The Statistical Analysis of Doubly Truncated Data : With Applications in R

✍ Scribed by Prof Carla Moreira, Jacobo de Uña-Álvarez, Rosa M. Crujeiras

• Publisher: Wiley
• Year: 2022
• Tongue: English
• Leaves: 195
• Series: Wiley Series in Probability and Statistics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
Title Page
Copyright
Contents
Preface
List of Abbreviations
Notation
Chapter 1 Introduction
1.1 Random Truncation
1.2 One‐sided Truncation
1.2.1 Left‐truncation
1.2.2 Right‐truncation
1.2.3 Truncation vs. Censoring
1.3 Double Truncation
1.4 Real Data Examples
1.4.1 Childhood Cancer Data
1.4.2 AIDS Blood Transfusion Data
1.4.3 Equipment‐S Rounded Failure Time Data
1.4.4 Quasar Data
1.4.5 Parkinson's Disease Data
1.4.6 Acute Coronary Syndrome Data
References
Chapter 2 One‐Sample Problems
2.1 Nonparametric Estimation of a Distribution Function
2.1.1 The NPMLE
2.1.2 Numerical Algorithms for Computing the NPMLE
2.1.3 Theoretical Properties of the NPMLE
2.1.4 Standard Errors and Confidence Limits
2.2 Semiparametric and Parametric Approaches
2.2.1 Semiparametric Approach
2.2.2 Parametric Approach
2.3 R Code for the Examples
2.3.1 Code for Example 2.1.8
2.3.2 Code for Examples 2.1.11 and 2.1.13
2.3.3 Code for Example 2.1.14
2.3.4 Code for Example 2.1.15
2.3.5 Code for Example 2.1.22
2.3.6 Code for Example 2.2.6
2.3.7 Code for Example 2.2.8
References
Chapter 3 Smoothing Methods
3.1 Some Background in Kernel Estimation
3.2 Estimating the Density Function
3.3 Asymptotic Properties
3.4 Data‐driven Bandwidth Selection
3.4.1 Normal Reference Bandwidth Selection
3.4.2 Plug‐in Bandwidth Selection
3.4.3 Least‐squares Cross‐validation Bandwidth Selection
3.4.4 Smoothed Bootstrap Bandwidth Selection
3.4.5 Bandwidth Selectors in Practice
3.5 Further Issues in Kernel Density Estimation
3.6 Estimating the Hazard Function
3.7 R Code for the Examples
3.7.1 Code for Example 3.2.1
3.7.2 Code for Examples 3.3.4 and 3.3.5
3.7.3 Code for Examples 3.4.2 and 3.4.3
3.7.4 Code for Example 3.5.1
3.7.5 Code for Example 3.6.4
3.7.6 Code for Example 3.6.5
References
Chapter 4 Regression Analysis
4.1 Observational Bias in Regression
4.2 Proportional Hazards Regression
4.3 Accelerated Failure Time Regression
4.4 Nonparametric Regression
4.5 R Code for the Examples
4.5.1 Code for Example 4.1.1
4.5.2 Code for Example 4.1.4
4.5.3 Code for Example 4.2.4
4.5.4 Code for Example 4.3.2
4.5.5 Code for Example 4.4.2
References
Chapter 5 Further Topics
5.1 Two‐Sample Problems
5.2 Competing Risks
5.2.1 Cumulative Incidences
5.2.2 Regression Models for Competing Risks
5.3 Testing for Quasi‐independence
5.4 Dependent Truncation
5.5 R Code for the Examples
5.5.1 Code for Example 5.1.3
5.5.2 Code for Example 5.2.4
5.5.3 Code for Example 5.2.6
5.5.4 Code for Example 5.3.1
5.5.5 Code for Example 5.4.3
References
A Packages and Functions in R
A.1 Computing the NPMLE and Standard Errors
A.2 Assessing the Existence and Uniqueness of the NPMLE
A.3 Semiparametric and Parametric Estimation
A.4 Kernel Estimation
A.5 Regression Analysis
A.6 Competing Risks
A.7 Simulating Data
A.8 Testing Quasi‐independence
A.9 Dependent Truncation
References
Index
EULA