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The Kaplan-Meier Estimator: New Insights and Applications in Multi-state Survival Analysis

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Computational Science and Its Applications – ICCSA 2023 Workshops (ICCSA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14112))

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Abstract

A topic that has received attention in statistical and medical literature is the estimation of survival for which the Kaplan-Meier product-limit estimator is the most commonly used estimator. This estimator is considered nonparametric because it does not rely on any assumptions about the probability distribution of the lifetime. The best known representation of the Kaplan-Meier estimator is based on a product of elementary probabilities whose underlying idea is the computation of conditional survival probabilities. The Kaplan-Meier estimator of survival can also be explained using the redistribution to the right algorithm, which removes the mass of a censored subject and redistributes this mass equally to all subjects who fail or are censored at later times. This paper presents additional alternative representations of this estimator, as well as applications and advantages of its use. One of these representations consists in defining the estimator as a sum of weights, which is a convenient form to estimate several quantities in the context of multi-state models. The estimator can also be represented as a weighted average of identically distributed terms, where the weights are obtained by using the inverse probability of censoring. The paper discusses how these formulations can be used to estimate several quantities in the context of multi-state models. Two real data examples are included for illustration of the methods.

Supported by Portuguese Foundation for Science and Technology, references UIDB/00013/2020, UIDP/00013/2020 and EXPL/MAT-STA/0956/2021.

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Authors and Affiliations

  1. Centre of Mathematics and Department of Mathematics, University of Minho, Guimarães, Portugal

    Luís Meira-Machado

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  1. Luís Meira-Machado
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Correspondence to Luís Meira-Machado .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Basilicata, Potenza, Italy

    Francesco Scorza

  6. University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

  7. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

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Meira-Machado, L. (2023). The Kaplan-Meier Estimator: New Insights and Applications in Multi-state Survival Analysis. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14112. Springer, Cham. https://doi.org/10.1007/978-3-031-37129-5_11

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  • DOI: https://doi.org/10.1007/978-3-031-37129-5_11

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-37129-5

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