History of applications of martingales in survival analysis.

By O. Aalen, Per Kragh Andersen, O. Borgan, R. Gill, N. Keiding. 2010

70 citations recorded by the source corpus.

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.

Subfields: Demography, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6d5f45cb707f8cde415c5a6c95d14ffcf5d2c053

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Citations in the corpus

Test Martingales, Bayes Factors and p-Values (2009, methodology): “Let us call an increasing function f : [1,∞)→ [0,∞) a martingale calibrator if it satisfies the following property: For any probability space (Ω,F ,P) and any test supermartingale (Xt,Ft) in this probability space there exists a test supermartingale (Yt,Ft) such that Yt ≥ f(X∗t ) for all t almost…”