Summary of relationships between exchangeability, biasing paths and bias

Area of Science:

• Epidemiology
• Causal Inference
• Biostatistics

Background:

• Confounding and selection bias are persistent challenges in epidemiological research.
• Evolving definitions and conceptualizations of bias have been advanced by concepts like exchangeability and causal graphs.
• The precise interrelations between bias, exchangeability, and causal graph structures require further elucidation.

Purpose of the Study:

• To summarize current definitions and views of confounding, selection bias, and exchangeability.
• To elucidate the interrelationships between bias, exchangeability, and biasing paths using causal graphs.
• To provide justification for key results concerning the implications between absence of biasing paths and exchangeability.

Main Methods:

• Review and synthesis of definitions and conceptualizations of bias and exchangeability.
• Application of causal graph frameworks to identify and represent biasing paths.
• Counterfactual model framework to define exchangeability.
• Demonstration of the relationship between absence of biasing paths and exchangeability, with and without the faithfulness assumption.

Main Results:

• Absence of a biasing path implies exchangeability.
• The reverse implication (exchangeability implies absence of a biasing path) does not necessarily hold without additional assumptions like faithfulness.
• The study demonstrates the close links between bias, exchangeability, and causal graph structures.

Conclusions:

• This work enhances the understanding of fundamental concepts in causal inference, particularly confounding, selection bias, and exchangeability.
• Clarifying the links between these concepts is vital for accurate causal effect estimation in observational studies.
• The findings facilitate more robust identification and control of bias in epidemiological research.