History of applications of martingales in survival analysis

TL;DR

This paper reviews the historical development and integration of martingale methods into survival analysis from the 1970s to the early 1990s, highlighting key contributions and technological transfer.

Contribution

It provides a comprehensive historical overview of how martingale techniques were incorporated into survival analysis, emphasizing the role of mathematical transfer and personal collaborations.

Findings

Martingale methods advanced survival analysis techniques.

Key publications consolidated the development in early 1990s.

French probability theory significantly influenced biostatistical methods.

Abstract

The paper traces the development of the use of martingale methods in survival analysis from the mid 1970's to the early 1990's. This development was initiated by Aalen's Berkeley PhD-thesis in 1975, progressed through the work on estimation of Markov transition probabilities, non-parametric tests and Cox's regression model in the late 1970's and early 1980's, and it was consolidated in the early 1990's with the publication of the monographs by Fleming and Harrington (1991) and Andersen, Borgan, Gill and Keiding (1993). 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.