Gompertz–Makeham Law Of Mortality
   HOME

TheInfoList



OR:

The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function, named after Benjamin Gompertz), which increases exponentially with age, and an age-independent component (the Makeham term, named after William Makeham). 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. In this case the formula simplifies to a Gompertz law of mortality. In 1825, Benjamin Gompertz proposed an exponential increase in death rates with age. __TOC__


Description

The Gompertz–Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window from about 30 to 80 years of age. At more advanced ages, some studies have found that death rates increase more slowly – a phenomenon known as the late-life mortality deceleration – but more recent studies disagree. The decline in the human
mortality rate Mortality rate, or death rate, is a measure of the number of deaths (in general, or due to a specific cause) in a particular Statistical population, population, scaled to the size of that population, per unit of time. Mortality rate is typically ...
before the 1950s was mostly due to a decrease in the age-independent (Makeham) mortality component, while the age-dependent (Gompertz) mortality component was surprisingly stable. Since the 1950s, a new mortality trend has started in the form of an unexpected decline in mortality rates at advanced ages and "rectangularization" of the survival curve. The
hazard function A hazard is a potential source of harm. Substances, events, or circumstances can constitute hazards when their nature would potentially allow them to cause damage to health, life, property, or any other interest of value. The probability of that ...
for the Gompertz-Makeham distribution is most often characterised as h(x)=\alpha e^ + \lambda . The empirical magnitude of the beta-parameter is about .085, implying a doubling of mortality every .69/.085 = 8 years (Denmark, 2006). The
quantile function In probability and statistics, the quantile function is a function Q: ,1\mapsto \mathbb which maps some probability x \in ,1/math> of a random variable v to the value of the variable y such that P(v\leq y) = x according to its probability distr ...
can be expressed in a
closed-form expression In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. ...
using the
Lambert W function In mathematics, the Lambert function, also called the omega function or product logarithm, is a multivalued function, namely the Branch point, branches of the converse relation of the function , where is any complex number and is the expone ...
: : Q(u)=\frac-\frac \ln(1-u)-\fracW_0\left frac\right/math> The Gompertz law is the same as a Fisher–Tippett distribution for the negative of age, restricted to negative values for the
random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...
(positive values for age).


See also

* Bathtub curve * Biodemography * Biodemography of human longevity *
Gerontology Gerontology ( ) is the study of the social, culture, cultural, psychology, psychological, cognitive, and biology, biological aspects of aging. The word was coined by Ilya Ilyich Mechnikov in 1903, from the Ancient Greek, Greek ('), meaning "o ...
*
Demography Demography () is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. Demographic analysis examine ...
*
Life table In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, the probability that a person of that age will die before their next birthday ("probability of death"). In ...
*
Maximum life span Maximum life span (or, for humans, maximum reported age at death) is a measure of the maximum amount of time one or more members of a population have been observed to survive between birth and death. The term can also denote an estimate of the maxi ...
* Reliability theory of aging and longevity


References

{{DEFAULTSORT:Gompertz-Makeham Law Of Mortality Actuarial science Medical aspects of death Population Senescence Statistical laws Applied probability