Multiple time scales in survival analysis

In some problems in survival analysis there may be more than one plausible measure of time for each individual. For example mileage may be a better indication of the age of a car than months. This paper considers the possibility of combining two (or more) time scales measured on each individual into a single scale. A collapsibility condition is proposed for regarding the combined scale as fully informative regarding survival. The resulting model may be regarded as a generalization of the usual accelerated life model that allows time-dependent covariates. Parametric methods for the choice of time scale, for testing the validity of the collapsibility assumption and for parametric inference about the failure distribution along the new scale are discussed. Two examples are used to illustrate the methods, namely Hyde's (1980) Channing House data and a large cohort mortality study of asbestos workers in Quebec.