Biomaterial Database

The analysis of survival (mortality) data: fitting Gompertz, Weibull, and logistic functions. 1994

D L Wilson

Department of Biology, University of Miami, Coral Gables, FL 33124.

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.

UI	MeSH Term	Description	Entries
D008297	Male		Males
D009026	Mortality	All deaths reported in a given population.	CFR Case Fatality Rate,Crude Death Rate,Crude Mortality Rate,Death Rate,Age Specific Death Rate,Age-Specific Death Rate,Case Fatality Rate,Decline, Mortality,Determinants, Mortality,Differential Mortality,Excess Mortality,Mortality Decline,Mortality Determinants,Mortality Rate,Mortality, Differential,Mortality, Excess,Age-Specific Death Rates,Case Fatality Rates,Crude Death Rates,Crude Mortality Rates,Death Rate, Age-Specific,Death Rate, Crude,Death Rates,Determinant, Mortality,Differential Mortalities,Excess Mortalities,Mortalities,Mortality Declines,Mortality Determinant,Mortality Rate, Crude,Mortality Rates,Rate, Age-Specific Death,Rate, Case Fatality,Rate, Crude Death,Rate, Crude Mortality,Rate, Death,Rate, Mortality,Rates, Case Fatality
D004175	Diptera	An order of the class Insecta. Wings, when present, number two and distinguish Diptera from other so-called flies, while the halteres, or reduced hindwings, separate Diptera from other insects with one pair of wings. The order includes the families Calliphoridae, Oestridae, Phoridae, SARCOPHAGIDAE, Scatophagidae, Sciaridae, SIMULIIDAE, Tabanidae, Therevidae, Trypetidae, CERATOPOGONIDAE; CHIRONOMIDAE; CULICIDAE; DROSOPHILIDAE; GLOSSINIDAE; MUSCIDAE; TEPHRITIDAE; and PSYCHODIDAE. The larval form of Diptera species are called maggots (see LARVA).	Flies, True,Flies,Dipteras,Fly,Fly, True,True Flies,True Fly
D004330	Drosophila	A genus of small, two-winged flies containing approximately 900 described species. These organisms are the most extensively studied of all genera from the standpoint of genetics and cytology.	Fruit Fly, Drosophila,Drosophila Fruit Flies,Drosophila Fruit Fly,Drosophilas,Flies, Drosophila Fruit,Fly, Drosophila Fruit,Fruit Flies, Drosophila
D005260	Female		Females
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D001517	Coleoptera	Order of winged insects also known as beetles comprising over 350,000 species in 150 families. They possess hard bodies with mouthparts adapted for chewing.	Beetles,Beetle
D015993	Life Tables	Summarizing techniques used to describe the pattern of mortality and survival in populations. These methods can be applied to the study not only of death, but also of any defined endpoint such as the onset of disease or the occurrence of disease complications.	Life Table Analysis,Life Table Methods,Life Table Models,Life Table Estimates,Life Table Method,Analyses, Life Table,Analysis, Life Table,Estimate, Life Table,Estimates, Life Table,Life Table,Life Table Analyses,Life Table Estimate,Life Table Model,Method, Life Table,Methods, Life Table,Model, Life Table,Models, Life Table,Tables, Life
D016015	Logistic Models	Statistical models which describe the relationship between a qualitative dependent variable (that is, one which can take only certain discrete values, such as the presence or absence of a disease) and an independent variable. A common application is in epidemiology for estimating an individual's risk (probability of a disease) as a function of a given risk factor.	Logistic Regression,Logit Models,Models, Logistic,Logistic Model,Logistic Regressions,Logit Model,Model, Logistic,Model, Logit,Models, Logit,Regression, Logistic,Regressions, Logistic