book

Event History Analysis with R

Name: Event History Analysis with R
Author: Göran Broström
ISBN: 9781439831670

by Göran Broström

April 2012

Beginner to intermediate

236 pages

4h 40m

English

CRC Press

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Preliminaries
Preface
Chapter 1 Event History and Survival Data
1.1 Introduction1.2 Survival Data1.3 Right Censoring1.4 Left Truncation1.5 Time Scales1.5.1 The Lexis Diagram1.6 Event History Data1.7 More Data SetsFigure 1.1Figure 1.2Figure 1.3Figure 1.4Figure 1.5
Chapter 2 Single Sample Data
2.1 Introduction2.2 Continuous Time Model Descriptions2.2.1 The Survival Function2.2.2 The Density Function2.2.3 The Hazard Function2.2.4 The cumulative hazard function2.3 Discrete Time Models2.4 Nonparametric Estimators2.4.1 The Hazard Atoms2.4.2 The Nelson–Aalen Estimator2.4.3 The Kaplan–Meier Estimator.2.5 Doing it in R2.5.1 Nonparametric Estimation2.5.2 Parametric EstimationFigure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Figure 2.6Figure 2.7Figure 2.8Figure 2.9Figure 2.10Figure 2.11Table 2.1
Chapter 3 Cox Regression
3.1 Introduction3.2 Proportional Hazards3.3 The Log-Rank Test3.3.1 Two Samples3.3.2 Several Samples3.4 Proportional Hazards in Continuous Time3.4.1 Proportional Hazards, Two Groups3.4.2 Proportional Hazards, More Than Two Groups3.4.3 The General Proportional Hazards Regression Model3.5 Estimation of the Baseline Hazard3.6 Explanatory Variables3.6.1 Continuous Covariates3.6.2 Factor Covariates3.7 Interactions3.7.1 Two Factors3.7.2 One Factor and one Continuous Covariate3.7.3 Two Continuous Covariates3.8 Interpretation of Parameter Estimates3.8.1 Continuous Covariate3.8.2 Factor3.9 Proportional Hazards in Discrete Time3.9.1 Logistic Regression3.10 Model Selection3.10.1 Model Selection in General3.11 Male Mortality3.11.1 Likelihood Ratio Test3.11.2 The Estimated Baseline Cumulative Hazard Function3.11.3 InteractionFigure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 3.6Figure 3.7Figure 3.8Figure 3.9Table 3.1Table 3.2Table 3.3Table 3.4Table 3.5Table 3.6
Chapter 4 Poisson Regression
4.1 Introduction4.2 The Poisson Distribution4.3 The Connection to Cox Regression4.4 The Connection to the Piecewise Constant Hazards Model4.5 Tabular Lifetime DataFigure 4.1Figure 4.2Figure 4.3Figure 4.4Figure 4.5
Chapter 5 More on Cox Regression
5.1 Introduction5.2 Time-Varying Covariates5.3 Communal covariates5.4 Tied Event Times5.5 Stratification5.6 Sampling of Risk Sets5.7 Residuals5.7.1 Martingale Residuals5.8 Checking Model Assumptions5.8.1 Proportionality5.8.2 Log-Linearity5.9 Fixed Study Period Survival5.10 Left- or Right-Censored DataFigure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Figure 5.6Figure 5.7Figure 5.8Figure 5.9Figure 5.10Figure 5.11Figure 5.12Table 5.1Table 5.2
Chapter 6 Parametric Models
6.1 Introduction6.2 Proportional Hazards Models6.2.1 The Weibull Model6.2.2 The Lognormal Model6.2.3 Comparing the Weibull and Lognormal Fits6.2.4 The Piecewise Constant Hazards (PCH) Model6.2.4.1 Testing the Proportionality Assumption with the PCH Model6.2.5 Choosing the best parametric model6.3 Accelerated Failure Time Models6.3.1 The AFT Regression Model6.3.2 Different Parametrizations6.3.3 AFT Models in R6.4 Proportional Hazards or AFT Model?6.5 Discrete Time ModelsFigure 6.1Figure 6.2Figure 6.3Figure 6.4Figure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.12Figure 6.13Figure 6.14Figure 6.15Figure 6.16Figure 6.17Figure 6.18Figure 6.19Figure 6.20
Chapter 7 Multivariate Survival Models
7.1 Introduction7.1.1 An Introductory Example7.2 Frailty Models7.2.1 The Simple Frailty Model7.2.2 The Shared Frailty Model7.3 Parametric Frailty Models7.4 StratificationFigure 7.1
Chapter 8 Competing Risks Models
8.1 Introduction8.2 Some Mathematics8.3 Estimation8.4 Meaningful Probabilities8.5 Regression8.6 R Code for Competing RisksFigure 8.1Figure 8.2Figure 8.3Table 8.1

Chapter 9 Causality and Matching
9.1 Introduction9.2 Philosophical Aspects of Causality9.3 Causal Inference9.3.1 Graphical Models9.3.2 Predictive causality9.3.3 Counterfactuals9.4 Aalen’s Additive Hazards Model9.5 Dynamic Path Analysis9.6 Matching9.6.1 Paired Data9.6.2 More than One Control9.7 ConclusionFigure 9.1Figure 9.2Figure 9.3
Appendix A Basic Statistical Concepts
A.1 IntroductionA.2 Statistical InferenceA.2.1 Point EstimationA.2.2 Interval EstimationA.2.3 Hypothesis TestingA.2.3.1 The Log-Rank TestA.3 Asymptotic theoryA.3.1 Partial likelihoodA.4 Model SelectionA.4.1 Nested ModelsTable A.1
Appendix B Survival Distributions
B.1 IntroductionB.2 Relevant Distributions in RB.2.1 The Exponential DistributionB.2.2 The Piecewise Constant Hazard DistributionB.2.3 The Weibull DistributionB.2.3.1 Graphical Test of the Weibull DistributionB.2.4 The Lognormal DistributionB.2.5 The Loglogistic DistributionB.2.6 The Gompertz DistributionB.2.7 The Gompertz–Makeham DistributionB.2.8 The Gamma DistributionB.3 Parametric Proportional Hazards and Accelerated Failure Time ModelsB.3.1 IntroductionB.3.2 The Proportional Hazards ModelB.3.2.1 Data and the Likelihood FunctionB.3.3 The Shape-Scale FamiliesB.3.3.1 The Weibull Family of DistributionsB.3.3.2 The EV family of distributionsB.3.3.3 The Gompertz Family of DistributionsB.3.3.4 Other Families of DistributionsB.3.4 The Accelerated Failure Time ModelB.3.4.1 Data and the Likelihood FunctionFigure B.1Figure B.2Figure B.3Figure B.4
Appendix C A Brief Introduction to R
C.1 R in GeneralC.1.1 R ObjectsC.1.2 Expressions and AssignmentsC.1.3 ObjectsC.1.4 Vectors and MatricesC.1.5 ListsC.1.6 Data FramesC.1.7 FactorsC.1.8 OperatorsC.1.9 RecyclingC.1.10 PrecedenceC.2 Some Standard R FunctionsC.2.1 SequencesC.2.2 Logical expressionC.2.3 IndexingC.2.4 Vectors and MatricesC.2.5 Conditional ExecutionC.2.6 LoopsC.2.7 VectorizingC.3 Writing FunctionsC.3.1 Calling ConventionsC.3.2 The Argument “...”C.3.3 Writing FunctionsC.3.4 Lazy EvaluationC.3.5 RecursionC.3.6 Vectorized FunctionsC.3.7 Scoping RulesC.4 GraphicsC.5 Probability FunctionsC.5.1 Some Useful R FunctionsC.5.1.1 MatchingC.5.1.2 General utility functionsC.6 Help in RC.7 Functions in eha and survivalC.7.1 Checking the Integrity of Survival DataC.8 Reading Data into RC.8.1 Reading Data from ASCII FilesC.8.2 Reading Foreign Data FilesFigure C.1Figure C.2Table C.1
Appendix D Survival Packages in R
D.1 IntroductionD.2 ehaD.3 survivalD.4 Other PackagesD.4.1 coxmeD.4.2 timeregD.4.3 cmprsk
Bibliography

Overview

With an emphasis on social science applications, Event History Analysis with R presents an introduction to survival and event history analysis using real-life examples. Keeping mathematical details to a minimum, the book covers key topics, including both discrete and continuous time data, parametric proportional hazards, and accelerated failure times.

Features

Introduces parametric proportional hazards models with baseline distributions like the Weibull, Gompertz, Lognormal, and Piecewise constant hazard distributions, in addition to traditional Cox regression
Presents mathematical details as well as technical material in an appendix
Includes real examples with applications in demography, econometrics, and epidemiology
Provides a dedicated R package, eha, containing special treatments, including making cuts in the Lexis diagram, creating communal covariates, and creating period statistics

A much-needed primer, Event History Analysis with R is a didactically excellent resource for students and practitioners of applied event history and survival analysis.

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