Fundamentals of Survival Data

Survival data stand out as a special statistical field. This paper tries to describe what survival data is and what makes it so special. Survival data concern times to some events. A key point is the successive observation of time, which on the one hand leads to some times not being observed so that...

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Bibliographic Details
Published in:Biometrics 1999-03, Vol.55 (1), p.13-22
Main Author: Hougaard, Philip
Format: Article
Language:English
Subjects:
Accelerated failure times
Analysis of Variance
Biometry
Bleeding
Censored data
Censoring
Censorship
Disease models
Frailty
Hazard function
Heart diseases
Humans
Menopause
Mortality
Parametric models
Proportional Hazards Models
Regression Analysis
Reliability functions
Survival Analysis
Survival data
Time Factors
Time-dependent covariates
Truncation
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Summary:Survival data stand out as a special statistical field. This paper tries to describe what survival data is and what makes it so special. Survival data concern times to some events. A key point is the successive observation of time, which on the one hand leads to some times not being observed so that all that is known is that they exceed some given times (censoring), and on the other hand implies that predictions regarding the future course should be conditional on the present status (truncation). In the simplest case, this condition is that the individual is alive. The successive conditioning makes the hazard function, which describes the probability of an event happening during a short interval given that the individual is alive today (or more generally able to experience the event), the most relevant concept. Standard distributions available (normal, log-normal, gamma, inverse Gaussian, and so forth) can account for censoring and truncation, but this is cumbersome. Besides, they fit badly because they are either symmetric or right skewed, but survival time distributions can easily be left-skewed positive variables. A few distributions satisfying these requirements are available, but often nonparametric methods are preferable as they account better conceptually for truncation and censoring and give a better fit. Finally, we compare the proportional hazards regression models with accelerated failure time models.
ISSN:0006-341X
1541-0420
DOI:10.1111/j.0006-341X.1999.00013.x