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Modeling Survival Data Using Frailty Models [Kietas viršelis]

  • Formatas: Hardback, 334 pages, aukštis x plotis: 235x156 mm, weight: 612 g, 25 black & white illustrations, 24 black & white tables
  • Išleidimo metai: 14-Jan-2011
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1439836671
  • ISBN-13: 9781439836675
Kitos knygos pagal šią temą:
Modeling Survival Data Using Frailty ModelsDidesnis paveikslėlis
  • Formatas: Hardback, 334 pages, aukštis x plotis: 235x156 mm, weight: 612 g, 25 black & white illustrations, 24 black & white tables
  • Išleidimo metai: 14-Jan-2011
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1439836671
  • ISBN-13: 9781439836675
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781439836675.html
Raktažodžiai:
When designing and analyzing a medical study, researchers focusing on survival data must take into account the heterogeneity of the study population: due to uncontrollable variation, some members change states more rapidly than others. Survival data measures the time to a certain event or change of state. For example, the event may be death, occurrence of disease, time to an epileptic seizure, or time from response until disease relapse. Frailty is a convenient method to introduce unobserved proportionality factors that modify the hazard functions of an individual. In spite of several new research developments on the topic, there are very few books devoted to frailty models. Modeling Survival Data Using Frailty Models covers recent advances in methodology and applications of frailty models, and presents survival analysis and frailty models ranging from fundamental to advanced. Eight data on survival times with covariates sets are discussed, and analysis is carried out using the R statistical package. This book covers: Basic concepts in survival analysis, shared frailty models and bivariate frailty models Parametric distributions and their corresponding regression models Nonparametric Kaplan--Meier estimation and Cox's proportional hazard model The concept of frailty and important frailty models Different estimation procedures such as EM and modified EM algorithms Logrank tests and CUSUM of chi-square tests for testing frailty Shared frailty models in different bivariate exponential and bivariate Weibull distributions Frailty models based on Levy processes Different estimation procedures in bivariate frailty models Correlated gamma frailty, lognormal and power variance function frailty models Additive frailty models Identifiability of bivariate frailty and correlated frailty models The problem of analyzing time to event data arises in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. Although the statistical tools presented in this book are applicable to all these disciplines, this book focuses on frailty in biological and medical statistics, and is designed to prepare students and professionals for experimental design and analysis.

Recenzijos

A statistician seeking guidance on the use of frailty models in genetic applications, two component systems, and/or Levy processes would benefit more from Hanagal's book. If someone wanted to find references on the use of frailty models, both books [ Hanagal; Weinke's Frailty Models in Survival Analysis] should be consulted because both books have extensive references (>300) and the references are largely non-overlapping. --William Mietlowski, Journal of Biopharmaceutical Statistics, January 2012

List of Tables
xiii
List of Figures
xv
Preface xvii
About the Author xix
I Basic Concepts in Survival Analysis
1 Introduction to Survival Analysis
3(16)
1.1 Introduction
3(1)
1.2 Bone Marrow Transplantation (BMT) for Leukemia
4(1)
1.3 Remission Duration from a Clinical Trial for Acute Leukemia
5(2)
1.4 Times of Infection of Kidney Dialysis Patients
7(1)
1.5 Kidney Infection Data
8(1)
1.6 Litters of Rats Data
8(1)
1.7 Kidney Dialysis (HLA) Patients Data
8(2)
1.8 Diabetic Retinopathy Data
10(2)
1.9 Myeloma Data
12(1)
1.10 Definitions and Notations
13(3)
1.10.1 Survival Function
13(1)
1.10.2 Failure (or Hazard) Rate
13(3)
1.11 Censoring
16(3)
1.11.1 Censored Type I Data
16(1)
1.11.2 Censored Type II Data
17(1)
1.11.3 Readout or Interval Censored Data
17(1)
1.11.4 Multicensored Data
17(1)
1.11.5 Separating out Failure Modes
18(1)
2 Some Parametric Methods
19(24)
2.1 Introduction
19(1)
2.2 Exponential Distribution
20(1)
2.3 Weibull Distribution
21(2)
2.4 Extreme Value Distributions
23(2)
2.5 Lognormal
25(1)
2.6 Gamma
26(3)
2.7 Loglogistic
29(1)
2.8 Maximum Likelihood Estimation
30(5)
2.9 Parametric Regression Models
35(8)
2.9.1 Example 2.1
40(1)
2.9.2 Example 2.2
41(2)
3 Nonparametric and Semiparametric Models
43(26)
3.1 Empirical Survival Function
43(1)
3.2 Graphical Plotting
44(6)
3.2.1 Probability Plotting
44(3)
3.2.2 Hazard and Cumulative Hazard Plotting
47(1)
3.2.3 Exponential and Weibull Hazard Plots
48(2)
3.3 Graphical Estimation
50(1)
3.4 Empirical Model Fitting: Distribution Free (Kaplan-Meier) Approach
51(8)
3.5 Comparison between Two Survival Functions
59(3)
3.6 Cox's Proportional Hazards Model
62(7)
II Univariate and Shared Frailty Models for Survival Data
69(134)
4 The Frailty Concept
71(10)
4.1 Introduction
71(2)
4.2 The Definition of Shared Frailty
73(1)
4.3 The Implications of Frailty
74(2)
4.4 The Conditional Parametrization
76(1)
4.5 The Marginal Parametrization
77(1)
4.6 Frailty as a Model for Omitted Covariates
78(1)
4.7 Frailty as a Model of Stochastic Hazard
78(1)
4.8 Identifiability of Frailty Models
79(2)
5 Various Frailty Models
81(24)
5.1 Introduction
81(1)
5.2 Gamma Frailty
81(2)
5.3 Positive Stable Frailty
83(2)
5.4 Power Variance Function Frailty
85(1)
5.5 Compound Poisson Frailty
86(3)
5.6 Compound Poisson Distribution with Random Scale
89(3)
5.7 Frailty Models in Hierarchical Likelihood
92(2)
5.8 Frailty Models in Mixture Distributions
94(3)
5.8.1 Gamma Frailty in Weibull Mixture
95(1)
5.8.2 Positive Stable Frailty in Weibull Mixture
96(1)
5.8.3 PVF Frailty in Weibull Mixture
96(1)
5.9 Piecewise Gamma Frailty Model
97(8)
5.9.1 Frailty Models and Dependence Function
99(3)
5.9.2 Example: Epilepsy Data
102(3)
6 Estimation Methods for Shared Frailty Models
105(14)
6.1 Introduction
105(1)
6.2 Inference for the Shared Frailty Model
106(2)
6.3 The EM Algorithm
108(2)
6.4 The Gamma Frailty Model
110(1)
6.5 The Positive Stable Frailty Model
111(2)
6.6 The Lognormal Frailty Model
113(1)
6.6.1 Application to Seizure Data
113(1)
6.7 Modified EM (MEM) Algorithm for Gamma Frailty Models
114(2)
6.8 Application
116(1)
6.9 Discussion
117(2)
7 Analysis of Survival Data in Shared Frailty Models
119(18)
7.1 Introduction
119(1)
7.2 Analysis for Bone Marrow Transplantation (BMT) Data
119(3)
7.3 Analysis for Acute Leukemia Data
122(3)
7.4 Analysis for HLA Data
125(4)
7.5 Analysis for Kidney Infection Data
129(2)
7.6 Analysis of Litters of Rats
131(2)
7.7 Analysis for Diabetic Retinopathy Data
133(4)
8 Tests of Hypotheses in Frailty Models
137(24)
8.1 Introduction
137(1)
8.2 Tests for Gamma Frailty Based on Likelihood Ratio and Score Tests
138(5)
8.2.1 The Model and the Main Results
139(3)
8.2.2 Analysis of Diabetic Retinopathy
142(1)
8.3 Logrank Tests for Testing β = 0
143(12)
8.3.1 Notations and Review
144(2)
8.3.2 Parametric Tests for Uncensored Samples
146(2)
8.3.3 Nonparametric Tests for Uncensored Samples
148(3)
8.3.4 Effect of Censoring
151(3)
8.3.5 Some Numerical Examples
154(1)
8.4 Test for Heterogeneity in Kidney Infection Data
155(6)
8.4.1 Models and Methods
157(4)
9 Shared Frailty in Bivariate Exponential and Weibull Models
161(24)
9.1 Introduction
161(1)
9.2 Bivariate Exponential Distributions
162(3)
9.2.1 Marshall-Olkin (M-0)
162(1)
9.2.2 Block-Basu (B-B)
163(1)
9.2.3 Freund
163(1)
9.2.4 Proschan-Sullo (P-S)
164(1)
9.3 Gamma Frailty in BVW Models
165(8)
9.3.1 Weibull Extension of BVE of Gumbel
165(4)
9.3.2 Weibull Extension of BVE of Marshall-Olkin
169(1)
9.3.3 Weibull Extension of BVE of Block-Basu
170(1)
9.3.4 Weibull Extension of BVE of Freund and Proschan-Sullo
171(2)
9.4 Positive Stable Frailty in BVW Models
173(3)
9.4.1 Weibull Extension of BVE of Gumbel
173(2)
9.4.2 Weibull Extension of BVE of Marshall-Olkin
175(1)
9.4.3 Weibull Extension of BVE of Block-Basu
175(1)
9.4.4 Weibull Extension of BVE of Freund and Proschan-Sullo
176(1)
9.5 Power Variance Function Frailty in BVW Models
176(2)
9.5.1 Weibull Extension of BVE Models
176(2)
9.6 Lognormal and Weibull Frailties in BVW Models
178(2)
9.6.1 Estimation of Parameters
178(2)
9.7 Compound Poisson Frailty in BVW Models
180(1)
9.8 Compound Poisson (with Random Scale) Frailty in BVW Models
180(1)
9.9 Estimation and Tests for Frailty under BVW Baseline
181(4)
10 Frailty Models Based on Levy Processes
185(18)
10.1 Introduction
185(4)
10.1.1 Biological Interpretation of Failure Rate
186(1)
10.1.2 A Model for Random Failure Rate Processes
187(2)
10.2 Levy Processes and Subordinators
189(4)
10.2.1 Standard Compound Poisson Process
190(1)
10.2.2 Compound Poisson Process with General Jump Distribution
191(1)
10.2.3 Gamma Processes
191(1)
10.2.4 Stable Processes
191(1)
10.2.5 PVF Processes
191(1)
10.2.6 Special Cases
192(1)
10.3 Proportional Hazards Derived from Levy Processes
193(2)
10.3.1 Example 10.1: Gamma Process
193(1)
10.3.2 Example 10.2: Compound Poisson Process
194(1)
10.4 Other Frailty Process Constructions
195(1)
10.5 Hierarchical Levy Frailty Models
196(7)
10.5.1 Application to the Infant Mortality Data
200(3)
III Bivariate Frailty Models for Survival Data
203(78)
11 Bivariate Frailty Models and Estimation Methods
205(18)
11.1 Introduction
205(1)
11.2 Bivariate Frailty Models and Laplace Transforms
206(1)
11.3 Proportional Hazard Model for Covariate Effects
207(1)
11.4 The Problem of Confounding
207(1)
11.5 A General Model of Covariate Dependence
208(2)
11.6 Pseudo-Frailty Model
210(1)
11.7 Likelihood Construction
211(1)
11.8 Semiparametric Representations
212(2)
11.9 Estimation Methods in Bivariate Frailty Models
214(9)
11.9.1 Two-Stage Estimation Method
214(1)
11.9.2 Basegroup Estimation Method
214(1)
11.9.3 Estimation Methods Based on the EM Algorithm
215(2)
11.9.4 Profile Estimation for Frailty Models
217(2)
11.9.5 Profile Estimation for Transformation Models
219(2)
11.9.6 Conclusions
221(2)
12 Correlated Frailty Models
223(20)
12.1 Introduction
223(2)
12.2 Correlated Gamma Frailty Model
225(1)
12.3 Correlated Power Variance Function Frailty Model
225(1)
12.4 Genetic Analysis of Duration
226(7)
12.4.1 Correlation Coefficient
227(2)
12.4.2 Six Genetic Models of Frailty
229(1)
12.4.3 Danish Twins Survival Data
230(1)
12.4.4 Results: Genetics of Frailty and Longevity
231(2)
12.5 General Bivariate Frailty Model
233(5)
12.5.1 Gamma Model
235(1)
12.5.2 Lognormal Model
236(1)
12.5.3 Estimation Strategies
237(1)
12.6 Correlated Compound Poisson Frailty for the Bivariate Survival Lifetimes
238(2)
12.7 Applications
240(3)
13 Additive Frailty Models
243(30)
13.1 Introduction
243(2)
13.2 Modeling Multivariate Survival Data Using the Frailty Model
245(1)
13.3 Correlated Frailty Model
246(1)
13.4 Relations to Other Frailty Models
247(8)
13.4.1 Shared Frailty Model
248(1)
13.4.2 Over-Dispersion Model
248(1)
13.4.3 Twin Model
248(1)
13.4.4 Litter Model
249(1)
13.4.5 Genetic Model
249(1)
13.4.6 Adoption Model
250(1)
13.4.7 Competing Risks
250(1)
13.4.8 Example
251(4)
13.5 Additive Genetic Gamma Frailty
255(8)
13.5.1 Example 13.1
255(1)
13.5.2 Example 13.2
256(1)
13.5.3 Example 13.3
257(2)
13.5.4 Application in Danish Adoptive Register Data
259(4)
13.6 Additive Genetic Gamma Frailty for Linkage Analysis of Diseases
263(10)
13.6.1 Genetic Frailties Defined by Multiple Unlinked Disease Loci
265(1)
13.6.2 Expected Genetic Frailties over the Inheritance Vectors
266(2)
13.6.3 Model for Age of Onset Data in a Family
268(1)
13.6.4 Conditional Hazards Ratio for Sib Pairs
268(2)
13.6.5 Estimation Methods and Test of Linkage
270(1)
13.6.6 Breast Cancer Data Example
270(3)
14 Identifiability of Bivariate Frailty Models
273(8)
14.1 Introduction
273(2)
14.2 Identifiability of Bivariate Frailty Models
275(1)
14.3 Identifiability of Correlated Frailty Models
276(1)
14.4 Non-Identifiability of Frailty Models without Observed Covariates
277(2)
14.4.1 Bivariate Frailty Models with Infinite Mean
277(1)
14.4.2 Bivariate Frailty Models with Finite Mean
278(1)
14.5 Discussion
279(2)
Appendix 281(10)
Bibliography 291(22)
Index 313
David D. Hanagal is a professor of statistics at the University of Pune in India.