Chapter 10. Poisson Methods for Censored Survival Data

  1. Stephen C. Newman

Published Online: 31 MAR 2003

DOI: 10.1002/0471272612.ch10

Book Title

Biostatistical Methods in Epidemiology

Biostatistical Methods in Epidemiology

Additional Information

How to Cite

Newman, S. C. (2003) Poisson Methods for Censored Survival Data, in Biostatistical Methods in Epidemiology, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471272612.ch10

Publication History

  1. Published Online: 31 MAR 2003
  2. Published Print: 11 JAN 2002

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. David J. Balding,
  2. Peter Bloomfield,
  3. Noel A.C. Cressie,
  4. Nicholas I. Fisher,
  5. Iain M. Johnstone,
  6. J.B. Kadane,
  7. Louise M. Ryan,
  8. David W. Scott,
  9. Adrian F.M. Smith,
  10. Jozef L. Teugels

ISBN Information

Print ISBN: 9780471369141

Online ISBN: 9780471272618

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CHAPTER TOOLS

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Keywords:

  • hazard ratio;
  • censored;
  • survival;
  • exact;
  • asymptotic;
  • weighted least squares;
  • Mantel–Haenszel

Summary

This chapter presents Poisson methods for analyzing single sample, unstratified, and stratified censored survival data. One of the aims is to compare exact, asymptotic, Mantel–Haenszel, and weighted least squares methods, and to demonstrate that in many applications the various methods produce similar numerical results. Another aim is to illustrate the correspondence between odds ratio methods for analysing closed cohort data based on the binomial and hypergeometric distributions, and hazard ratio methods for analyzing censored survival data based on the Poisson distribution. Recommendations are provided for choosing methods for particular situations.

The section and subsection headings of the chapter are as follows:

  • Poisson Methods for Single Sample Survival Data

    • Weibull and Exponential Distributions

    • Assessment of the Exponential Assumption

      • Graphical Assessment

      • Cox–Oakes Test of Exponentiality

    • Poisson Distribution

    • Exact Methods for a Single Sample

      • Hypothesis Test

      • Confidence Interval

    • Asymptotic Methods for a Single Sample

      • Confidence Interval

      • Hypothesis Test

  • Poisson Methods for Unstratified Survival Data

    • Asymptotic (Unconditional) Methods for a Single 1 × 2 Table

      • Point Estimate

      • Log-Hazard Ratio Transformation

      • Confidence Interval

      • Wald and Likelihood Ratio Tests of Association

    • Exact Conditional Methods for a Single 1 × 2 Table

      • Conditional Poisson Distribution

      • Confidence Interval

      • Exact Test of Association

    • Asymptotic (Conditional) Methods for a Single 1 × 2 Table

      • Point Estimate

      • Confidence Interval

    • Mantel–Haenszel Test of Association for Person-Time Data

    • Asymptotic Methods for a Single 1 × 2 Table

    • Assessment of the Poisson-Exponential Assumption

  • Poisson Methods for Stratified Survival Data

    • Asymptotic (Unconditional) Methods for K (1 × 2) Tables

      • Point Estimates and Fitted Counts

      • Confidence Interval

      • Tests of Association, Homogeneity, and Trend

    • Asymptotic (Conditional) Methods for K (1 × 2) Tables

    • Mantel–Haenszel Estimate of the Hazard Ratio

    • Weighted Least Squares Methods for K (1 × 2) Tables

    • Standardized Hazard Ratio

    • Summary of Examples and Recommendations

    • Methods for K (1 × 1) Tables

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