Bias factor, maximum bias and the E-value: insight and extended applications.

Area of Science:

• Epidemiology
• Biostatistics
• Observational Studies

Background:

• Unmeasured confounding can distort the relationship between exposures and outcomes in observational research.
• Sensitivity analyses, like the E-value, aim to adjust for such biases but face limitations.
• The E-value offers a user-friendly approach to assess the robustness of causal evidence against unmeasured confounding.

Purpose of the Study:

• To address practical limitations of the current E-value calculation.
• To expand the applicability of the E-value to all confounding scenarios, including those with negative confounder-outcome associations.
• To provide E-value calculations interpretable on the odds ratio scale.

Main Methods:

• Explored the relationship between bias factor and B bias, the statistical underpinnings of the E-value.
• Developed novel E-value formulas for previously inapplicable situations.
• Derived E-value formulas for the odds ratio scale.

Main Results:

• New E-value formulas increase applicability across diverse confounding scenarios (e.g., negative confounder-outcome relations).
• E-value calculations are now available on the odds ratio scale, aligning interpretation with observed data.
• The expanded E-value provides a more versatile tool for sensitivity analyses.

Conclusions:

• The E-value is a valuable component of modern sensitivity analyses for unmeasured confounding.
• Expanded formulas enhance the E-value's utility and address its limitations.
• The enhanced E-value facilitates more robust causal inference from observational studies.