Gompertz-Makeham law of mortality

The Gompertz-Makeham law states that death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age. In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.) the age-independent mortality component is often negligible, and in this case the formula simplifies to a Gompertz law of mortality (proposed by Benjamin Gompertz in 1825) with exponential increase in death rates with age.

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The Gompertz-Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window of about 30-80 years. At more advanced ages the death rates do not increase as fast as predicted by this mortality law - a phenomenon known as the late-life mortality deceleration.

Historical decline in human mortality before 1950s was mostly due to decrease in the age-independent mortality component (Makeham parameter), while the age-dependent mortality component (the Gompertz function) was surprisingly stable in history before 1950s. After that a new mortality trend has started leading to unexpected decline in mortality rates at advanced ages and 'de-rectangularization' of the survival curve.

In terms of reliability theory the Gompertz-Makeham law of mortality represents a failure law, where the hazard rate is a mixture of non-aging failure distribution, and the aging failure distribution with exponential increase in failure rates.

The Gompertz law is the same as a Fisher-Tippett distribution for the negative of age, restricted to negative values for the random variable (positive values for age).

See also

• Ageing
• Biodemography
• Biodemography of human longevity
• Biogerontology
• Demography
• Life table
• Maximum life span
• Mortality
• Reliability theory of aging and longevity

Further reading

• Leonid A. Gavrilov & Natalia S. Gavrilova (1991), The Biology of Life Span: A Quantitative Approach. New York: Harwood Academic Publisher, ISBN 978-3-7186-4983-9

• Gavrilov, L.A., Nosov, V.N. A new trend in human mortality decline: derectangularization of the survival curve. Age, 1985, 8(3): 93-93.

• Gavrilov, L.A., Gavrilova, N.S., Nosov, V.N. Human life span stopped increasing: Why? Gerontology, 1983, 29(3): 176-180. PMID 6852544

• Gompertz, B., (1825). On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society of London, Vol. 115 (1825)pp. 513-585.

• Makeham, W. M. "On the Law of Mortality and the Construction of Annuity Tables." J. Inst. Actuaries and Assur. Mag. 8, 301-310, 1860.