Time Scales in Epidemiological Analysis: An Empirical Comparison

TL;DR

This paper empirically compares the use of observation time and chronological age as time scales in Cox proportional hazards models, revealing that they can produce different results even under seemingly similar conditions.

Contribution

It provides an empirical analysis of the impact of different time scales on Cox model results using a large dataset on blood pressure and heart disease death.

Findings

Different time scales can lead to divergent results in Cox models.

Empirical evidence shows the choice of time scale affects analysis outcomes.

Results vary even when conditions suggest similar results.

Abstract

The Cox proportional hazards model is routinely used to analyze time-to-event data. To use this model requires the definition of a unique well-defined time scale. Most often, observation time is used as the time scale for both clinical and observational studies. Recently after a suggestion that it may be a more appropriate scale, chronological age has begun to appear as the time scale used in some reports. There appears to be no general consensus about which time scale is appropriate for any given analysis. It has been suggested that if the baseline hazard is exponential or if the age-at-entry is independent of covariates used in the model, then the two time scales provide similar results. In this report we provide an empirical examination of the results using the two different time scales using a large collection of data sets to examine the relationship between systolic blood pressure and coronary heart disease death (CHD death). We demonstrate, in this empirical example that the two time-scales can lead to differing results even when these two conditions appear to hold.