2" data-path="final.html"><a href="final.html#benifits-of-ps"><i class="fa fa-check"></i><b>11.2</b> Benifits of PS</a></li>
<li class="chapter" data-level="11.3" data-path="final.html"><a href="final.html#limitations-of-ps"><i class="fa fa-check"></i><b>11.3</b> Limitations of PS</a></li>
<li class="chapter" data-level="11.4" data-path="final.html"><a href="final.html#when-ps-may-not-be-useful"><i class="fa fa-check"></i><b>11.4</b> When PS may not be useful?</a></li>
<li class="chapter" data-level="11.5" data-path="final.html"><a href="final.html#software"><i class="fa fa-check"></i><b>11.5</b> Software</a></li>
<li class="chapter" data-level="11.6" data-path="final.html"><a href="final.html#further-resources"><i class="fa fa-check"></i><b>11.6</b> Further Resources</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
<li class="divider"></li>
<li><a href="https://ehsank.com/" target="blank">Ehsan Karim</a></li>
</ul>
</nav>
</div>
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<h1>
<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Understanding Propensity Score Matching</a>
</h1>
</div>
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<div class="page-inner">
<section class="normal" id="section-">
<div id="s2" class="section level1 hasAnchor" number="5">
<h1><span class="header-section-number">Chapter 5</span> Step 2: Propensity score Matching<a href="s2.html#s2" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<ul>
<li>PS is a continuous variable.
<ul>
<li>Exact matching is not feasible.</li>
<li>Below is an example of control patient (treatment = 0) with PS = 0.25</li>
<li>We want to find a treated patient (treatment = 1) with PS closest to 0.25.</li>
</ul></li>
</ul>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="s2.html#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="fu">require</span>(cobalt)</span>
<span id="cb37-2"><a href="s2.html#cb37-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb37-3"><a href="s2.html#cb37-3" aria-hidden="true" tabindex="-1"></a><span class="fu">bal.plot</span>(analytic, <span class="at">var.name =</span> <span class="st">"PS"</span>, </span>
<span id="cb37-4"><a href="s2.html#cb37-4" aria-hidden="true" tabindex="-1"></a> <span class="at">treat =</span> <span class="st">"diabetes"</span>, </span>
<span id="cb37-5"><a href="s2.html#cb37-5" aria-hidden="true" tabindex="-1"></a> <span class="at">which =</span> <span class="st">"both"</span>, </span>
<span id="cb37-6"><a href="s2.html#cb37-6" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> analytic) <span class="sc">+</span> </span>
<span id="cb37-7"><a href="s2.html#cb37-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="at">xintercept=</span><span class="fl">0.25</span>, <span class="at">linetype=</span><span class="st">"dashed"</span>, <span class="at">color =</span> <span class="st">"red"</span>)</span></code></pre></div>
<p><img src="UnderstandingPropensityScore_files/figure-html/ps2cc444-1.png" width="672" /></p>
<div id="matching-method-nn" class="section level2 hasAnchor" number="5.1">
<h2><span class="header-section-number">5.1</span> Matching method NN<a href="s2.html#matching-method-nn" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Match using estimates propensity scores with the following choices (simplest choices)</p>
<ul>
<li><strong>Matching method</strong>:
<ul>
<li>nearest-neighbor (NN) matching</li>
</ul></li>
<li><strong>Can the same subject be chosen only once?</strong>:
<ul>
<li>matching without replacement</li>
</ul></li>
<li><strong>Closeness of the treated-untreated subjects</strong>:
<ul>
<li>with caliper = .2*SD of logit of propensity score</li>
</ul></li>
<li><strong>Ratio of treated-untreated subjects</strong>:
<ul>
<li>with 1:1 ratio (pair-matching)</li>
</ul></li>
</ul>
<p><img src="images/nn.png" width="50%" /></p>
</div>
<div id="initial-fit" class="section level2 hasAnchor" number="5.2">
<h2><span class="header-section-number">5.2</span> Initial fit<a href="s2.html#initial-fit" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>1:1 NN Match using estimates propensity scores</p>
<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="s2.html#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">123</span>)</span>
<span id="cb38-2"><a href="s2.html#cb38-2" aria-hidden="true" tabindex="-1"></a><span class="fu">require</span>(MatchIt)</span>
<span id="cb38-3"><a href="s2.html#cb38-3" aria-hidden="true" tabindex="-1"></a>match.obj <span class="ot"><-</span> <span class="fu">matchit</span>(ps.formula, <span class="at">data =</span> analytic,</span>
<span id="cb38-4"><a href="s2.html#cb38-4" aria-hidden="true" tabindex="-1"></a> <span class="at">distance =</span> <span class="st">'logit'</span>, </span>
<span id="cb38-5"><a href="s2.html#cb38-5" aria-hidden="true" tabindex="-1"></a> <span class="at">method =</span> <span class="st">"nearest"</span>, </span>
<span id="cb38-6"><a href="s2.html#cb38-6" aria-hidden="true" tabindex="-1"></a> <span class="at">replace=</span><span class="cn">FALSE</span>,</span>
<span id="cb38-7"><a href="s2.html#cb38-7" aria-hidden="true" tabindex="-1"></a> <span class="at">ratio =</span> <span class="dv">1</span>)</span>
<span id="cb38-8"><a href="s2.html#cb38-8" aria-hidden="true" tabindex="-1"></a>analytic<span class="sc">$</span>PS <span class="ot"><-</span> match.obj<span class="sc">$</span>distance</span>
<span id="cb38-9"><a href="s2.html#cb38-9" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(match.obj<span class="sc">$</span>distance)</span></code></pre></div>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.003916 0.068128 0.169946 0.211268 0.312987 0.925132</code></pre>
<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb40-1"><a href="s2.html#cb40-1" aria-hidden="true" tabindex="-1"></a>match.obj</span></code></pre></div>
<pre><code>## A matchit object
## - method: 1:1 nearest neighbor matching without replacement
## - distance: Propensity score
## - estimated with logistic regression
## - number of obs.: 1562 (original), 660 (matched)
## - target estimand: ATT
## - covariates: gender, age, race, education, married, bmi</code></pre>
</div>
<div id="fine-tuning-add-caliper" class="section level2 hasAnchor" number="5.3">
<h2><span class="header-section-number">5.3</span> Fine tuning: add caliper<a href="s2.html#fine-tuning-add-caliper" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>2 SD of logit of the propensity score is suggested as a caliper to allow better comparability of the groups.</p>
<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb42-1"><a href="s2.html#cb42-1" aria-hidden="true" tabindex="-1"></a>logitPS <span class="ot"><-</span> <span class="sc">-</span><span class="fu">log</span>(<span class="dv">1</span><span class="sc">/</span>analytic<span class="sc">$</span>PS <span class="sc">-</span> <span class="dv">1</span>) </span>
<span id="cb42-2"><a href="s2.html#cb42-2" aria-hidden="true" tabindex="-1"></a><span class="co"># logit of the propensity score</span></span>
<span id="cb42-3"><a href="s2.html#cb42-3" aria-hidden="true" tabindex="-1"></a>.<span class="dv">2</span><span class="sc">*</span><span class="fu">sd</span>(logitPS) <span class="co"># suggested in the literature</span></span></code></pre></div>
<pre><code>## [1] 0.2606266</code></pre>
<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb44-1"><a href="s2.html#cb44-1" aria-hidden="true" tabindex="-1"></a><span class="co"># choosing too strict PS has unintended consequences </span></span></code></pre></div>
<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb45-1"><a href="s2.html#cb45-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">123</span>)</span>
<span id="cb45-2"><a href="s2.html#cb45-2" aria-hidden="true" tabindex="-1"></a><span class="fu">require</span>(MatchIt)</span>
<span id="cb45-3"><a href="s2.html#cb45-3" aria-hidden="true" tabindex="-1"></a>match.obj <span class="ot"><-</span> <span class="fu">matchit</span>(ps.formula, <span class="at">data =</span> analytic,</span>
<span id="cb45-4"><a href="s2.html#cb45-4" aria-hidden="true" tabindex="-1"></a> <span class="at">distance =</span> <span class="st">'logit'</span>, </span>
<span id="cb45-5"><a href="s2.html#cb45-5" aria-hidden="true" tabindex="-1"></a> <span class="at">method =</span> <span class="st">"nearest"</span>, </span>
<span id="cb45-6"><a href="s2.html#cb45-6" aria-hidden="true" tabindex="-1"></a> <span class="at">replace=</span><span class="cn">FALSE</span>,</span>
<span id="cb45-7"><a href="s2.html#cb45-7" aria-hidden="true" tabindex="-1"></a> <span class="at">caliper =</span> .<span class="dv">2</span><span class="sc">*</span><span class="fu">sd</span>(logitPS), </span>
<span id="cb45-8"><a href="s2.html#cb45-8" aria-hidden="true" tabindex="-1"></a> <span class="at">ratio =</span> <span class="dv">1</span>)</span>
<span id="cb45-9"><a href="s2.html#cb45-9" aria-hidden="true" tabindex="-1"></a>analytic<span class="sc">$</span>PS <span class="ot"><-</span> match.obj<span class="sc">$</span>distance</span>
<span id="cb45-10"><a href="s2.html#cb45-10" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(match.obj<span class="sc">$</span>distance)</span></code></pre></div>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.003916 0.068128 0.169946 0.211268 0.312987 0.925132</code></pre>
<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb47-1"><a href="s2.html#cb47-1" aria-hidden="true" tabindex="-1"></a>match.obj</span></code></pre></div>
<pre><code>## A matchit object
## - method: 1:1 nearest neighbor matching without replacement
## - distance: Propensity score [caliper]
## - estimated with logistic regression
## - caliper: <distance> (0.045)
## - number of obs.: 1562 (original), 632 (matched)
## - target estimand: ATT
## - covariates: gender, age, race, education, married, bmi</code></pre>
</div>
<div id="things-to-keep-track-of" class="section level2 hasAnchor" number="5.4">
<h2><span class="header-section-number">5.4</span> Things to keep track of<a href="s2.html#things-to-keep-track-of" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>original sample size</li>
<li>matched sample size</li>
<li>percent reduction in sample</li>
<li>how many matched sets</li>
<li>some can be discarded because of no match; whether some sets are unequal</li>
</ul>
</div>
<div id="matches" class="section level2 hasAnchor" number="5.5">
<h2><span class="header-section-number">5.5</span> Matches<a href="s2.html#matches" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Taking a closer look at the matches</p>
<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb49-1"><a href="s2.html#cb49-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Ref: https://lists.gking.harvard.edu/pipermail/matchit/2013-October/000559.html</span></span>
<span id="cb49-2"><a href="s2.html#cb49-2" aria-hidden="true" tabindex="-1"></a>matches <span class="ot"><-</span> <span class="fu">as.data.frame</span>(match.obj<span class="sc">$</span>match.matrix)</span>
<span id="cb49-3"><a href="s2.html#cb49-3" aria-hidden="true" tabindex="-1"></a><span class="fu">colnames</span>(matches)<span class="ot"><-</span><span class="fu">c</span>(<span class="st">"matched_unit"</span>)</span>
<span id="cb49-4"><a href="s2.html#cb49-4" aria-hidden="true" tabindex="-1"></a>matches<span class="sc">$</span>matched_unit<span class="ot"><-</span><span class="fu">as.numeric</span>(</span>
<span id="cb49-5"><a href="s2.html#cb49-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.character</span>(matches<span class="sc">$</span>matched_unit))</span>
<span id="cb49-6"><a href="s2.html#cb49-6" aria-hidden="true" tabindex="-1"></a>matches<span class="sc">$</span>treated_unit<span class="ot"><-</span><span class="fu">as.numeric</span>(<span class="fu">rownames</span>(matches))</span>
<span id="cb49-7"><a href="s2.html#cb49-7" aria-hidden="true" tabindex="-1"></a>matches.only<span class="ot"><-</span>matches[<span class="sc">!</span><span class="fu">is.na</span>(matches<span class="sc">$</span>matched_unit),]</span>
<span id="cb49-8"><a href="s2.html#cb49-8" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(matches.only)</span></code></pre></div>
<pre><code>## matched_unit treated_unit
## 40 8496 40
## 56 3139 56
## 65 4192 65
## 66 94 66
## 86 2212 86
## 110 7154 110</code></pre>
<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb51-1"><a href="s2.html#cb51-1" aria-hidden="true" tabindex="-1"></a>matched.data <span class="ot"><-</span> <span class="fu">match.data</span>(match.obj)</span>
<span id="cb51-2"><a href="s2.html#cb51-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(<span class="fu">table</span>(matched.data<span class="sc">$</span>subclass))</span></code></pre></div>
<pre><code>##
## 1 2 3 4 5 6
## 2 2 2 2 2 2</code></pre>
<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb53-1"><a href="s2.html#cb53-1" aria-hidden="true" tabindex="-1"></a><span class="fu">length</span>(<span class="fu">table</span>(matched.data<span class="sc">$</span>subclass))</span></code></pre></div>
<pre><code>## [1] 316</code></pre>
</div>
<div id="other-matching-algorithms" class="section level2 hasAnchor" number="5.6">
<h2><span class="header-section-number">5.6</span> Other matching algorithms<a href="s2.html#other-matching-algorithms" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>Variable NN ratio (e.g., 1:10) is usually better.</li>
<li>matching with replacement also possible</li>
</ul>
<p>But creates issue when calculating variances (but can be easily handled by controlling for ‘matching weights’).</p>
<p>Other possibilities</p>
<ul>
<li>Optimal</li>
<li>genetic matching</li>
<li>CEM</li>
</ul>
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