Statistical Models Based on Counting Processes

1. Front Matter

   Pages i-xi

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2. Introduction

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 1-44

3. The Mathematical Background

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 45-120

4. Model Specification and Censoring

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 121-175

5. Nonparametric Estimation

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 176-331

6. Nonparametric Hypothesis Testing

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 332-400

7. Parametric Models

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 401-475

8. Regression Models

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 476-591

9. Asymptotic Efficiency

   • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

   Pages 592-659

10. Frailty Models

    • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

    Pages 660-674

11. Multivariate Time Scales

    • Per Kragh Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding

    Pages 675-708

12. Back Matter

    Pages 709-768

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Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a- half decades. The exposition of the theory is integrated with careful presentation of many practical examples, almost exclusively from the authors' own experience, with detailed numerical and graphical illustrations. Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in concrete detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliabilty engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject.
"This book is a masterful account of the counting process approach...is certain to be the standard reference for the area, and should be on the bookshelf of anyone interested in event-history analysis." International Statistical Institute Short Book Reviews "...this impressive reference, which contains a a wealth of powerful mathematics, practical examples, and analytic insights, as well as a complete integration of historical developments and recent advances in event history analysis." Journal of the American Statistical Association

• censoring
• estimator
• likelihood
• survival analysis

"This book is a masterful account of the counting process approach...is certain to be the standard reference for the area, and should be on the bookshelf of anyone interested in event-history analysis." International Statistical Institute Short Book Reviews

"...this impressive reference, which contains a a wealth of powerful mathematics, practical examples, and analytic insights, as well as a complete integration of historical developments and recent advances in event history analysis." Journal of the American Statistical Association

• Statistical Research Unit, University of Copenhagen, Copenhagen, Denmark

  Per Kragh Andersen, Niels Keiding

• Institute of Mathematics, University of Oslo, Oslo, Norway

  Ørnulf Borgan

• Faculty of Mathematics, University of Utrecht, Utrecht, The Netherlands

  Richard D. Gill

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