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A log-linear relationship between reported impairments and age: implications for the multistage hypothesis
W F Forbes1, M E Thompson, N Agwani
1Program in Gerontology, University of Waterloo, Ontario, Canada.
Journal of Gerontology
|January 1, 1993
Summary
Mortality and disease incidence rates show age-related patterns, often visualized with log-linear or log-log plots. This study explores impairment rates and age, suggesting a multistage model may explain these relationships.
Area of Science:
- Gerontology
- Epidemiology
- Biostatistics
Background:
- Age is a significant factor in mortality and disease incidence.
- Log-linear (Gompertz-type) and log-log plots are used to model age-related rates.
- Multistage models are often employed for incidence rate relationships.
Purpose of the Study:
- To investigate the relationship between various impairment rates and age.
- To compare log-linear and log-log plot representations for impairment rates.
- To explore potential models, including multistage models, for these relationships.
Main Methods:
- Analysis of data from the Hertfordshire Ageing Study (HALS).
- Comparison of log-linear and log-log graphical representations of impairment rates versus age.
- Consideration of multistage models for prevalence data.
Main Results:
- Both log-linear and log-log plots can represent the relationship between impairment rates and age.
- Impairment rates, being prevalence rates, may require different modeling approaches than incidence rates.
- A multistage model involving simultaneous independent events is proposed as a potential fit.
Conclusions:
- The relationship between impairment rates and age can be visualized using both log-linear and log-log plots.
- The underlying mechanisms for age-related impairments may be explained by a multistage model.
- Further investigation into simultaneous independent events is warranted for modeling prevalence.