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E-raamat: Statistical Analysis of Doubly Truncated Data: With Applications in R

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A thorough treatment of the statistical methods used to analyze doubly truncated data

In The Statistical Analysis of Doubly Truncated Data, an expert team of statisticians delivers an up-to-date review of existing methods used to deal with randomly truncated data, with a focus on the challenging problem of random double truncation. The authors comprehensively introduce doubly truncated data before moving on to discussions of the latest developments in the field.

The book offers readers examples with R code along with real data from astronomy, engineering, and the biomedical sciences to illustrate and highlight the methods described within. Linear regression models for doubly truncated responses are provided and the influence of the bandwidth in the performance of kernel-type estimators, as well as guidelines for the selection of the smoothing parameter, are explored.

Fully nonparametric and semiparametric estimators are explored and illustrated with real data. R code for reproducing the data examples is also provided. The book also offers:

  • A thorough introduction to the existing methods that deal with randomly truncated data
  • Comprehensive explorations of linear regression models for doubly truncated responses
  • Practical discussions of the influence of bandwidth in the performance of kernel-type estimators and guidelines for the selection of the smoothing parameter
  • In-depth examinations of nonparametric and semiparametric estimators

Perfect for statistical professionals with some background in mathematical statistics, biostatisticians, and mathematicians with an interest in survival analysis and epidemiology, The Statistical Analysis of Doubly Truncated Data is also an invaluable addition to the libraries of biomedical scientists and practitioners, as well as postgraduate students studying survival analysis.

Preface xi
List of Abbreviations
xiii
Notation xv
1 Introduction
1(12)
1.1 Random Truncation
1(1)
1.2 One-sided Truncation
2(1)
1.2.1 Left-truncation
2(1)
1.2.2 Right-truncation
2(1)
1.2.3 Truncation vs. Censoring
3(1)
1.3 Double Truncation
3(2)
1.4 Real Data Examples
5(8)
1.4.1 Childhood Cancer Data
5(1)
1.4.2 AIDS Blood Transfusion Data
6(1)
1.4.3 Equipment-S Rounded Failure Time Data
7(1)
1.4.4 Quasar Data
7(1)
1.4.5 Parkinson's Disease Data
8(1)
1.4.6 Acute Coronary Syndrome Data
9(1)
References
10(3)
2 One-Sample Problems
13(56)
2.1 Nonparametric Estimation of a Distribution Function
13(30)
2.1.1 The NPMLE
14(7)
2.1.2 Numerical Algorithms for Computing the NPMLE
21(3)
2.1.3 Theoretical Properties of the NPMLE
24(12)
2.1.4 Standard Errors and Confidence Limits
36(7)
2.2 Semiparametric and Parametric Approaches
43(13)
2.2.1 Semiparametric Approach
44(8)
2.2.2 Parametric Approach
52(4)
2.3 R Code for the Examples
56(13)
2.3.1 Code for Example 2.1.8
56(1)
2.3.2 Code for Examples 2.1.11 and 2.1.13
56(2)
2.3.3 Code for Example 2.1.14
58(1)
2.3.4 Code for Example 2.1.15
59(1)
2.3.5 Code for Example 2.1.22
60(1)
2.3.6 Code for Example 2.2.6
61(1)
2.3.7 Code for Example 2.2.8
62(3)
References
65(4)
3 Smoothing Methods
69(40)
3.1 Some Background in Kernel Estimation
69(2)
3.2 Estimating the Density Function
71(1)
3.3 Asymptotic Properties
71(6)
3.4 Data-driven Bandwidth Selection
77(11)
3.4.1 Normal Reference Bandwidth Selection
78(1)
3.4.2 Plug-in Bandwidth Selection
79(1)
3.4.3 Least-squares Cross-validation Bandwidth Selection
80(1)
3.4.4 Smoothed Bootstrap Bandwidth Selection
81(1)
3.4.5 Bandwidth Selectors in Practice
82(6)
3.5 Further Issues in Kernel Density Estimation
88(2)
3.6 Estimating the Hazard Function
90(8)
3.7 R Code for the Examples
98(11)
3.7.1 Code for Example 3.2.1
98(1)
3.7.2 Code for Examples 3.3.4 and 3.3.5
99(1)
3.7.3 Code for Examples 3.4.2 and 3.4.3
100(2)
3.7.4 Code for Example 3.5.1
102(2)
3.7.5 Code for Example 3.6.4
104(1)
3.7.6 Code for Example 3.6.5
105(1)
References
106(3)
4 Regression Analysis
109(22)
4.1 Observational Bias in Regression
109(5)
4.2 Proportional Hazards Regression
114(3)
4.3 Accelerated Failure Time Regression
117(4)
4.4 Nonparametric Regression
121(5)
4.5 R Code for the Examples
126(5)
4.5.1 Code for Example 4.1.1
126(1)
4.5.2 Code for Example 4.1.4
126(1)
4.5.3 Code for Example 4.2.4
127(1)
4.5.4 Code for Example 4.3.2
127(1)
4.5.5 Code for Example 4.4.2
128(1)
References
129(2)
5 Further Topics
131(34)
5.1 Two-Sample Problems
132(5)
5.2 Competing Risks
137(9)
5.2.1 Cumulative Incidences
139(3)
5.2.2 Regression Models for Competing Risks
142(4)
5.3 Testing for Quasi-independence
146(4)
5.4 Dependent Truncation
150(7)
5.5 R Code for the Examples
157(8)
5.5.1 Code for Example 5.1.3
157(2)
5.5.2 Code for Example 5.2.4
159(1)
5.5.3 Code for Example 5.2.6
160(1)
5.5.4 Code for Example 5.3.1
161(1)
5.5.5 Code for Example 5.4.3
161(1)
References
162(3)
A Packages and Functions in R
165(8)
A.1 Computing the NPMLE and Standard Errors
166(1)
A.2 Assessing the Existence and Uniqueness of the NPMLE
167(1)
A.3 Semiparametric and Parametric Estimation
168(1)
A.4 Kernel Estimation
168(1)
A.5 Regression Analysis
169(1)
A.6 Competing Risks
169(1)
A.7 Simulating Data
170(1)
A.8 Testing Quasi-independence
170(1)
A.9 Dependent Truncation
170(3)
References
171(2)
Index 173
Jacobo de Uña-Álvarez is Professor at the Department of Statistics and Operations Research, University of Vigo, Spain.

Carla Moreira is Associate Researcher at the Centre of Mathematics, School of Sciences, University of Minho in Portugal. She is also affiliated to the Statistical Inference, Decision and Operations Research group, University of Vigo, Spain, and to the Epidemiology Research unit, Institute of Public Health, University of Porto, Portugal.

Rosa M. Crujeiras is Associate Professor at the Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, Spain.
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