Classical Competing Risks

Classical Competing Risks

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Description

If something can fail, it can often fail in one of several ways and sometimes in more than one way at a time. There is always some cause of failure, and almost always, more than one possible cause. In one sense, then, survival analysis is a lost cause. The methods of Competing Risks have often been neglected in the survival analysis literature. Written by a leading statistician, Classical Competing Risks thoroughly examines the probability framework and statistical analysis of data of Competing Risks. The author explores both the theory of the subject and the practicalities of fitting the models to data. In a coherent, self-contained, and sequential account, the treatment moves from the bare bones of the Competing Risks setup and the associated likelihood functions through survival analysis using hazard functions. It examines discrete failure times and the difficulties of identifiability, and concludes with an introduction to the counting-process approach and the associated martingale theory. With a dearth of modern treatments on the subject and the importance of its methods, this book fills a long-standing gap in the literature with a carefully organized exposition, real data sets, numerous examples, and clear, readable prose. If you work with lifetime data, Classical Competing Risks presents a modern, comprehensive overview of the methodology and theory you need.show more

Product details

  • Hardback | 200 pages
  • 165.1 x 237.2 x 16.5mm | 408.24g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 11 black & white tables
  • 1584881755
  • 9781584881759

Review quote

"an excellent self-contained treatment of competing risksthe chapter on identifiability issues collects results, which are not much discussed in other books on survival analysisthe book is fun to read" - Short Book Reviews of the ISI "Classical Competing Risks is self-contained and well written at a level accessible to graduate students and applied statisticians alike." - Journal of the American Statistical Association "best described as a highly focused, extremely compact, introductionThe reviewed reliability concepts span hazard functions, maximum likelihood estimation of reliability model parameters, multivariate survival distributions, partial likelihood functions, and reliability model checking. This succinct and comprehensive tour of reliability is an important side benefit of the bookThe author's writing style keeps the dryness of the mathematics from overwhelming the book. He maintains an honest appreciation of the limits of what he can achieve in a relatively small space. He sprinkles various personal comments and asides that, although not simplifying the mathematics, at least prevent the book from seeming strictly a core text. a well-organized, enriching encouragement to learn more about a subject deserving of more widespread appreciation in the reliability community. - Joseph D. Conklin, U.S. Census Bureau in Technometrics, August 2002show more

Table of contents

CONTINUOUS FAILURE TIMES AND THEIR CAUSES Basic Probability Functions Some Small Data Sets Hazard Functions Regression Models PARAMETRIC LIKELIHOOD INFERENCE The Likelihood for Competing Risks Model Checking Inference Some Examples Masked Systems LATENT FAILURE TIMES: PROBABILITY DISTRIBUTIONS Basic Probability Functions Some Examples Marginal vs. Sub-Distributions Independent Risks A Risk-Removal Model LIKELIHOOD FUNCTIONS FOR UNIVARIATE SURVIVAL DATA Discrete and Continuous Failure Times Discrete Failure Times: Estimation Continuous Failure Times: Random Samples Continuous Failure Times: Explanatory Variables Discrete Failure Times Again Time-Dependent Covariates DISCRETE FAILURE TIMES IN COMPETING RISKS Basic Probability Functions Latent Failure Times Some Examples Based on Bernoulli Trials Likelihood Functions HAZARD-BASED METHODS FOR CONTINUOUS FAILURE TIMES Latent Failure Times vs. Hazard Modelling Some Examples of Hazard Modelling Nonparametric Methods for Random Samples Proportional Hazards and Partial Likelihood LATENT FAILURE TIMES: IDENTIFIABILITY CRISES The Cox-Tsiatis Impasse More General Identifiability Results Specified Marginals Discrete Failure Times Regression Case Censoring of Survival Data Parametric Identifiability MARTINGALE COUNTING PROCESSESES IN SURVIVAL DATA Introduction Back to Basics: Probability Spaces and Conditional Expectation Filtrations Martingales Counting Processes Product Integrals Survival Data Non-parametric Estimation Non-parametric Testing Regression Models Epilogue APPENDIX 1: Numerical Maximisation of Likelihood Functions APPENDIX 2: Bayesian Computation Bibliography Indexshow more