Conversion between Regression Coefficient and Relative Measure
(Exponential and Logarithmic Relationship)
Regression Coefficient Lower Limit Upper Limit
    Relative measures Lower Limit Upper Limit

If limits of Confidence Interval are Provided, The standard error can also be calculated.

Confidence Level
Standard Error of [log(Relative Measure) | Regression Coefficient]

Explanation:

  • Relative measurs include: Odds Ratio (OR), Relative Risk (RR), and Hazard Ratio (HR), all of which can be estimated through regression analysis (logistic regression, modified Poisson regression, and Cox regression).
  • Regression analysis yields a regression coefficient, which can be converted into a corresponding relative measure via exponentiation (exp(regression coefficient)).
  • Relative measures can be transformed back to regression coefficients using the natural logarithm transformation, loge(relative measure).
  • For meta-analysis of relative measures, the relative measures are first converted to regression coefficients, which are then combined. The final meta-analysis result is converted back to a relative measure for interpretation.

Reference:

[1] Rosner, Bernard (Bernard A.). Fundamentals of Biostatistics. Boston :Brooks/Cole, Cengage Learning, 2011.