Martingales in Survival Analysis

Abstract

The paper traces the development of the use of martingale methods in survival analysis from the mid 1970s to the early 1990s. This development was initiated by Aalen’s Berkeley Ph.D.-thesis in 1975, progressed in the late 1970s and early 1980s through work on the estimation of Markov transition probabilities, non-parametric tests and Cox’s regression model, and was consolidated in the early 1990s with the publication of the monographs by Fleming and Harrington and by Andersen, Borgan, Gill and Keiding. The development was made possible by an unusually fast technology transfer of pure mathematical concepts, primarily from French probability, into practical biostatistical methodology, and we attempt to outline some of the personal relationships that helped this happen. We also point out that survival analysis was ready for this development since the martingale ideas inherent in the deep understanding of temporal development so intrinsic to the French theory of processes were already quite close to the surface in survival analysis.