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Modelling time to event with observations made at arbitrary times

Sperrin, Matthew and Buchan, Iain (2013) Modelling time to event with observations made at arbitrary times. Statistics in Medicine, 32 (1). pp. 99-109.

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Abstract

We introduce new methods of analysing time to event data via extended versions of the proportional hazards and accelerated failure time (AFT) models. In many time to event studies, the time of first observation is arbitrary, in the sense that no risk modifying event occurs. This is particularly common in epidemiological studies. We show formally that, in these situations, it is not sensible to take the first observation as the time origin, either in AFT or proportional hazards type models. Instead, we advocate using age of the subject as the time scale. We account for the fact that baseline observations may be made at different ages in different patients via a two stage procedure. First, we marginally regress any potentially age-varying covariates against age, retaining the residuals. These residuals are then used as covariates in the fitting of either an AFT model or a proportional hazards model. We call the procedures residual accelerated failure time (RAFT) regression and residual proportional hazards (RPH) regression respectively. We compare standard AFT with RAFT, and demonstrate superior predictive ability of RAFT in real examples. In epidemiology, this has real implications in terms of risk communication to both patients and policy makers.

Item Type: Article
Journal or Publication Title: Statistics in Medicine
Uncontrolled Keywords: accelerated failure time ; proportional hazards ; survival analysis ; time origin ; time-varying covariates
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 55028
Deposited By: ep_importer_pure
Deposited On: 11 Jun 2012 10:31
Refereed?: Yes
Published?: Published
Last Modified: 16 Oct 2013 15:24
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/55028

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