A formal causal interpretation of the case-crossover design

Area of Science:

• Epidemiology
• Causal Inference
• Biostatistics

Background:

• The case-crossover design is frequently used to assess transient exposures' effects on acute outcomes.
• Previous justifications for its validity and causal interpretation were informal.
• A formal counterfactual framework has not been applied to this design until now.

Purpose of the Study:

• To formally place the case-crossover design within a counterfactual framework.
• To clarify the assumptions and interpretation of the case-crossover design.
• To identify and analyze potential biases in the case-crossover design.

Main Methods:

• Formal counterfactual framework applied to the case-crossover design.
• Identification and analysis of bias due to common causes of the outcome.
• Simulations to demonstrate the bias's importance.
• Derivation of the estimator's limit to analyze sensitivity to treatment effect heterogeneity.

Main Results:

• A previously unrecognized bias arises from strong common causes of the outcome at different person-times when the treatment effect is non-null.
• The case-crossover estimator's sensitivity to treatment effect heterogeneity was analyzed.
• Simulations confirmed the potential importance of the identified bias.

Conclusions:

• The case-crossover design can be valuable for testing the causal null hypothesis with baseline confounders.
• Practitioners should exercise increased caution when using the case-crossover design for point estimation of causal effects due to potential bias.