Case-Crossover vs Case-Control: Choosing the Right Causal Design

🎯 Context: DEPTh Classification = Etiologic (Causal) Challenge

Both designs ask: Does exposure X cause outcome Y? But their logic diverges sharply depending on exposure type, timing, and the unit of comparison.

🔬 Conceptual Foundations

Design Feature	Case-Crossover	Case-Control
Exposure	Transient or abrupt (e.g., exertion, stress, pollutant spike)	Persistent or cumulative (e.g., smoking, hypertension)
Outcome	Acute event with rapid onset (e.g., MI, injury, seizure)	Any event, acute or chronic
Study Base	Cases only – each case is their own control	Cases + Controls – selected from a source population
Comparator	Same person at different times → self-matching	Different people → matched or unmatched
Confounding control	Strong for fixed traits (e.g., sex, SES)	Requires explicit control for both fixed and time-varying confounders
Bias Risk	Exposure misclassification (especially timing); carryover effects	Control selection bias; residual confounding

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📈 Visual Sketch: Case-Crossover Timeline

Let’s plot a timeline for someone who had a myocardial infarction on Day 0:

      |------------|------------|------------|
     -30d        -14d          0           +14d
(Control)   (Control)     [MI EVENT]   (Excluded)

• Hazard window: −1 to 0 days before the event

• Control windows: −14 to −7 days, or other prior time frames

• Compare exposure odds (e.g., exertion) in hazard vs. control windows

This within-person comparison eliminates confounding by sex, chronic comorbidities, and personality.

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📚 Real-World Example

• Case-Crossover: Does heavy coffee intake trigger atrial fibrillation episodes?→ Each person with AF is compared during a "hazard" period (e.g., 24 hrs before episode) vs. prior “control” days.

• Case-Control: Does long-term coffee consumption increase AF risk?→ Compare people with AF (cases) to similar people without AF (controls), assessing average intake over years.
  

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🛡️ Causal Inference Logic

• Case-Crossover Equation:

  P(Exposure in Hazard Window) ÷ P(Exposure in Control Window)

  → Within-individual odds ratio (akin to matched pair analysis)

• Case-Control Equation:

  
  

• 
  

  → Requires careful adjustment for confounders via DAGs, stratification, or regression
  

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🧪 When to Use Which?

If your exposure is...	And the outcome is...	→ Use:
Transient (e.g., air pollution)	Sudden/acute (e.g., asthma)	Case-Crossover
Cumulative (e.g., diet pattern)	Any (e.g., cancer, DM)	Case-Control

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✅ Key Takeaways

• Case-Crossover = within-person design, best for acute-onset outcomes and short-lived exposures.

• Case-Control = between-person design, suitable for chronic exposures and rare outcomes.

• Always align design with the biological timing of the exposure-to-outcome logic.

• Misaligning design to exposure/outcome type → biased or uninterpretable findings.