LEADER 06585nam 2200553 450 001 996466390803316 005 20220610113537.0 010 $a3-030-33439-2 035 $a(CKB)4100000011902685 035 $a(MiAaPQ)EBC6576315 035 $a(Au-PeEL)EBL6576315 035 $a(OCoLC)1248899908 035 $a(PPN)255293704 035 $a(EXLCZ)994100000011902685 100 $a20211213d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSurvival analysis proportional and non-proportional hazards regression /$fJohn O'Quigley 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (476 pages) 311 $a3-030-33438-4 320 $aIncludes bibliographical references and index. 327 $aIntro -- 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 -- 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. 327 $a7.3 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 ?2 -- 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. 327 $a11.12 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. 606 $aHazardous substances$xRisk assessment 606 $aRegression analysis 606 $aSubstàncies perilloses$2thub 606 $aAvaluació del risc$2thub 606 $aAnàlisi de regressió$2thub 608 $aLlibres electrònics$2thub 615 0$aHazardous substances$xRisk assessment. 615 0$aRegression analysis. 615 7$aSubstàncies perilloses 615 7$aAvaluació del risc 615 7$aAnàlisi de regressió 676 $a363.17 700 $aO'Quigley$b John$0847320 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466390803316 996 $aSurvival Analysis$91892652 997 $aUNISA