Gompertz–Makeham law of mortality

Gompertz–Makeham Law of Mortality refers to a mathematical model that describes the human mortality rate as a function of age. This law combines two components: the Gompertz function, which increases exponentially with age, accounting for the age-dependent component of mortality, and the Makeham term, which is constant, representing age-independent factors that affect mortality. The Gompertz–Makeham law is a cornerstone in the field of actuarial science, demography, and gerontology, providing insights into the dynamics of aging and mortality.

Overview

The Gompertz–Makeham law posits that the human mortality rate is the sum of an age-independent component and an age-dependent component that increases exponentially with age. The formula can be expressed as:

\[ \mu(x) = \lambda + \beta e^{\alpha x} \]

where:

• \(\mu(x)\) is the force of mortality at age \(x\),
• \(\lambda\) is the Makeham term (age-independent mortality rate),
• \(\beta\) and \(\alpha\) are constants,
• \(e\) is the base of the natural logarithm,
• \(x\) is the age.

Historical Background

The law is named after Benjamin Gompertz, a British mathematician who, in 1825, first proposed the exponential increase of mortality with age. Later, William Makeham in 1860 added the constant term to account for deaths due to external causes, independent of age. This combination of their work resulted in the Gompertz–Makeham law of mortality.

Applications

The Gompertz–Makeham law has been widely used in various fields:

• In actuarial science, it helps in calculating life insurance premiums and pension costs.
• Demography uses it to analyze population dynamics and predict life expectancy trends.
• Gerontology applies it to study the biology of aging and the effectiveness of anti-aging interventions.

Limitations

While the Gompertz–Makeham law provides a robust model for understanding mortality rates, it has limitations. It may not accurately predict mortality at very young and very old ages. Additionally, the model assumes that the parameters are constant over time, which may not hold true due to advancements in medicine and changes in lifestyle.

Recent Developments

Recent research in biogerontology has focused on understanding the biological underpinnings of the Gompertz function, exploring how genetic and environmental factors influence the parameters of the model. Advances in data science and machine learning have also enabled more sophisticated models that can account for the variability and complexity of human mortality.

See Also

• Life expectancy
• Actuarial science
• Demography
• Gerontology

References

• File:USGompertzCurve.svg