Modelling time to event with observations made at arbitrary times

TL;DR

This paper proposes new methods for analyzing time-to-event data when observations are made at arbitrary times, emphasizing the use of age as the time scale and introducing residual-based models for improved prediction.

Contribution

It introduces RAFT and RPH models that account for arbitrary observation times by using residuals, improving upon standard AFT and proportional hazards models.

Findings

RAFT shows superior predictive ability over standard AFT.

Using age as the time scale is more appropriate when observations are made arbitrarily.

Methods have significant implications for epidemiological risk communication.

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.