Cox regression with alternative concepts of waiting time: the new orleans yellow fever epidemic of 1853

Abstract

Event data can often be analysed using different concepts of waiting time. Our application offers three choices: calendar-time, age, and duration of residence in New Orleans. We exploit the semi-parametric features of Cox regression and estimate parallel specifications in which mortality risk is treated as an arbitrary function of one of the three alternative time measures, while the remaining two enter the hazard parametrically. Comparisons of the parameter estimates with the corresponding estimates of the baseline hazards form the crux of a simple specification checking procedure. In our formal treatment we rely on Aalen's Multiplicative Intensity formulation and tackle complications such as left-truncation, functional form specification, and choice-based sampling.