"Translating" All-Cause Mortality Rate Ratios or Hazard Ratios to Age-, Longevity-, and Probability-Based Measures

Area of Science:

• Epidemiology
• Biostatistics
• Demography

Background:

• Epidemiologists frequently use hazard ratios (HR) or standardized mortality ratios (SMR) to compare mortality rates.
• These ratios are often difficult for the public to interpret in terms of real-world impact.
• Translating these statistical measures into more intuitive metrics like longevity differences is rarely done.

Purpose of the Study:

• To describe the appropriate conditions for translating mortality ratios into age-, time-, or probability-based measures.
• To provide heuristics for understanding these translation formulas.
• To clarify the limitations of different translation methods.

Main Methods:

• Review of existing literature on translating hazard ratios and standardized mortality ratios.
• Analysis of the mathematical conditions under which different translation metrics are valid.
• Explanation of the assumptions and limitations of "effective age" and "probability of being outlived" metrics.

Main Results:

• The "effective age" and longevity difference metrics are appropriate only when the hazard ratio is constant across ages and mortality rates are log-linear with age.
• "Probability/odds of being outlived" is applicable when the hazard ratio is constant, but does not quantify the magnitude of age or longevity differences.
• The study outlines the specific settings where each translation method is valid and provides underlying principles.

Conclusions:

• Translating mortality ratios into intuitive measures like longevity or effective age enhances communication.
• Understanding the specific conditions and limitations of these translations is crucial for accurate interpretation.
• The "probability of being outlived" metric offers broader applicability but less specific magnitude information than "effective age" or longevity differences.