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<!DOCTYPE html>
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<title>Chapter 11 Final Words | Understanding Propensity Score Matching</title>
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<meta name="twitter:title" content="Chapter 11 Final Words | Understanding Propensity Score Matching" />
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<meta name="author" content="Ehsan Karim" />
<meta name="date" content="2023-03-19" />
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<ul class="summary">
<li><a href="./">Understanding Propensity Score Matching</a></li>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Preamble</a>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html#description"><i class="fa fa-check"></i>Description</a>
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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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<h1>
<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Understanding Propensity Score Matching</a>
</h1>
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<section class="normal" id="section-">
<div id="final" class="section level1 hasAnchor" number="11">
<h1><span class="header-section-number">Chapter 11</span> Final Words<a href="final.html#final" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<div id="common-misconception" class="section level2 hasAnchor" number="11.1">
<h2><span class="header-section-number">11.1</span> Common misconception<a href="final.html#common-misconception" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>PS results = ‘causal’;</li>
<li>regression = ‘non-causal’.</li>
</ul>
<p>No. ‘Results from both methods should lead to the same conclusions.’ <span class="citation">(<a href="#ref-d1998propensity" role="doc-biblioref">D’Agostino Jr 1998</a>)</span></p>
<p>When the results deviate, important to investigate why!</p>
<p>Establishing causality requires establishing temporarily and integration of subject area expertise.</p>
</div>
<div id="benifits-of-ps" class="section level2 hasAnchor" number="11.2">
<h2><span class="header-section-number">11.2</span> Benifits of PS<a href="final.html#benifits-of-ps" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li><p><strong>Intuitive</strong>: compare two similar groups</p></li>
<li><p><strong>2-step process</strong></p>
<ul>
<li>Encourages researchers to think about the treatment generation process</li>
<li>Fit outcome model with only important variables.</li>
<li>Allowing to think more about design stage (nice separation from outcome model building process).</li>
</ul></li>
<li><p>Fit <strong>rich PS model</strong> (with higher order terms); focusing on prediction; worry less about overparameterization.</p></li>
<li><p><strong>Reduce dimension</strong>, helpful when exposure frequent but outcome rare (event per variable).</p>
<ul>
<li>Smaller outcome model may be helpful in diagnostic checks.</li>
</ul></li>
<li><p><strong>Diagnostics</strong></p>
<ul>
<li>Diagnostics (balance checking) much easier compared to residual plot/influence</li>
<li>Graphical comparison helps identify areas of non-overlap.</li>
</ul></li>
</ul>
</div>
<div id="limitations-of-ps" class="section level2 hasAnchor" number="11.3">
<h2><span class="header-section-number">11.3</span> Limitations of PS<a href="final.html#limitations-of-ps" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>Matching population vs. target population: often not the same.
<ul>
<li>PS matching may give effect estimate of a subset, which may be difficult to identify in the actual population!</li>
</ul></li>
<li>May delete a lot of subjects from the study!</li>
<li>SMD is very commonly used, but may not be enough to judge balance. Check other useful summaries.</li>
</ul>
</div>
<div id="when-ps-may-not-be-useful" class="section level2 hasAnchor" number="11.4">
<h2><span class="header-section-number">11.4</span> When PS may not be useful?<a href="final.html#when-ps-may-not-be-useful" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>When outcome is common (5 times the available number of variables), then PS may not have any advantage over rregression modelling [<a href="http://hbiostat.org/doc/bbr.pdf">ref, 17-5</a>; March 20, 2022].</li>
<li>PS can do nothing about unmeasured confounding, neither can outcome regression.
<ul>
<li>Consider instrumental variable (IV) approaches.</li>
</ul></li>
<li>Non-parametric (ML) approaches can be used to relax linearity assumption in estimating PS, but variance estimation becomes difficult.
<ul>
<li>Double robust methods should be used when non-parametric (ML) approaches are used.</li>
<li>See more on <span class="citation">Lee, Lessler, and Stuart (<a href="#ref-lee2010improving" role="doc-biblioref">2010</a>)</span>, <span class="citation">Pirracchio, Petersen, and Van Der Laan (<a href="#ref-pirracchio2015improving" role="doc-biblioref">2015</a>)</span>, <span class="citation">Alam, Moodie, and Stephens (<a href="#ref-alam2019should" role="doc-biblioref">2019</a>)</span>, <span class="citation">Naimi, Mishler, and Kennedy (<a href="#ref-naimi2017challenges" role="doc-biblioref">2017</a>)</span> and <span class="citation">Balzer and Westling (<a href="#ref-balzer2021demystifying" role="doc-biblioref">2021</a>)</span></li>
</ul></li>
</ul>
</div>
<div id="software" class="section level2 hasAnchor" number="11.5">
<h2><span class="header-section-number">11.5</span> Software<a href="final.html#software" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>Useful R packages
<ul>
<li>MatchIt</li>
<li>cobalt</li>
<li>Matching</li>
<li>twang</li>
</ul></li>
<li>Also see
<ul>
<li><a href="http://www.biostat.jhsph.edu/~estuart/propensityscoresoftware.html">Elizabeth Stuart’s Propensity Score Software Page</a> for SAS, STATA, SPSS, Excel packages</li>
</ul></li>
</ul>
</div>
<div id="further-resources" class="section level2 hasAnchor" number="11.6">
<h2><span class="header-section-number">11.6</span> Further Resources<a href="final.html#further-resources" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li><a href="https://ehsank.com/workshops/">My workshop page</a></li>
<li><a href="https://www.youtube.com/watch?v=-9W6h0MVrKI&list=PL2yD6frXhFob_Mvfg21Y01t_yu1aC9NnP&index=22">My YouTube channel</a> for related PS materials</li>
<li><a href="https://ehsank.com/webapps/">Teaching by WebApps</a>: particularly this <a href="https://ehsanx.shinyapps.io/project1/">one</a>.</li>
<li><a href="https://www.youtube.com/watch?v=T7M4r3htN2w">Understanding propensity score weighting</a></li>
<li><a href="https://ehsanx.github.io/TMLEworkshop/">More advanced methods, such as TMLE</a></li>
</ul>
</div>
</div>
<h3>References<a href="references.html#references" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-alam2019should" class="csl-entry">
Alam, Shomoita, Erica EM Moodie, and David A Stephens. 2019. <span>“Should a Propensity Score Model Be Super? The Utility of Ensemble Procedures for Causal Adjustment.”</span> <em>Statistics in Medicine</em> 38 (9): 1690–1702.
</div>
<div id="ref-balzer2021demystifying" class="csl-entry">
Balzer, Laura B, and Ted Westling. 2021. <span>“Demystifying Statistical Inference When Using Machine Learning in Causal Research.”</span> <em>American Journal of Epidemiology</em>.
</div>
<div id="ref-d1998propensity" class="csl-entry">
D’Agostino Jr, Ralph B. 1998. <span>“Propensity Score Methods for Bias Reduction in the Comparison of a Treatment to a Non-Randomized Control Group.”</span> <em>Statistics in Medicine</em> 17 (19): 2265–81.
</div>
<div id="ref-lee2010improving" class="csl-entry">
Lee, Brian K, Justin Lessler, and Elizabeth A Stuart. 2010. <span>“Improving Propensity Score Weighting Using Machine Learning.”</span> <em>Statistics in Medicine</em> 29 (3): 337–46.
</div>
<div id="ref-naimi2017challenges" class="csl-entry">
Naimi, Ashley I, Alan E Mishler, and Edward H Kennedy. 2017. <span>“Challenges in Obtaining Valid Causal Effect Estimates with Machine Learning Algorithms.”</span> <em>arXiv Preprint arXiv:1711.07137</em>.
</div>
<div id="ref-pirracchio2015improving" class="csl-entry">
Pirracchio, Romain, Maya L Petersen, and Mark Van Der Laan. 2015. <span>“Improving Propensity Score Estimators’ Robustness to Model Misspecification Using Super Learner.”</span> <em>American Journal of Epidemiology</em> 181 (2): 108–19.
</div>
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