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<h1 class="quarto-secondary-nav-title"><span class="chapter-number">21</span> <span class="chapter-title">hdDRS with a binary outcome</span></h1>
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<h2 id="toc-title">Table of contents</h2>
<ul>
<li><a href="#step-0-analytic-data" id="toc-step-0-analytic-data" class="nav-link active" data-scroll-target="#step-0-analytic-data"><span class="toc-section-number">21.1</span> Step 0: Analytic data</a></li>
<li><a href="#step-6-disease-risk-score-drs" id="toc-step-6-disease-risk-score-drs" class="nav-link" data-scroll-target="#step-6-disease-risk-score-drs"><span class="toc-section-number">21.2</span> Step 6: Disease risk score (DRS)</a>
<ul class="collapse">
<li><a href="#create-drs-formula" id="toc-create-drs-formula" class="nav-link" data-scroll-target="#create-drs-formula"><span class="toc-section-number">21.2.1</span> Create DRS formula</a></li>
<li><a href="#unexposed-cohort" id="toc-unexposed-cohort" class="nav-link" data-scroll-target="#unexposed-cohort"><span class="toc-section-number">21.2.2</span> Unexposed cohort</a></li>
<li><a href="#fit-drs-model" id="toc-fit-drs-model" class="nav-link" data-scroll-target="#fit-drs-model"><span class="toc-section-number">21.2.3</span> Fit DRS model</a></li>
<li><a href="#obtain-drs" id="toc-obtain-drs" class="nav-link" data-scroll-target="#obtain-drs"><span class="toc-section-number">21.2.4</span> Obtain DRS</a></li>
</ul></li>
<li><a href="#step-7-association" id="toc-step-7-association" class="nav-link" data-scroll-target="#step-7-association"><span class="toc-section-number">21.3</span> Step 7: Association</a>
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<li><a href="#adjtsing-for-deciles-of-drs" id="toc-adjtsing-for-deciles-of-drs" class="nav-link" data-scroll-target="#adjtsing-for-deciles-of-drs"><span class="toc-section-number">21.3.1</span> Adjtsing for deciles of DRS</a></li>
<li><a href="#adjtsing-for-deciles-of-drs-and-covariates" id="toc-adjtsing-for-deciles-of-drs-and-covariates" class="nav-link" data-scroll-target="#adjtsing-for-deciles-of-drs-and-covariates"><span class="toc-section-number">21.3.2</span> Adjtsing for deciles of DRS and covariates</a></li>
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<h1 class="title d-none d-lg-block"><span class="chapter-number">21</span> <span class="chapter-title">hdDRS with a binary outcome</span></h1>
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<p>Similar to hdPS, there are seven steps in High-dimensional disease risk score (hdDRS). However, the sixth step is different. In the sixth step, we fit a propensity score model in the hdPS analysis, while we fit a disease risk score model in the hdDRS analysis. Moreover in the seventh step, estimating the treatment/exposure effect with the matched or inverse probability weighted data is a popular choice in the hdPS analysis, while adjusting for deciles of the disease risk score is a popular choice in the hdDRS analysis.</p>
<table class="table">
<thead>
<tr class="header">
<th>#</th>
<th>hdPS</th>
<th>hdDRS</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Step 1</td>
<td>Proxy sources</td>
<td>Proxy sources</td>
</tr>
<tr class="even">
<td>Step 2</td>
<td>Empirical</td>
<td>Empirical</td>
</tr>
<tr class="odd">
<td>Step 3</td>
<td>Recurrence</td>
<td>Recurrence</td>
</tr>
<tr class="even">
<td>Step 4</td>
<td>Prioritize</td>
<td>Prioritize</td>
</tr>
<tr class="odd">
<td>Step 5</td>
<td>Covariates</td>
<td>Covariates</td>
</tr>
<tr class="even">
<td>Step 6</td>
<td>Propensity score</td>
<td>Disease risk score</td>
</tr>
<tr class="odd">
<td>Step 7</td>
<td>Association</td>
<td>Association</td>
</tr>
</tbody>
</table>
<div class="callout-tip callout callout-style-default callout-captioned">
<div class="callout-header d-flex align-content-center">
<div class="callout-icon-container">
<i class="callout-icon"></i>
</div>
<div class="callout-caption-container flex-fill">
hdPS vs hdDRS
</div>
</div>
<div class="callout-body-container callout-body">
<ul>
<li>Utilizing these empirically identified proxies with investigator-specified measured confounders, the hdPS and hdDRS are proposed to reduce residual confounding bias.</li>
<li>Both methods have seven steps.</li>
<li>The sixth step is different: in the hdPS analysis, we we model the exposure (propensity score model), while in the hdDRS analysis, we model the outcome (disease risk score model).</li>
</ul>
</div>
</div>
<div class="no-row-height column-margin column-container"><div class="">
<p><span class="citation" data-cites="kumamaru2016comparison hossain2025harnessing2">(<a href="references.html#ref-kumamaru2016comparison" role="doc-biblioref">Kumamaru et al. 2016</a>; <a href="references.html#ref-hossain2025harnessing2" role="doc-biblioref">Hossain 2025</a>)</span></p>
</div></div><section id="step-0-analytic-data" class="level2" data-number="21.1">
<h2 data-number="21.1" class="anchored" data-anchor-id="step-0-analytic-data"><span class="header-section-number">21.1</span> Step 0: Analytic data</h2>
<p>We will use the same NHANES data for this hdDRS demonstration as we did for the hdPS with a binary exposure and a binary outcome demonstration.</p>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-2_d129f175eb4b4fca65ef4b56e27db6ff">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">dim</span>(hdps.data)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="co">#> [1] 3839 78</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="step-6-disease-risk-score-drs" class="level2 page-columns page-full" data-number="21.2">
<h2 data-number="21.2" class="anchored" data-anchor-id="step-6-disease-risk-score-drs"><span class="header-section-number">21.2</span> Step 6: Disease risk score (DRS)</h2>
<p>Hansen (2008) shows that the DRS has a balancing property, called prognostic balance. Individuals sharing a similar DRS value can be regarded as having the same risk/prognosis for the outcome. In contrast, the propensity score has a covariate balance property.</p>
<div class="no-row-height column-margin column-container"><div class="">
<p><span class="citation" data-cites="hansen2008prognostic">(<a href="references.html#ref-hansen2008prognostic" role="doc-biblioref">Hansen 2008</a>)</span></p>
</div></div><section id="create-drs-formula" class="level3" data-number="21.2.1">
<h3 data-number="21.2.1" class="anchored" data-anchor-id="create-drs-formula"><span class="header-section-number">21.2.1</span> Create DRS formula</h3>
<p>With a binary outcome, there are two approaches to estimate the disease risk score (DRS):</p>
<ul>
<li>Fitting DRS model on unexposed individuals: Covariates include the investigator-specified and empirical covariates</li>
<li>Fitting DRS model on the full cohort: Covariates include the exposure, investigator-specified and empirical covariates.</li>
</ul>
<p>In this example, we will focus on fitting the DRS model on unexposed individuals:</p>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-3_9a34ea95214b7677e26776d138a19d0d">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>hdps.data<span class="sc">$</span>outcome <span class="ot"><-</span> <span class="fu">as.numeric</span>(<span class="fu">I</span>(hdps.data<span class="sc">$</span>diabetes<span class="sc">==</span><span class="st">'Yes'</span>))</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>proxy.list.sel <span class="ot"><-</span> <span class="fu">names</span>(out3<span class="sc">$</span>autoselected_covariate_df[,<span class="sc">-</span><span class="dv">1</span>])</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>proxyform <span class="ot"><-</span> <span class="fu">paste0</span>(proxy.list.sel, <span class="at">collapse =</span> <span class="st">"+"</span>)</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>covform <span class="ot"><-</span> <span class="fu">paste0</span>(investigator.specified.covariates, <span class="at">collapse =</span> <span class="st">" + "</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-4_047488db91dca7c0be96a5dddaf7d7bd">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>rhsformula <span class="ot"><-</span> <span class="fu">paste0</span>(<span class="fu">c</span>(covform, proxyform), <span class="at">collapse =</span> <span class="st">"+"</span>)</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>drs.formula <span class="ot"><-</span> <span class="fu">as.formula</span>(<span class="fu">paste0</span>(<span class="st">"outcome"</span>, <span class="st">"~"</span>, rhsformula))</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>drs.formula</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="co">#> outcome ~ age.cat + sex + education + race + marital + income + </span></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a><span class="co">#> born + year + diabetes.family.history + medical.access + </span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a><span class="co">#> smoking + diet.healthy + physical.activity + sleep + uric.acid + </span></span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a><span class="co">#> protein.total + bilirubin.total + phosphorus + sodium + potassium + </span></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a><span class="co">#> globulin + calcium.total + systolicBP + diastolicBP + high.cholesterol + </span></span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_I10_once + rec_dx_R73_once + rec_dx_I10_frequent + </span></span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_R60_once + rec_dx_E78_once + rec_dx_M79_once + rec_dx_I51_once + </span></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_M10_once + rec_dx_I50_once + rec_dx_K21_once + rec_dx_D75_once + </span></span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_Z79_once + rec_dx_F41_once + rec_dx_M1A_once + rec_dx_E87_once + </span></span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_R12_once + rec_dx_R51_once + rec_dx_J45_once + rec_dx_I50_frequent + </span></span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_L70_once + rec_dx_M25_once + rec_dx_I63_once + rec_dx_R39_once + </span></span>
<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_N28_once + rec_dx_K25_once + rec_dx_F90_once + rec_dx_B00_once + </span></span>
<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_J42_once + rec_dx_R41_once + rec_dx_I20_once + rec_dx_M54_once + </span></span>
<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_J44_once + rec_dx_K08_once + rec_dx_I21_once + rec_dx_F32_once + </span></span>
<span id="cb3-18"><a href="#cb3-18" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_J30_once + rec_dx_F43_once + rec_dx_R06_once + rec_dx_I48_once + </span></span>
<span id="cb3-19"><a href="#cb3-19" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_R32_once + rec_dx_R42_once + rec_dx_N92_once + rec_dx_N95_once + </span></span>
<span id="cb3-20"><a href="#cb3-20" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_M19_once + rec_dx_E07_once + rec_dx_R25_once + rec_dx_G43_once + </span></span>
<span id="cb3-21"><a href="#cb3-21" aria-hidden="true" tabindex="-1"></a><span class="co">#> rec_dx_R52_once + rec_dx_M81_once + rec_dx_T78_once</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="unexposed-cohort" class="level3" data-number="21.2.2">
<h3 data-number="21.2.2" class="anchored" data-anchor-id="unexposed-cohort"><span class="header-section-number">21.2.2</span> Unexposed cohort</h3>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-5_9fe0d9b7390153de38621d06285174e2">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Unexposed cohort</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>dat.unexposed <span class="ot"><-</span> <span class="fu">subset</span>(hdps.data, obese <span class="sc">==</span> <span class="st">"No"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="fit-drs-model" class="level3" data-number="21.2.3">
<h3 data-number="21.2.3" class="anchored" data-anchor-id="fit-drs-model"><span class="header-section-number">21.2.3</span> Fit DRS model</h3>
<p>Here we fit a logistic regression model on the unexposed individuals. Similar to the hdPS example, we are adding only the main effects in the non-transformed form.</p>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-6_154fd149203935b13db42e3fc519a462">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>fit.drs <span class="ot"><-</span> <span class="fu">glm</span>(drs.formula, <span class="at">data =</span> dat.unexposed, <span class="at">family =</span> binomial)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="obtain-drs" class="level3 page-columns page-full" data-number="21.2.4">
<h3 data-number="21.2.4" class="anchored" data-anchor-id="obtain-drs"><span class="header-section-number">21.2.4</span> Obtain DRS</h3>
<p>Now we can obtain the DRS for the full cohort and check the summary. Unlike in hdPS, balance checking is difficult in hdDRS analysis. There are some proposed matching and weighting techniques with hdDRS where balance checking is possible. These techniques are developed/proposed with only investigator-specified covariates. In this demonstration, we adjust our outcome model for deciles of the DRS, which is a common practice in the hdDRS literature.</p>
<div class="no-row-height column-margin column-container"><div class="">
<p><span class="citation" data-cites="wyss2015matching nguyen2024confounder">(<a href="references.html#ref-wyss2015matching" role="doc-biblioref">Wyss et al. 2015</a>; <a href="references.html#ref-nguyen2024confounder" role="doc-biblioref">Nguyen et al. 2024</a>)</span></p>
</div></div><div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-7_ac9bdc7800c28c1ea2f15ccf1ca7de33">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>hdps.data<span class="sc">$</span>drs <span class="ot"><-</span> <span class="fu">predict</span>(fit.drs, <span class="at">type =</span> <span class="st">"response"</span>, <span class="at">newdata =</span> hdps.data)</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Sumamry</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(hdps.data<span class="sc">$</span>drs)</span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="co">#> Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="co">#> 0.00000 0.01666 0.07709 0.19312 0.26457 0.99992</span></span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a><span class="co"># Summary by exposure status</span></span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a><span class="fu">tapply</span>(hdps.data<span class="sc">$</span>drs, hdps.data<span class="sc">$</span>obese, summary)</span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a><span class="co">#> $No</span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a><span class="co">#> Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a><span class="co">#> 0.00000 0.01664 0.06980 0.17814 0.23025 0.99963 </span></span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a><span class="co">#> </span></span>
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a><span class="co">#> $Yes</span></span>
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a><span class="co">#> Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a><span class="co">#> 0.00000 0.01670 0.08679 0.21374 0.30472 0.99992</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
</section>
<section id="step-7-association" class="level2" data-number="21.3">
<h2 data-number="21.3" class="anchored" data-anchor-id="step-7-association"><span class="header-section-number">21.3</span> Step 7: Association</h2>
<section id="adjtsing-for-deciles-of-drs" class="level3" data-number="21.3.1">
<h3 data-number="21.3.1" class="anchored" data-anchor-id="adjtsing-for-deciles-of-drs"><span class="header-section-number">21.3.1</span> Adjtsing for deciles of DRS</h3>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-8_65ecca397c81c9e641ae995fb2bd8546">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Deciles of DRS</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>hdps.data<span class="sc">$</span>drs.decile <span class="ot"><-</span> <span class="fu">as.factor</span>(dplyr<span class="sc">::</span><span class="fu">ntile</span>(hdps.data<span class="sc">$</span>drs, <span class="dv">10</span>))</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Outcome analysis</span></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>fit.hddrs <span class="ot"><-</span> <span class="fu">glm</span>(outcome <span class="sc">~</span> obese <span class="sc">+</span> drs.decile, </span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> hdps.data,</span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> binomial)</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a><span class="fu">publish</span>(fit.hddrs, <span class="at">pvalue.method =</span> <span class="st">"robust"</span>, <span class="at">confint.method =</span> <span class="st">"robust"</span>, </span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a> <span class="at">print =</span> F)<span class="sc">$</span>regressionTable[<span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>,]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</section>
<section id="adjtsing-for-deciles-of-drs-and-covariates" class="level3" data-number="21.3.2">
<h3 data-number="21.3.2" class="anchored" data-anchor-id="adjtsing-for-deciles-of-drs-and-covariates"><span class="header-section-number">21.3.2</span> Adjtsing for deciles of DRS and covariates</h3>
<p>Another popular approach is to adjust for deciles of the DRS as well as for the investigator-specified covariates:</p>
<div class="cell" data-hash="hddrs1_cache/html/unnamed-chunk-9_331ee781bfb67e953c2940d6f19a7cdb">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Outcome analysis</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>fit.hddrs1 <span class="ot"><-</span> <span class="fu">glm</span>(outcome <span class="sc">~</span> obese <span class="sc">+</span> drs.decile <span class="sc">+</span> age.cat <span class="sc">+</span> sex <span class="sc">+</span> education <span class="sc">+</span> </span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> race <span class="sc">+</span> marital <span class="sc">+</span> income <span class="sc">+</span> born <span class="sc">+</span> year <span class="sc">+</span> </span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a> diabetes.family.history <span class="sc">+</span> medical.access <span class="sc">+</span> smoking <span class="sc">+</span> </span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a> diet.healthy <span class="sc">+</span> physical.activity <span class="sc">+</span> sleep <span class="sc">+</span> uric.acid <span class="sc">+</span> </span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a> protein.total <span class="sc">+</span> bilirubin.total <span class="sc">+</span> phosphorus <span class="sc">+</span> sodium <span class="sc">+</span> </span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a> potassium <span class="sc">+</span> globulin <span class="sc">+</span> calcium.total <span class="sc">+</span> systolicBP <span class="sc">+</span> </span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a> diastolicBP <span class="sc">+</span> high.cholesterol, <span class="at">data =</span> hdps.data,</span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> binomial)</span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a><span class="fu">publish</span>(fit.hddrs1, <span class="at">pvalue.method =</span> <span class="st">"robust"</span>, <span class="at">confint.method =</span> <span class="st">"robust"</span>, </span>
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a> <span class="at">print =</span> F)<span class="sc">$</span>regressionTable[<span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>,]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div id="refs" class="references csl-bib-body hanging-indent" role="doc-bibliography" style="display: none">
<div id="ref-hansen2008prognostic" class="csl-entry" role="doc-biblioentry">
Hansen, Ben B. 2008. <span>“The Prognostic Analogue of the Propensity Score.”</span> <em>Biometrika</em> 95 (2): 481–88.
</div>
<div id="ref-hossain2025harnessing2" class="csl-entry" role="doc-biblioentry">
Hossain, Md Belal. 2025. <span>“Chapter 2: High-Dimensional Disease Risk Score for Dealing with Residual Confounding in Estimating Treatment Effects with a Survival Outcome.”</span> In. Harnessing the power of causal inference; predictive analytics for survival outcomes with health administrative data: applications to tuberculosis research.
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<div id="ref-kumamaru2016comparison" class="csl-entry" role="doc-biblioentry">
Kumamaru, Hiraku, Joshua J Gagne, Robert J Glynn, Soko Setoguchi, and Sebastian Schneeweiss. 2016. <span>“Comparison of High-Dimensional Confounder Summary Scores in Comparative Studies of Newly Marketed Medications.”</span> <em>Journal of Clinical Epidemiology</em> 76: 200–208.
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Nguyen, Tri-Long, Thomas PA Debray, Bora Youn, Gabrielle Simoneau, and Gary S Collins. 2024. <span>“Confounder Adjustment Using the Disease Risk Score: A Proposal for Weighting Methods.”</span> <em>American Journal of Epidemiology</em> 193 (2): 377–88.
</div>
<div id="ref-wyss2015matching" class="csl-entry" role="doc-biblioentry">
Wyss, Richard, Alan R Ellis, M Alan Brookhart, Michele Jonsson Funk, Cynthia J Girman, Ross J Simpson Jr, and Til Stürmer. 2015. <span>“Matching on the Disease Risk Score in Comparative Effectiveness Research of New Treatments.”</span> <em>Pharmacoepidemiology and Drug Safety</em> 24 (9): 951–61.
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