The analysis of survival (mortality) data: Fitting Gompertz, Weibull, and logistic functions

David L. Wilson

Research output: Contribution to journalArticle

113 Citations (Scopus)

Abstract

Survival functions are fitted to survival data from several large populations. The Gompertz survival function corresponds to exponential mortality rate increases with time. The Weibull survival function corresponds to mortality rates that increase as a power function of time. A two-parameter, logistic survival function is introduced, and corresponds to mortality rates that increase, and then decrease, with time. A three-parameter logistic-mortality function also is examined. It reflects mortality rates that rise, and then plateau, with age. Data are from published studies of medflies, Drosophila, house flies, flour beetles, and humans. Some survival data are better fit by a logistic survival function than by the more traditionally used Gompertz or Weibull functions. Gompertz, Weibull, or logistic survival functions often fit the survival of 95+% of a population, and the 'tails' of the survival curves usually appear to fall between the values predicted by the three functions. For some populations, such 'tails' appear to be too complex to be fit well by any simple function. Survival data for males and females in some populations are best fit by different functions. Populations of 100 or more are needed to distinguish among the functions. When testing effects of environmental or genetic manipulations on survival, it has been common to determine the changes in parameter values for a given function, such as Gompertz. It may be equally important to determine whether the best-fit function has changed as well.

Original languageEnglish
Pages (from-to)15-33
Number of pages19
JournalMechanisms of Ageing and Development
Volume74
Issue number1-2
DOIs
StatePublished - Jan 1 1994

Fingerprint

Survival Analysis
Logistics
Survival
Mortality
Population
Tail
Ceratitis capitata
Beetles
Flour
Diptera
Drosophila

Keywords

  • Aging
  • Gompertz
  • Mortality

ASJC Scopus subject areas

  • Aging
  • Biochemistry
  • Developmental Biology
  • Developmental Neuroscience

Cite this

The analysis of survival (mortality) data : Fitting Gompertz, Weibull, and logistic functions. / Wilson, David L.

In: Mechanisms of Ageing and Development, Vol. 74, No. 1-2, 01.01.1994, p. 15-33.

Research output: Contribution to journalArticle

@article{3b4afa13ebfb4f47af575fef5851d47f,
title = "The analysis of survival (mortality) data: Fitting Gompertz, Weibull, and logistic functions",
abstract = "Survival functions are fitted to survival data from several large populations. The Gompertz survival function corresponds to exponential mortality rate increases with time. The Weibull survival function corresponds to mortality rates that increase as a power function of time. A two-parameter, logistic survival function is introduced, and corresponds to mortality rates that increase, and then decrease, with time. A three-parameter logistic-mortality function also is examined. It reflects mortality rates that rise, and then plateau, with age. Data are from published studies of medflies, Drosophila, house flies, flour beetles, and humans. Some survival data are better fit by a logistic survival function than by the more traditionally used Gompertz or Weibull functions. Gompertz, Weibull, or logistic survival functions often fit the survival of 95+{\%} of a population, and the 'tails' of the survival curves usually appear to fall between the values predicted by the three functions. For some populations, such 'tails' appear to be too complex to be fit well by any simple function. Survival data for males and females in some populations are best fit by different functions. Populations of 100 or more are needed to distinguish among the functions. When testing effects of environmental or genetic manipulations on survival, it has been common to determine the changes in parameter values for a given function, such as Gompertz. It may be equally important to determine whether the best-fit function has changed as well.",
keywords = "Aging, Gompertz, Mortality",
author = "Wilson, {David L.}",
year = "1994",
month = "1",
day = "1",
doi = "10.1016/0047-6374(94)90095-7",
language = "English",
volume = "74",
pages = "15--33",
journal = "Mechanisms of Ageing and Development",
issn = "0047-6374",
publisher = "Elsevier Ireland Ltd",
number = "1-2",

}

TY - JOUR

T1 - The analysis of survival (mortality) data

T2 - Fitting Gompertz, Weibull, and logistic functions

AU - Wilson, David L.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - Survival functions are fitted to survival data from several large populations. The Gompertz survival function corresponds to exponential mortality rate increases with time. The Weibull survival function corresponds to mortality rates that increase as a power function of time. A two-parameter, logistic survival function is introduced, and corresponds to mortality rates that increase, and then decrease, with time. A three-parameter logistic-mortality function also is examined. It reflects mortality rates that rise, and then plateau, with age. Data are from published studies of medflies, Drosophila, house flies, flour beetles, and humans. Some survival data are better fit by a logistic survival function than by the more traditionally used Gompertz or Weibull functions. Gompertz, Weibull, or logistic survival functions often fit the survival of 95+% of a population, and the 'tails' of the survival curves usually appear to fall between the values predicted by the three functions. For some populations, such 'tails' appear to be too complex to be fit well by any simple function. Survival data for males and females in some populations are best fit by different functions. Populations of 100 or more are needed to distinguish among the functions. When testing effects of environmental or genetic manipulations on survival, it has been common to determine the changes in parameter values for a given function, such as Gompertz. It may be equally important to determine whether the best-fit function has changed as well.

AB - Survival functions are fitted to survival data from several large populations. The Gompertz survival function corresponds to exponential mortality rate increases with time. The Weibull survival function corresponds to mortality rates that increase as a power function of time. A two-parameter, logistic survival function is introduced, and corresponds to mortality rates that increase, and then decrease, with time. A three-parameter logistic-mortality function also is examined. It reflects mortality rates that rise, and then plateau, with age. Data are from published studies of medflies, Drosophila, house flies, flour beetles, and humans. Some survival data are better fit by a logistic survival function than by the more traditionally used Gompertz or Weibull functions. Gompertz, Weibull, or logistic survival functions often fit the survival of 95+% of a population, and the 'tails' of the survival curves usually appear to fall between the values predicted by the three functions. For some populations, such 'tails' appear to be too complex to be fit well by any simple function. Survival data for males and females in some populations are best fit by different functions. Populations of 100 or more are needed to distinguish among the functions. When testing effects of environmental or genetic manipulations on survival, it has been common to determine the changes in parameter values for a given function, such as Gompertz. It may be equally important to determine whether the best-fit function has changed as well.

KW - Aging

KW - Gompertz

KW - Mortality

UR - http://www.scopus.com/inward/record.url?scp=0028242346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028242346&partnerID=8YFLogxK

U2 - 10.1016/0047-6374(94)90095-7

DO - 10.1016/0047-6374(94)90095-7

M3 - Article

C2 - 7934205

AN - SCOPUS:0028242346

VL - 74

SP - 15

EP - 33

JO - Mechanisms of Ageing and Development

JF - Mechanisms of Ageing and Development

SN - 0047-6374

IS - 1-2

ER -