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Created June 4, 2025 01:46
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Examples of how the scientific estimand 'Does increasing HDL-C markers improve cardiovascular outcomes' could be answerable via a wide variety of quantitative estimands. Note, the numbers and equations should be taken lightly. They have been loosely constructed to convey the gestalt of what the HDL estimand multiverse could have looked like.
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hdl_estimand_examples.html
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>HDL Cholesterol: Eight Representative Estimands</title>
<style>
* {
margin: 0;
padding: 0;
box-sizing: border-box;
}
body {
font-family: 'Inter', -apple-system, BlinkMacSystemFont, sans-serif;
background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
min-height: 100vh;
color: #333;
padding: 20px;
}
.container {
max-width: 1600px;
margin: 0 auto;
background: white;
border-radius: 20px;
box-shadow: 0 20px 60px rgba(0,0,0,0.1);
padding: 40px;
}
.header {
text-align: center;
margin-bottom: 40px;
}
.header h1 {
font-size: 2.2rem;
font-weight: 700;
color: #1e293b;
margin-bottom: 15px;
}
.header p {
font-size: 1.1rem;
color: #64748b;
max-width: 1000px;
margin: 0 auto;
line-height: 1.6;
}
.scope-note {
background: #f0f9ff;
border-left: 4px solid #0ea5e9;
border-radius: 8px;
padding: 20px;
margin: 30px 0;
font-size: 0.95rem;
color: #0c4a6e;
line-height: 1.5;
}
.validity-warning {
background: #fef2f2;
border: 2px solid #ef4444;
color: #dc2626;
border-radius: 15px;
padding: 25px;
margin: 30px 0;
text-align: center;
}
.validity-warning h3 {
font-size: 1.3rem;
margin-bottom: 15px;
color: #dc2626;
}
.validity-warning p {
line-height: 1.6;
color: #991b1b;
}
.estimand-matrix {
display: grid;
grid-template-columns: repeat(2, 1fr);
gap: 20px;
margin: 40px 0;
}
.estimand-card {
background: #f8fafc;
border-radius: 12px;
padding: 25px;
border-left: 6px solid #667eea;
box-shadow: 0 10px 25px rgba(0,0,0,0.08);
transition: all 0.3s ease;
position: relative;
}
.estimand-card.biased {
background: #fef2f2;
border-left-color: #ef4444;
}
.estimand-card.genetic {
background: #ecfdf5;
border-left-color: #059669;
}
.estimand-card.trial {
background: #f3e8ff;
border-left-color: #7c3aed;
}
.estimand-card:hover {
transform: translateY(-3px);
box-shadow: 0 15px 35px rgba(0,0,0,0.15);
}
.estimand-number {
position: absolute;
top: 15px;
right: 15px;
width: 30px;
height: 30px;
background: #e2e8f0;
border-radius: 50%;
display: flex;
align-items: center;
justify-content: center;
font-weight: 700;
font-size: 0.9rem;
color: #1e293b;
}
.biased .estimand-number {
background: #fecaca;
color: #991b1b;
}
.genetic .estimand-number {
background: #bbf7d0;
color: #166534;
}
.trial .estimand-number {
background: #ddd6fe;
color: #5b21b6;
}
.estimand-type {
font-weight: 700;
font-size: 1.1rem;
color: #1e293b;
margin-bottom: 15px;
padding-right: 40px;
line-height: 1.3;
}
.estimand-formula {
background: white;
padding: 15px;
border-radius: 8px;
font-family: 'Monaco', 'Menlo', 'Courier New', monospace;
font-size: 0.85rem;
margin: 15px 0;
border: 1px solid #e2e8f0;
line-height: 1.5;
}
.formula-line {
margin: 6px 0;
}
.estimand-result {
font-weight: 600;
margin: 15px 0;
font-size: 1rem;
padding: 10px;
border-radius: 6px;
background: #f0fdf4;
color: #166534;
border-left: 3px solid #22c55e;
}
.biased .estimand-result {
background: #fef2f2;
color: #dc2626;
border-left-color: #ef4444;
}
.estimand-interpretation {
font-size: 0.9rem;
color: #374151;
line-height: 1.5;
margin-top: 12px;
}
.timeline-note {
background: #fffbeb;
border: 1px solid #fbbf24;
color: #92400e;
border-radius: 10px;
padding: 20px;
margin: 30px 0;
text-align: center;
}
.timeline-note h4 {
font-size: 1.1rem;
margin-bottom: 10px;
color: #78350f;
}
.key-insight {
background: #f0f9ff;
border-radius: 15px;
padding: 30px;
margin: 40px 0;
border-left: 5px solid #0ea5e9;
}
.key-insight h3 {
font-size: 1.4rem;
margin-bottom: 20px;
color: #0c4a6e;
}
.key-insight p {
line-height: 1.6;
font-size: 1.05rem;
color: #0f172a;
}
@media (max-width: 1200px) {
.estimand-matrix {
grid-template-columns: 1fr;
gap: 15px;
}
.header h1 {
font-size: 2rem;
}
.container {
padding: 25px;
}
}
.strong {
font-weight: 700;
color: #1e293b;
}
</style>
</head>
<body>
<div class="container">
<div class="header">
<h1>HDL Cholesterol: Eight Representative Estimands</h1>
<p>The same scientific question—"Does HDL cholesterol protect against cardiovascular disease?"—can be operationalized through diverse quantitative approaches across study designs and analytical methods. These eight estimands represent compelling examples of methodological diversity, illustrating how rigorous quantitative epistemology requires evidence across multiple analytical lenses. These eight estimands are exemplar approaches selected from the much larger "estimand multiverse" available for interrogating HDL-cardiovascular relationships.</p>
</div>
<div class="estimand-matrix">
<div class="estimand-card biased">
<div class="estimand-number">1</div>
<div class="estimand-type">Controls for Total Cholesterol</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Survival Model:</strong></div>
<div class="formula-line">λ(t|HDL,TC,X) = λ₀(t) × exp(β₁·HDL + β₂·TC + β₃·X)</div>
<div class="formula-line"><strong>Constraint:</strong> TC = HDL + LDL + VLDL</div>
</div>
<div class="estimand-result">HR = 0.75 (95% CI: 0.68-0.83)</div>
<div class="estimand-interpretation">
<span class="strong">Mathematical artifact:</span> Conditioning on total cholesterol creates spurious negative correlation between HDL and atherogenic lipoproteins, inflating apparent protection by ~33%.
</div>
</div>
<div class="estimand-card">
<div class="estimand-number">2</div>
<div class="estimand-type">Doesn't Control for Total Cholesterol</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Survival Model:</strong></div>
<div class="formula-line">λ(t|HDL,X) = λ₀(t) × exp(β₁·HDL + β₃·X)</div>
<div class="formula-line"><strong>Available:</strong> 1995+ in large cohorts</div>
</div>
<div class="estimand-result">HR = 0.95 (95% CI: 0.88-1.03)</div>
<div class="estimand-interpretation">
Without collider adjustment, protective association attenuates toward null. This 20% reduction in effect size was observable in early cohort studies but dismissed as "residual confounding."
</div>
</div>
<div class="estimand-card genetic">
<div class="estimand-number">3</div>
<div class="estimand-type">Mendelian Randomization via HDL Genetic Instrument</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Two-Stage Framework:</strong></div>
<div class="formula-line">Stage 1: HDL = α₀ + α₁·G + α₂·X + ε₁</div>
<div class="formula-line">Stage 2: λ(t|Ĝ,X) = λ₀(t) × exp(β·Ĝ + γ·X)</div>
<div class="formula-line"><strong>Available:</strong> 2005+ with GWAS data</div>
</div>
<div class="estimand-result">OR = 0.99 (95% CI: 0.88-1.11)</div>
<div class="estimand-interpretation">
Genetic randomization eliminates confounding through random allocation at conception. Null result provides unbiased causal estimate, directly contradicting observational findings from Estimand 1.
</div>
</div>
<div class="estimand-card trial">
<div class="estimand-number">4</div>
<div class="estimand-type">HDL-Biomarker Mediated Trial Effects</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Mediation Framework:</strong></div>
<div class="formula-line">λ(t|Z,M,X) = λ₀(t) × exp(β₁·Z + β₂·M + β₃·Z×M + γ·X)</div>
<div class="formula-line"><strong>Key Target:</strong> β₂ (biomarker-outcome association)</div>
</div>
<div class="estimand-result">β₂ ≈ 0 despite M: +30% to +100% HDL</div>
<div class="estimand-interpretation">
Multiple CETP inhibitor trials show dramatic HDL increases without cardiovascular benefit. The disconnect between biomarker change and clinical outcomes confirms HDL concentration is not causally protective.
</div>
</div>
<div class="estimand-card">
<div class="estimand-number">5</div>
<div class="estimand-type">Proportion of Treatment Effect Explained by HDL</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Mediation Framework:</strong></div>
<div class="formula-line">PME = (β_total - β_direct) / β_total</div>
<div class="formula-line"><strong>Available:</strong> 1995+ in statin trials</div>
</div>
<div class="estimand-result">PME ≈ 5-15% despite HDL increases</div>
<div class="estimand-interpretation">
Statin trials show massive cardiovascular benefits with minimal mediation through HDL changes. This proportion-mediated analysis was feasible in early statin trials but largely ignored.
</div>
</div>
<div class="estimand-card trial">
<div class="estimand-number">6</div>
<div class="estimand-type">Principal Stratum Effect via Statin Intervention</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Stratification Framework:</strong></div>
<div class="formula-line">E[Y₁ - Y₀ | S(1) = S(0) = s]</div>
<div class="formula-line"><strong>Target:</strong> Effects within HDL response groups</div>
</div>
<div class="estimand-result">Similar benefits across HDL response strata</div>
<div class="estimand-interpretation">
Patients with larger HDL responses to statins don't show correspondingly larger cardiovascular benefits. This stratified analysis contradicts HDL causality hypothesis.
</div>
</div>
<div class="estimand-card">
<div class="estimand-number">7</div>
<div class="estimand-type">Cross-Trial Biomarker-Efficacy Meta-Regression</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Meta-Regression Framework:</strong></div>
<div class="formula-line">β_j = α + γ × ΔHDL_j + ε_j</div>
<div class="formula-line"><strong>Target:</strong> γ (biomarker-efficacy relationship)</div>
</div>
<div class="estimand-result">γ ≈ 0 (no efficacy-biomarker correlation)</div>
<div class="estimand-interpretation">
Trials achieving larger HDL increases don't demonstrate greater cardiovascular benefits. Cross-trial correlation analysis provides trial-level evidence against HDL causality.
</div>
</div>
<div class="estimand-card genetic">
<div class="estimand-number">8</div>
<div class="estimand-type">Multi-Mechanism Genetic Instrument Comparison</div>
<div class="estimand-formula">
<div class="formula-line"><strong>Instrument Heterogeneity:</strong></div>
<div class="formula-line">β_HDL-specific vs β_pleiotropic</div>
<div class="formula-line"><strong>Target:</strong> Mechanism-specific effects</div>
</div>
<div class="estimand-result">Both instrument types: null effects</div>
<div class="estimand-interpretation">
Comparing "pure" HDL variants versus multi-lipid variants shows concordant null results. This rules out pathway-specific protective effects and strengthens causal inference.
</div>
</div>
</div>
<div class="timeline-note">
<h4>Historical Timeline Reality Check</h4>
<p><strong>1995-2005:</strong> Estimands 2, 3 (early GWAS), and 5 were feasible and showed attenuated/null effects. <strong>2007-2017:</strong> $15+ billion invested in CETP inhibitors despite mounting contradictory evidence. <strong>2012+:</strong> Robust MR studies (Estimand 3) consistently null. The mathematical inevitability of collider bias was knowable from first principles.</p>
</div>
<div class="key-insight">
<h3>The Power of Estimand Diversity</h3>
<p>
This matrix demonstrates why rigorous quantitative epistemology requires evidence across multiple estimands before drawing causal conclusions. While <strong>Estimand 1</strong> suggested strong protection (HR=0.75), <strong>Estimands 2-8</strong> consistently point toward null or minimal effects. The convergence across diverse methodological approaches—from bias-corrected observational analyses to genetic instruments to trial-based mediation—provides compelling evidence that HDL concentration itself is not causally protective. The HDL case serves as a paradigmatic example of how estimand confusion (reporting one quantity but interpreting it as another) can persist for decades when combined with statistical artifacts, ultimately misdirecting billions in research investment.
</p>
</div>
</div>
</body>
</html>
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