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Record Nr. |
UNISA996466390803316 |
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Autore |
O'Quigley John |
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Titolo |
Survival analysis proportional and non-proportional hazards regression / / John O'Quigley |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (476 pages) |
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Disciplina |
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Soggetti |
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Hazardous substances - Risk assessment |
Regression analysis |
Substàncies perilloses |
Avaluació del risc |
Anàlisi de regressió |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- Summary of main notation -- 1 Introduction -- 1.1 Chapter summary -- 1.2 Context and motivation -- 1.3 Some examples -- 1.4 Main objectives -- 1.5 Neglected and underdeveloped topics -- 1.6 Model-based prediction -- 1.7 Data sets -- 1.8 Use as a graduate text -- 1.9 Classwork and homework -- 2 Survival analysis methodology -- 2.1 Chapter summary -- 2.2 Context and motivation -- 2.3 Basic tools -- 2.4 Some potential models -- 2.5 Censoring -- 2.6 Competing risks -- 2.7 Classwork and homework -- 3 Survival without covariates -- 3.1 Chapter summary -- 3.2 Context and motivation -- 3.3 Parametric models for survival functions -- 3.4 Empirical estimate (no censoring) -- 3.5 Kaplan-Meier (empirical estimate with censoring) -- 3.6 Nelson-Aalen estimate of survival -- 3.7 Model verification using empirical estimate -- 3.8 Classwork and homework -- 3.9 Outline of proofs -- 4 Proportional hazards models -- 4.1 Chapter summary -- 4.2 Context and motivation -- 4.3 General or non-proportional hazards model -- 4.4 Proportional hazards model -- 4.5 Cox regression model -- 4.6 Modeling multivariate problems -- |
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4.7 Classwork and homework -- 5 Proportional hazards models in epidemiology -- 5.1 Chapter summary -- 5.2 Context and motivation -- 5.3 Odds ratio, relative risk, and 2times2 tables -- 5.4 Logistic regression and proportional hazards -- 5.5 Survival in specific groups -- 5.6 Genetic epidemiology -- 5.7 Classwork and homework -- 6 Non-proportional hazards models -- 6.1 Chapter summary -- 6.2 Context and motivation -- 6.3 Partially proportional hazards models -- 6.4 Partitioning of the time axis -- 6.5 Time-dependent covariates -- 6.6 Linear and alternative model formulations -- 6.7 Classwork and homework -- 7 Model-based estimating equations -- 7.1 Chapter summary -- 7.2 Context and motivation. |
7.3 Likelihood solution for parametric models -- 7.4 Semi-parametric estimating equations -- 7.5 Estimating equations using moments -- 7.6 Incorrectly specified models -- 7.7 Estimating equations in small samples -- 7.8 Classwork and homework -- 7.9 Outline of proofs -- 8 Survival given covariate information -- 8.1 Chapter summary -- 8.2 Context and motivation -- 8.3 Probability that Ti is greater than Tj -- 8.4 Conditional survival given ZinH -- 8.5 Other relative risk forms -- 8.6 Informative censoring -- 8.7 Classwork and homework -- 8.8 Outline of proofs -- 9 Regression effect process -- 9.1 Chapter summary -- 9.2 Context and motivation -- 9.3 Elements of the regression effect process -- 9.4 Univariate regression effect process -- 9.5 Regression effect processes for several covariates -- 9.6 Iterated logarithm for effective sample size -- 9.7 Classwork and homework -- 9.8 Outline of proofs -- 10 Model construction guided by regression effect process -- 10.1 Chapter summary -- 10.2 Context and motivation -- 10.3 Classical graphical methods -- 10.4 Confidence bands for regression effect process -- 10.5 Structured tests for time dependency -- 10.6 Predictive ability of a regression model -- 10.7 The R2 estimate of Ω2 -- 10.8 Using R2 and fit to build models -- 10.9 Some simulated situations -- 10.10 Illustrations from clinical studies -- 10.11 Classwork and homework -- 10.12 Outline of proofs -- 11 Hypothesis tests based on regression effect process -- 11.1 Chapter summary -- 11.2 Context and motivation -- 11.3 Some commonly employed tests -- 11.4 Tests based on the regression effect process -- 11.5 Choosing the best test statistic -- 11.6 Relative efficiency of competing tests -- 11.7 Supremum tests over cutpoints -- 11.8 Some simulated comparisons -- 11.9 Illustrations -- 11.10 Some further thoughts -- 11.11 Classwork and homework. |
11.12 Outline of proofs -- A Probability -- A.1 Essential tools for survival problems -- A.2 Integration and measure -- A.3 Random variables and probability measure -- A.4 Convergence for random variables -- A.5 Topology and distance measures -- A.6 Distributions and densities -- A.7 Multivariate and copula models -- A.8 Expectation -- A.9 Order statistics and their expectations -- A.10 Approximations -- B Stochastic processes -- B.1 Broad overview -- B.2 Brownian motion -- B.3 Counting processes and martingales -- B.4 Inference for martingales and stochastic integrals -- C Limit theorems -- C.1 Empirical processes and central limit theorems -- C.2 Limit theorems for sums of random variables -- C.3 Functional central limit theorem -- C.4 Brownian motion as limit process -- C.5 Empirical distribution function -- D Inferential tools -- D.1 Theory of estimating equations -- D.2 Efficiency in estimation and in tests -- D.3 Inference using resampling techniques -- D.4 Conditional, marginal, and partial likelihood -- E Simulating data under the non-proportional hazards model -- E.1 Method 1-Change-point models -- E.2 Method 2-Non-proportional hazards models -- Further exercises and proofs -- Bibliography -- Index. |
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