Catalogue


Proportional hazards regression [electronic resource] /
John O'Quigley.
imprint
New York : Springer, c2008.
description
xvii, 542 p. : ill. ; 24 cm.
ISBN
0387251480 (hbk.), 9780387251486 (hbk.)
format(s)
Book
More Details
imprint
New York : Springer, c2008.
isbn
0387251480 (hbk.)
9780387251486 (hbk.)
restrictions
Licensed for access by U. of T. users.
catalogue key
8040216
 
Includes bibliographical references and index.
A Look Inside
About the Author
Author Affiliation
John O'Quigley is Director of Research at the French Institut National de la Sante et de la Recherche Medicale and Professor of Mathematics at the University of California at San Diego.
Reviews
Review Quotes
From the reviews: "The book is clearly intended to be student-friendly. Each chapter begins with a section called Summary and a following one called motivation; each chapter ends with some exercises and class projects. ... It is very carefully written, with detailed explanation and discussion everywhere. ... I believe that the book can be thoroughly recommended to the student starting his research in the field and to the practitioner who needs to understand some of the theory." (Martin Crowder, International Statistical Review, Vol. 76 (3), 2008)
From the reviews:"The book is clearly intended to be student-friendly. Each chapter begins with a section called Summary and a following one called motivation; each chapter ends with some exercises and class projects. … It is very carefully written, with detailed explanation and discussion everywhere. … I believe that the book can be thoroughly recommended to the student starting his research in the field and to the practitioner who needs to understand some of the theory." (Martin Crowder, International Statistical Review, Vol. 76 (3), 2008)
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Back Cover Copy
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models-proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter-which underlie modern survival analysis. Unlike other books in this area the emphasis is not on measure theoretic arguments for stochastic integrals and martingales. Instead, while inference based on counting processes and the theory of martingales is covered, much greater weight is placed on more traditional results such as the functional central limit theorem. This change in emphasis allows us in the book to devote much greater consideration to practical issues in modeling. The implications of different models, their practical interpretation, the predictive ability of any model, model construction, and model selection as well as the whole area of mis-specified models receive a great deal of attention. The book is aimed at both those interested in theory and those interested in applications. Many examples and illustrations are provided. The required mathematical and statistical background for those relatively new to the field is carefully outlined so that the material is accessible to a broad range of levels. John O'Quigley-Director of Research at the French Institut National de la Santé et de la Recherche Médicale and Professor of Mathematics at the University of California at San Diego-has published extensively on the subject of survival analysis, both in theoretical and applied journals. He has taught and carried out collaborative research at several of the world's leading departments of mathematics and statistics including the University of Washington, the Fred Hutchinson Cancer Research Center in Seattle, Harvard University, and Lancaster University, UK.
Back Cover Copy
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models-proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter-which underlie modern survival analysis. Unlike other books in this area the emphasis is not on measure theoretic arguments for stochastic integrals and martingales. Instead, while inference based on counting processes and the theory of martingales is covered, much greater weight is placed on more traditional results such as the functional central limit theorem. This change in emphasis allows us in the book to devote much greater consideration to practical issues in modeling. The implications of different models, their practical interpretation, the predictive ability of any model, model construction, and model selection as well as the whole area of mis-specified models receive a great deal of attention. The book is aimed at both those interested in theory and those interested in applications. Many examples and illustrations are provided. The required mathematical and statistical background for those relatively new to the field is carefully outlined so that the material is accessible to a broad range of levels.John O'Quigley-Director of Research at the French Institut National de la Santé et de la Recherche Médicale and Professor of Mathematics at the University of California at San Diego-has published extensively on the subject of survival analysis, both in theoretical and applied journals. He has taught and carried out collaborative research at several of the world's leading departments of mathematics and statistics including the University of Washington, the Fred Hutchinson Cancer Research Center in Seattle, Harvard University, and Lancaster University, UK.
Long Description
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models ? proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter ? which underlie modern survival analysis. Unlike other books in this area the emphasis is not on measure theoretic arguments for stochastic integrals and martingales. Instead, while inference based on counting processes and the theory of martingales is covered, much greater weight is placed on more traditional results such as the functional central limit theorem.
Main Description
*Differs from most recent works in this area in that it is mostly concerned with methodological issues rather than the analysis itself *Novel yet rigorous approach sees less weight given to counting processes and martingale theory than is now common *Classical methods of inference used The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models-proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter-which underlie modern survival analysis. Unlike other books in this area the emphasis is not on measure theoretic arguments for stochastic integrals and martingales. Instead, while inference based on counting processes and the theory of martingales is covered, much greater weight is placed on more traditional results such as the functional central limit theorem. This change in emphasis allows us in the book to devote much greater consideration to practical issues in modeling. The implications of different models, their practical interpretation, the predictive ability of any model, model construction, and model selection as well as the whole area of mis-specified models receive a great deal of attention. The book is aimed at both those interested in theory and those interested in applications. Many examples and illustrations are provided. The required mathematical and statistical background for those relatively new to the field is carefully outlined so that the material is accessible to a broad range of levels. John OQuigley-Director of Research at the French Institut National de la Sante et de la Recherche Medicale and Professor of Mathematics at the University of California at San Diego-has published extensively
Main Description
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models - proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter - which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.
Main Description
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.
Main Description
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models - proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter - which underlie modern survival analysis. Unlike other books in this area the emphasis is not on measure theoretic arguments for stochastic integrals and martingales. Instead, while inference based on counting processes and the theory of martingales is covered, much greater weight is placed on more traditional results such as the functional central limit theorem.
Unpaid Annotation
PRELIMINARY ONLY--NOT FOR WEBSITE There are some important, significant departures from much current thinking in the area of proportional hazards regression. Less weight is given to counting processes and martingale theory than is now common. More classical methods of inference are used and while solid theoretically, this is not a mathematical text.
Unpaid Annotation
PRELIMINARY ONLY--NOT FOR WEBSITEThere are some important, significant departures from much current thinking in the area of proportional hazards regression. Less weight is given to counting processes and martingale theory than is now common. More classical methods of inference are used and while solid theoretically, this is not a mathematical text.
Table of Contents
Introductionp. 1
Summaryp. 1
Motivationp. 1
Objectivesp. 6
Controversiesp. 7
Data setsp. 10
Use as a graduate textp. 10
Exercises and class projectsp. 11
Background: Probabilityp. 13
Summaryp. 13
Motivationp. 14
Integration and measurep. 14
Random variables and probability measurep. 17
Distributions and densitiesp. 19
Expectationp. 24
Order statistics and their expectationsp. 26
Entropy and variancep. 32
Approximationsp. 36
Stochastic processesp. 41
Brownian motionp. 42
Counting processes and martingalesp. 51
Exercises and class projectsp. 59
Background: General inferencep. 63
Summaryp. 63
Motivationp. 64
Limit theorems for sums of random variablesp. 64
Functional Central Limit Theoremp. 68
Empirical distribution functionp. 71
Inference for martingales and stochastic integralsp. 74
Estimating equationsp. 80
Inference using resampling techniquesp. 88
Explained variationp. 91
Exercises and class projectsp. 99
Background: Survival analysisp. 103
Summaryp. 103
Motivationp. 103
Basic toolsp. 104
Some potential modelsp. 112
Censoringp. 120
Competing risks as a particular type of censoringp. 124
Exercises and class projectsp. 125
Marginal survivalp. 129
Summaryp. 129
Motivationp. 129
Maximum likelihood estimationp. 130
Empirical estimate (no censoring)p. 136
Empirical estimate (with censoring)p. 138
Exercises and class projectsp. 148
Regression models and subject heterogeneityp. 151
Summaryp. 151
Motivationp. 152
General or nonproportional hazards modelp. 153
Proportional hazards modelp. 154
The Cox regression modelp. 155
Modeling multivariate problemsp. 165
Partially proportional hazards modelsp. 172
Non proportional hazards model with interceptp. 183
Time-dependent covariatesp. 186
Time-dependent covariates and non proportional hazards modelsp. 188
Proportional hazards models in epidemiologyp. 189
Exercises and class projectsp. 199
Inference: Estimating equationsp. 203
Summaryp. 203
Motivationp. 204
The observationsp. 205
Main theoremp. 207
The estimating equationsp. 219
Consistency and asymptotic normality of [beta]p. 225
Interpretation for [beta]* as average effectp. 226
Exercises and class projectsp. 228
Inference: Functions of Brownian motionp. 231
Summaryp. 231
Motivationp. 232
Brownian motion approximationsp. 233
Non and partially proportional hazards modelsp. 238
Tests based on functions of Brownian motionp. 239
Multivariate modelp. 249
Graphical representation of regression effectsp. 254
Operating characteristics of testsp. 258
Goodness-of-fit testsp. 260
Exercises and class projectsp. 263
Inference: Likelihoodp. 267
Summaryp. 267
Motivationp. 267
Likelihood solution for parametric modelsp. 268
Likelihood solution for exponential modelsp. 270
Semi-parametric likelihood solutionp. 275
Other likelihood expressionsp. 280
Goodness-of-fit of likelihood estimatesp. 287
Exercises and class projectsp. 292
Inference: Stochastic integralsp. 295
Summaryp. 295
Motivationp. 295
Counting process framework to the modelp. 296
Some nonparametric statisticsp. 298
Stochastic integral representation of score statisticp. 299
Exercises and class projectsp. 308
Inference: Small samplesp. 311
Summaryp. 311
Motivationp. 311
Additive and multiplicative modelsp. 312
Estimation: First two momentsp. 315
Edgeworth and saddlepoint approximationsp. 316
Distribution of estimating equationp. 318
Simulation studiesp. 323
Examplep. 327
Further pointsp. 329
Exercises and class projectsp. 330
Inference: Changepoint modelsp. 331
Summaryp. 331
Motivationp. 331
Some changepoint modelsp. 333
Inference when [gamma] is knownp. 334
Inference when [gamma] is unknownp. 335
Maximum of log-rank type testsp. 338
Computational aspectsp. 339
Two groups with crossing hazardsp. 342
Illustrationsp. 347
Some guidelines in model and test selectionp. 354
Exercises and class projectsp. 358
Explained variationp. 359
Summaryp. 359
Motivationp. 359
Finding a suitable measure of R[superscript 2]p. 361
An R[superscript 2] measure based on Schoenfeld residualsp. 366
Finite sample properties of R[superscript 2] and R[superscript 2 subscript epsilon]p. 370
Large sample propertiesp. 371
Interpretationp. 375
Simulation resultsp. 379
Extensionsp. 381
Theoretical construction for distance measuresp. 386
Isolation method for bias-reductionp. 390
Illustrations from studies in cancerp. 395
Exercises and class projectsp. 403
Explained randomnessp. 407
Summaryp. 407
Motivationp. 407
Information gain and explained randomnessp. 409
Explained randomness in Z given Tp. 411
Approximation of [rho superscript 2 subscript 1] by [rho superscript 2 subscript 2]p. 416
Simple working approximation of [rho superscript 2 subscript 1] and [rho superscript 2 subscript 2]p. 417
Multiple coefficient of explained randomnessp. 420
Partially explained randomnessp. 421
Isolation method for bias-reductionp. 422
Simulationsp. 423
Illustrationsp. 426
Further extensionsp. 429
Exercises and class projectsp. 435
Survival given covariatesp. 437
Summaryp. 437
Motivationp. 438
Probability that T[subscript i] is greater than T[subscript j]p. 438
Estimating conditional survival given that Z = zp. 441
Estimating conditional survival given Z [set membership] Hp. 442
Estimating the variance of S(t[vertical bar]Z [set membership] H)p. 444
Relative merits of competing estimatorsp. 448
Illustrationsp. 448
Generalization under multiplicative relative riskp. 451
Informative censoringp. 454
Exercises and class projectsp. 460
Proofs of theorems, lemmas and corollariesp. 463
Bibliographyp. 477
Indexp. 539
Table of Contents provided by Ingram. All Rights Reserved.

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