science

Late-life mortality deceleration

Late-life mortality deceleration is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Late-life mortality deceleration rather than just read about it. In short: In gerontology, late-life mortality deceleration is the disputed theory that hazard rate increases at a decreasing rate in late life rather than increasing exponentially as in the Gompertz law. Late-life mortality deceleration is a well-established phenomenon in insects, which often spend much of their lives in a constant hazard rate region, but it is much more controversial in mammals.

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Reference excerpt

In gerontology, late-life mortality deceleration is the disputed theory that hazard rate increases at a decreasing rate in late life rather than increasing exponentially as in the Gompertz law. Late-life mortality deceleration is a well-established phenomenon in insects, which often spend much of their lives in a constant hazard rate region, but it is much more controversial in mammals. Rodent studies have found varying conclusions, with some finding short-term periods of mortality deceleration in mice, others not finding such. Baboon studies show no mortality deceleration. An analogous deceleration occurs in the failure rate of manufactured products; this analogy is elaborated in the reliability theory of aging and longevity. Late-life mortality deceleration was first proposed as occurring in human aging in Gompertz (1825) (which also introduced the Gompertz law), and observed as occurring in humans in Greenwood & Irwin (1939), and has since become one of the pillars of the biodemography of human longevity – see history; here "late life" is typically "after 85 years of age". However, a recent paper, Gavrilov & Gavrilova (2011), concludes that mortality deceleration is negligible up to the age of 106 in the population studied (beyond this point, reliable data were unavailable) and that the Gompertz law is a good fit, with previous observations of deceleration being spurious, with various causes, including bad data and methodological problems – see criticism. According to a 2018 paper, statistical errors are the main cause of apparent mortality deceleration in humans.

Phenomena Three related terms are used in this context:

Late-life mortality deceleration Hazard rate increasing at a decreasing rate (rather than increasing log-linearly as in the Gompertz law). Mortality leveling-off More strongly, hazard rate eventually stops increasing (or rather, asymptotes towards a limit), and then proceeds at a constant rate (or rather, approaches a constant rate), yielding (slightly sub-) exponential decay, as in radioactive decay. Late-life mortality plateau This is used synonymously with "mortality leveling-off", or rather to refer to the region where hazard rate is approximately constant.

History A brief historical review is given in Gavrilov & Gavrilova (2011, 2. Mortality at Advanced Ages: A Historical Review (pp. 433–435)); a detailed survey is given in Olshansky (1998). Late-life mortality deceleration was first proposed as occurring in human aging, in Gompertz (1825), which also introduced the Gompertz law. It was observed and quantified in Greenwood & Irwin (1939), and reproduced in many later studies. Greenwood and Irwin wrote:

"the increase of mortality rate with age advances at a slackening rate, that nearly all, perhaps all, methods of graduation of the type of Gompertz's formula over-state senile mortality" "the possibility that with advancing age the rate of mortality asymptotes to a finite value" "the limiting values of qx [one-year probability of death] are 0.439 for women and 0.544 for men" Following these studies, late-life mortality deceleration became one of the pillars of the theory of biodemography of human longevity, and models have incorporated it. It has been criticized at times, and recently has been very seriously criticized; see below.

Criticism Statistical studies of extreme longevity are difficult for a number of factors. Firstly, because few people live to very old ages, a very large population is required for such studies, ideally all born and living in similar conditions (same country, same birth year). In small countries, a single birth year cohort is insufficiently numerous for statistics, and thus multiple years are often used. Secondly, due to the great ages, accurate records of persons living over 100 years require records dating from the late 19th or early 20th century, when such record-keeping was often not high-quality; further, there is a tendency to exaggerate one's age, which distorts data. Thirdly, granularity is an issue – ideally exact day of birth and death would be used; using only year of birth and death introduces granularity, which adds bias (as discussed below). Gavrilov & Gavrilova (2011) examined single birth-year cohorts from the United States Death Master File, using the method of extinct generations, and found that the effect disappeared if various distorting factors were removed. Specifically, they conclude that mortality deceleration is negligible up to the age of 106 in the population studied (beyond this point, reliable data were unavailable) and that the Gompertz law is a good fit, with previous observations of deceleration being spurious, with various causes, discussed below.

Why was mortality deceleration observed? Given that mortality deceleration in humans had been observed in various studies, but disappeared on the careful analysis (of single-year cohorts in the US) in Gavrilov & Gavrilova (2011), it is natural to ask what causes this discrepancy – why was mortality deceleration observed? Gavrilov & Gavrilova (2011) propose several causes; notably, in each instance when such a factor is corrected or diminished, the fit with the Gompertz law becomes better. Data quality:

Age exaggeration There is at times a tendency for old people to exaggerate their ages; this reduces apparent age-specific mortality rates. Technical:

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Illustrations

Worked examples

Example 1 — a first encounter with Late-life mortality deceleration

Start with the simplest possible case. Write down what Late-life mortality deceleration claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Late-life mortality deceleration before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Late-life mortality deceleration ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Late-life mortality deceleration

In research: Late-life mortality deceleration appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Late-life mortality deceleration in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Late-life mortality deceleration is common in secondary-school and first-year university syllabi. It links to neighbouring topics Actuarial science, Senescence, so understanding it makes those chapters shorter.
In everyday life: Look for Late-life mortality deceleration outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

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Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

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