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.

Additional recommended knowledge

Daily Visual Balance Check

What is the Correct Way to Check Repeatability in Balances?

Guide to balance cleaning: 8 simple steps

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.