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Modeling Discrete Time-to-Event Data 1st ed. 2016 [Kõva köide]

  • Formaat: Hardback, 247 pages, kõrgus x laius: 235x155 mm, kaal: 5148 g, 3 Illustrations, color; 55 Illustrations, black and white; X, 247 p. 58 illus., 3 illus. in color., 1 Hardback
  • Sari: Springer Series in Statistics
  • Ilmumisaeg: 22-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319281569
  • ISBN-13: 9783319281568
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  • Formaat: Hardback, 247 pages, kõrgus x laius: 235x155 mm, kaal: 5148 g, 3 Illustrations, color; 55 Illustrations, black and white; X, 247 p. 58 illus., 3 illus. in color., 1 Hardback
  • Sari: Springer Series in Statistics
  • Ilmumisaeg: 22-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319281569
  • ISBN-13: 9783319281568
Teised raamatud teemal:
This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis

in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.

Introduction.- The Life Table.- Basic Regression Models.- Evaluation and Model Choice.- Nonparametric Modelling and Smooth Effects.- Tree-Based Approaches.- High-Dimensional Models - Structuring and Selection of Predictors.- Competing Risks Models.- Multiple-Spell Analysis.- Frailty Models and Heterogeneity.- Multiple-Spell Analysis.- List of Examples.- Bibliography.- Subject Index.- Author Index.

Arvustused

Modeling Discrete Time-to-Event Data provides an excellent overview of a field that is underrepresented in the literature. At what it aims to do, striking a balance between theory and practice, this book does a great job. Its readers will understand not only what to do, but also how to do it. I believe that this book can easily find a place on the shelf of statisticians who have an interest in survival analysis. (Theodor Adrian Balan, Biometrical Journal, Vol. 61 (1), January, 2019)

1 Introduction
1(14)
1.1 Survival and Time-to-Event Data
1(3)
1.2 Continuous Versus Discrete Survival
4(2)
1.3 Overview
6(1)
1.4 Examples
7(8)
2 The Life Table
15(20)
2.1 Life Table Estimates
15(10)
2.1.1 Distributional Aspects
19(1)
2.1.2 Smooth Life Table Estimators
20(3)
2.1.3 Heterogeneous Intervals
23(2)
2.2 Kaplan-Meier Estimator
25(2)
2.3 Life Tables in Demography
27(4)
2.4 Literature and Further Reading
31(1)
2.5 Software
31(1)
2.6 Exercises
32(3)
3 Basic Regression Models
35(38)
3.1 The Discrete Hazard Function
35(2)
3.2 Parametric Regression Models
37(11)
3.2.1 Logistic Discrete Hazards: The Proportional Continuation Ratio Model
38(4)
3.2.2 Alternative Models
42(6)
3.3 Discrete and Continuous Hazards
48(3)
3.3.1 Concepts for Continuous Time
48(2)
3.3.2 The Proportional Hazards Model
50(1)
3.4 Estimation
51(8)
3.4.1 Standard Errors
58(1)
3.5 Time-Varying Covariates
59(5)
3.6 Continuous Versus Discrete Proportional Hazards
64(3)
3.7 Subject-Specific Interval Censoring
67(3)
3.8 Literature and Further Reading
70(1)
3.9 Software
70(1)
3.10 Exercises
71(2)
4 Evaluation and Model Choice
73(32)
4.1 Relevance of Predictors: Tests
73(4)
4.2 Residuals and Goodness-of-Fit
77(9)
4.2.1 No Censoring
78(2)
4.2.2 Deviance in the Case of Censoring
80(1)
4.2.3 Martingale Residuals
81(5)
4.3 Measuring Predictive Performance
86(10)
4.3.1 Predictive Deviance and R2 Coefficients
86(2)
4.3.2 Prediction Error Curves
88(4)
4.3.3 Discrimination Measures
92(4)
4.4 Choice of Link Function and Flexible Links
96(5)
4.4.1 Families of Response Functions
97(4)
4.4.2 Nonparametric Estimation of Link Functions
101(1)
4.5 Literature and Further Reading
101(1)
4.6 Software
102(1)
4.7 Exercises
102(3)
5 Nonparametric Modeling and Smooth Effects
105(24)
5.1 Smooth Baseline Hazard
105(10)
5.1.1 Estimation
109(3)
5.1.2 Smooth Life Table Estimates
112(3)
5.2 Additive Models
115(3)
5.3 Time-Varying Coefficients
118(4)
5.3.1 Penalty for Smooth Time-Varying Effects and Selection
119(2)
5.3.2 Time-Varying Effects and Additive Models
121(1)
5.4 Inclusion of Calendar Time
122(2)
5.5 Literature and Further Reading
124(1)
5.6 Software
125(1)
5.7 Exercises
125(4)
6 Tree-Based Approaches
129(20)
6.1 Recursive Partitioning
130(2)
6.2 Recursive Partitioning Based on Covariate-Free Discrete Hazard Models
132(1)
6.3 Recursive Partitioning with Binary Outcome
133(8)
6.4 Ensemble Methods
141(3)
6.4.1 Bagging
141(1)
6.4.2 Random Forests
142(2)
6.5 Literature and Further Reading
144(1)
6.6 Software
144(1)
6.7 Exercises
144(5)
7 High-Dimensional Models: Structuring and Selection of Predictors
149(18)
7.1 Penalized Likelihood Approaches
151(4)
7.2 Boosting
155(7)
7.2.1 Generic Boosting Algorithm for Arbitrary Outcomes
155(3)
7.2.2 Application to Discrete Hazard Models
158(4)
7.3 Extension to Additive Predictors
162(1)
7.4 Literature and Further Reading
163(1)
7.5 Software
164(1)
7.6 Exercises
164(3)
8 Competing Risks Models
167(18)
8.1 Parametric Models
167(5)
8.1.1 Multinomial Logit Model
169(1)
8.1.2 Ordered Target Events
170(1)
8.1.3 General Form
170(1)
8.1.4 Separate Modeling of Single Targets
171(1)
8.2 Maximum Likelihood Estimation
172(3)
8.3 Variable Selection
175(5)
8.4 Literature and Further Reading
180(1)
8.5 Software
181(1)
8.6 Exercises
181(4)
9 Frailty Models and Heterogeneity
185(28)
9.1 Discrete Hazard Frailty Model
186(6)
9.1.1 Individual and Population Level Hazard
186(2)
9.1.2 Basic Frailty Model Including Covariates
188(2)
9.1.3 Modeling with Frailties
190(2)
9.2 Estimation of Frailty Models
192(2)
9.3 Extensions to Additive Models Including Frailty
194(3)
9.4 Variable Selection in Frailty Models
197(2)
9.5 Fixed-Effects Model
199(2)
9.6 Finite Mixture Models
201(7)
9.6.1 Extensions to Covariate-Dependent Mixture Probabilities
203(1)
9.6.2 The Cure Model
204(3)
9.6.3 Estimation for Finite Mixtures
207(1)
9.7 Sequential Models in Item Response Theory
208(1)
9.8 Literature and Further Reading
209(1)
9.9 Software
210(1)
9.10 Exercises
211(2)
10 Multiple-Spell Analysis
213(12)
10.1 Multiple Spells
213(3)
10.1.1 Estimation
214(2)
10.2 Multiple Spells as Repeated Measurements
216(3)
10.3 Generalized Estimation Approach to Repeated Measurements
219(2)
10.4 Literature and Further Reading
221(1)
10.5 Software
221(1)
10.6 Exercises
221(4)
References 225(12)
List of Examples 237(2)
Subject Index 239(4)
Author Index 243
Gerhard Tutz is a professor of statistics at the Department of Statistics at the University of Munich. He has published several books with Springer.Matthias Schmid is a professor of Medical Biometry, Informatics and Epidemiology at the University of Bonn. He received his diploma (2004) and his Ph.D. (2007) in statistics at the University of Munich and his habilitation (2012) in biostatistics at the University of Erlangen. Before working in Bonn, he was professor of computational statistics at the Department of Statistics at the University of Munich (2013-2014).