REGRESSION MODELS FOR INTERVAL CENSORED SURVIVAL DATA: APPLICATION TO HIV INFECTION IN DANISH HOMOSEXUAL MEN
✍ Scribed by BENDIX CARSTENSEN
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 740 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0277-6715
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✦ Synopsis
This paper shows how to fit excess and relative risk regression models to interval censored survival data, and how to implement the models in standard statistical software. The methods developed are used for the analysis of HIV infection rates in a cohort of Danish homosexual men.
1. Introduction
Interval censored data arise when dates of occurrence of events are not known exactly but only by intervals, that is, when it is either known that an event occurred between two dates of testing, or only that no event has occurred by some date. Such data may arise when people are tested for some (typically asymptomatic) condition like HIV-positivity at fixed dates, but where not all have been tested on all occasions, so that for some people we may only know, for example, that HIV-infection occurred during two or three adjacent intervals. Data of this kind are often termed 'panel data'.
A special case is grouped data, where the status of everyone is known at all of a set of fixed time points. Grouped data are easily handled by standard methods because the likelihood factorizes to a set of conditional probabilities. The interval censoring problem becomes non-trivial when the status of some people is unknown at some time points.
Sometimes the event of interest is ill-defined in terms of exact date of occurrence, because a substantial span of time may pass from event to symptoms (for example, onset of cirrhosis of the liver). If ascertainment of the condition is retrospective through hospital records or the like, we may have interval censoring where the intervals in which events are known to have occurred have no or very few common endpoints between individuals. This can also arise with panel data if the time scale of interest is not calendar time, but, for example, age.
Censoring with no or few common endpoints is in principle not different from the first kind, since we can define (a very large) number of fixed intervals by using all endpoints occurring in the data. In the 'non-parametric' setting, as discussed by Peto,' Turnbull' and Becker and M e l b ~e , ~ this may create some problems with standard errors of estimates, since these methods essentially estimate one parameter per interval.
This paper extends the method of Becker and Melbye to regression models for the intensities of the underlying process. Both additive excess risk models and additive and multiplicative relative risk models will be considered. In this extension it is necessary to assume piecewise constant intensities, but this will not in practice be a serious limitation of the models.