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Martingales in Survival Analysis

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The Splendors and Miseries of Martingales

Part of the book series: Trends in the History of Science ((TRENDSHISTORYSCIENCE))

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.

Niels Keilding (1944–2022) was affiliated to the Department of Biostatistics, University of Copenhagen, Denmark. In March 2022, before the final publication of this book, Niels Keiding passed away. Niels had been a main contributor to the field of survival analysis based on martingales and he took the initiative to establishing the group of authors of the 1993 monograph ‘Statistical Models Based on Counting processes’.

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Acknowledgements

Niels Keiding and Per Kragh Andersen were supported by National Cancer Institute; Grant Number: R01-54706-13 and Danish Natural Science Research Council; Grant Number: 272-06-0442. We are grateful to Judith Lok for comments on the use of martingales in causal inference.

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Authors and Affiliations

  1. Department of Biostatistics, University of Oslo, Oslo, Norway

    Odd O. Aalen

  2. Department of Biostatistics, University of Copenhagen, Copenhagen, Denmark

    Per K. Andersen & Niels Keiding

  3. Department of Mathematics, University of Oslo, Oslo, Norway

    Ørnulf Borgan

  4. Mathematical Institute, Leiden University, Leiden, Netherlands

    Richard D. Gill

Authors
  1. Odd O. Aalen
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  2. Per K. Andersen
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  3. Ørnulf Borgan
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  4. Richard D. Gill
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  5. Niels Keiding
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Corresponding author

Correspondence to Odd O. Aalen .

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Editors and Affiliations

  1. LPSM, Sorbonne Université, Paris, France

    Laurent Mazliak

  2. Rutgers Business School, Newark, NJ, USA

    Glenn Shafer

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Aalen, O.O., Andersen, P.K., Borgan, Ø., Gill, R.D., Keiding, N. (2022). Martingales in Survival Analysis. In: Mazliak, L., Shafer, G. (eds) The Splendors and Miseries of Martingales. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-05988-9_13

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