On Multiple Time Scales and Collapsibility

This article delves into the intriguing world of multiple time scales and collapsibility, focusing on their application in survival analysis. It begins by examining the impact of smoking on life expectancy, highlighting the compelling yet oversimplified communication methods used to convey these risks. The article then explores the concept of an exchange rate between different measures of time, drawing parallels with other contexts such as the age and mileage of a car. A key focus is the notion of collapsibility, introduced by Oakes (1995), which is recapitulated and reviewed in this anniversary issue of LIDA. The article also discusses the challenges of interpreting individual behavior and the complexities of simplifying counterfactual statements. It concludes by presenting a comprehensive approach to semiparametric estimation, highlighting the strengths and limitations of various methods. This article is a must-read for professionals seeking to deepen their understanding of these complex topics and their practical applications.