1st Edition

Analysis of Failure and Survival Data

By Peter J. Smith Copyright 2002
    266 Pages 27 B/W Illustrations
    by Chapman & Hall

    266 Pages
    by Chapman & Hall

    266 Pages 27 B/W Illustrations
    by Chapman & Hall

    Analysis of Failure and Survival Data is an essential textbook for graduate-level students of survival analysis and reliability and a valuable reference for practitioners. It focuses on the many techniques that appear in popular software packages, including plotting product-limit survival curves, hazard plots, and probability plots in the context of censored data. The author integrates S-Plus and Minitab output throughout the text, along with a variety of real data sets so readers can see how the theory and methods are applied. He also incorporates exercises in each chapter that provide valuable problem-solving experience.

    In addition to all of this, the book also brings to light the most recent linear regression techniques. Most importantly, it includes a definitive account of the Buckley-James method for censored linear regression, found to be the best performing method when a Cox proportional hazards method is not appropriate.

    Applying the theories of survival analysis and reliability requires more background and experience than students typically receive at the undergraduate level. Mastering the contents of this book will help prepare students to begin performing research in survival analysis and reliability and provide seasoned practitioners with a deeper understanding of the field.

    SURVIVAL DISTRIBUTIONS
    Basic Concepts
    Survival Functions
    Using Data to Estimate the Survival Function
    Mean Time to Failure
    Towards the Hazard Function
    Life Expectancy at Age t

    HAZARD MODELS
    The Constant Hazard Model
    The Power Hazard Model\
    Exponential Hazards
    Other Hazards
    IFR

    RELIABILITY OF SYSTEMS
    Coherent Systems and Structure Functions
    Simple Reliability
    Independent Components
    Paths and Cuts
    Associated Components
    Time Dependent Reliability

    DATA PLOTS
    Empirical Survivor Function
    Sample Quantile Function
    Probability Plots
    Hazard Plots

    CENSORING AND LIFETABLES
    Truncation
    Type I Censoring
    Type II Censoring
    Lifetable Estimates
    Greenwood's Formula

    THE PRODUCT-LIMIT ESTIMATOR
    Notation
    Self-Consistency
    Standard Errors
    Redistribute-to-the-Right Algorithm
    Hazard Plotting
    QQ-Plots for Censored Data

    PARAMETRIC SURVIVAL MODELS UNDER CENSORING
    Likelihood: Type I Censoring
    Likelihood: Type II Censoring
    Likelihood: Random Censoring
    Maximum Likelihood Procedures
    The Exponential Model
    The Weibull Model

    FITTING PARAMETRIC REGRESSION MODELS
    Basic Concepts of Proportional Hazards
    Proportional Hazards for Weibull Data
    Basic Concepts of Accelerated Lifetimes
    Accelerated Lifetimes for Weibull Data
    Diagnostics for Choosing Between Models
    Model Fitting

    COX PROPORTIONAL HAZARDS
    The Cox Model
    Maximum Likelihood Procedures
    P = 1 and the Log-Rank Test
    Estimating Baseline Survival

    LINEAR REGRESSION WITH CENSORED DATA
    Introduction
    Miller's Method
    Koul-Susarla-Van Ryzin Estimators
    Buckley-James Regression Methods
    Multivariate Designs
    Properties of Buckley-James Estimators
    Renovation and Least Squares

    BUCKLEY-JAMES DIAGNOSTICS AND APPLICATIONS
    Censored Regression Diagnostics
    Applications to Heart Transplant Data
    Plots of Renovated Data

    Biography

    Smith, Peter J.

    " This book begins with a broad and basic introduction to methods for handling censored failure time data, applying these to both medical and reliability data. It then focuses intensively on the Buckley-James generalizations of the linear model for censored data. This is in contrast to most texts in this field, which focus the discussion of regression models on the theory and application of the proportional hazards (Cox) model. This book is of interest both as an easily comprehended introduction to survival analysis (with medical and reliability applications) and as an in-depth reference on the Buckley-James linear failure time model. … For a researcher with little background in failure time methods and with an interest in focusing on the extension of linear models to censored data, Analysis of Failure and Survival Data could be a useful contribution."
    -Technometrics, November 2002

    "…the depth and breadth of the coverage constitutes the novel and useful contribution of this text to the current collection of texts on survival analysis… Students new to the concepts of censored data analysis will find the first nine chapters informative and useful, and research specialists in survival analysis will find the last two chapters enlightening and broadening… Throughout the book, the material is presented clearly, and emphasis is placed on explaining the ideas that drive the methodology. …Also refreshing is the use of non-biomedical examples for illustrations…"
    - Journal of the American Statistical Association, September 2003

    "Throughout the text the author helpfully highlights definitions and important results and his style of writing is clear. ...this is a good book for a reader who is new to the area. …Certainly I am pleased to have a copy on my shelves."
    -A. C. Kimber, Biometrics, December 2002