A simple model for linking life tables by survival-mortality ratios

Area of Science:

• Demography
• Biostatistics
• Epidemiology

Background:

• Mortality patterns are crucial for public health and population studies.
• Analyzing changes in life table functions provides insights into demographic shifts.
• Existing methods may have limitations in projecting long-term mortality trends.

Purpose of the Study:

• To propose a new mathematical model for understanding and projecting changes in mortality over time.
• To establish a relationship between survivorship probabilities at different time points.

Main Methods:

• A mathematical model was developed assuming the rate of change in survivorship probability is proportional to its current value and the probability of dying.
• The model's core result is a linear relationship between the logit functions of survivorship probabilities at different times.
• The model was validated using U.S. life tables (1950, 1970) and Coale and Demeny's regional model life tables.

Main Results:

• The proposed model establishes a linear relationship with a slope of one between the logit functions of survivorship probabilities at different time points.
• The model demonstrated strong predictive accuracy when tested with U.S. life tables.
• The model showed accurate projections even with significant differences in life expectancy (up to 20 years) when using regional model life tables.

Conclusions:

• The developed model offers a robust and accurate method for analyzing and projecting mortality variation.
• The linear relationship identified provides a simplified yet powerful tool for demographic analysis.
• This approach has significant implications for population studies, public health policy, and actuarial science.