Analysis of Failure and Survival Data

Analysis of Failure and Survival Data

by Peter J. Smith

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Overview

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.

Product Details

ISBN-13: 9781351989671
Publisher: CRC Press
Publication date: 07/28/2017
Series: Chapman & Hall/CRC Texts in Statistical Science
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 266
File size: 6 MB

Table of Contents

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

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