History of applications of martingales in survival analysis
arxiv(2010)
摘要
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.
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