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

ISBN-13: 9781119951377 / Angielski / Twarda / 2021 / 192 str.

Jacobo J. de U?a-Alvarez; Rosa R. Crujeiras; Carla C. Moreira

Spis treści

Preface xiList of Abbreviations xiiiNotation xv1 Introduction 11.1 Random Truncation 11.2 One-sided Truncation 21.2.1 Left-truncation 21.2.2 Right-truncation 21.2.3 Truncation vs. Censoring 31.3 Double Truncation 31.4 Real Data Examples 51.4.1 Childhood Cancer Data 51.4.2 AIDS Blood Transfusion Data 61.4.3 Equipment-S Rounded Failure Time Data 71.4.4 Quasar Data 71.4.5 Parkinson's Disease Data 81.4.6 Acute Coronary Syndrome Data 9References 102 One-Sample Problems 132.1 Nonparametric Estimation of a Distribution Function 132.1.1 The NPMLE 142.1.2 Numerical Algorithms for Computing the NPMLE 212.1.3 Theoretical Properties of the NPMLE 242.1.4 Standard Errors and Confidence Limits 362.2 Semiparametric and Parametric Approaches 432.2.1 Semiparametric Approach 442.2.2 Parametric Approach 522.3 R Code for the Examples 562.3.1 Code for Example 2.1.8 562.3.2 Code for Examples 2.1.11 and 2.1.13 562.3.3 Code for Example 2.1.14 582.3.4 Code for Example 2.1.15 592.3.5 Code for Example 2.1.22 602.3.6 Code for Example 2.2.6 612.3.7 Code for Example 2.2.8 62References 653 Smoothing Methods 693.1 Some Background in Kernel Estimation 693.2 Estimating the Density Function 713.3 Asymptotic Properties 713.4 Data-driven Bandwidth Selection 773.4.1 Normal Reference Bandwidth Selection 783.4.2 Plug-in Bandwidth Selection 793.4.3 Least-squares Cross-validation Bandwidth Selection 803.4.4 Smoothed Bootstrap Bandwidth Selection 813.4.5 Bandwidth Selectors in Practice 823.5 Further Issues in Kernel Density Estimation 883.6 Estimating the Hazard Function 903.7 R Code for the Examples 983.7.1 Code for Example 3.2.1 983.7.2 Code for Examples 3.3.4 and 3.3.5 993.7.3 Code for Examples 3.4.2 and 3.4.3 1003.7.4 Code for Example 3.5.1 1023.7.5 Code for Example 3.6.4 1043.7.6 Code for Example 3.6.5 105References 1064 Regression Analysis 1094.1 Observational Bias in Regression 1094.2 Proportional Hazards Regression 1144.3 Accelerated Failure Time Regression 1174.4 Nonparametric Regression 1214.5 R Code for the Examples 1264.5.1 Code for Example 4.1.1 1264.5.2 Code for Example 4.1.4 1264.5.3 Code for Example 4.2.4 1274.5.4 Code for Example 4.3.2 1274.5.5 Code for Example 4.4.2 128References 1295 Further Topics 1315.1 Two-Sample Problems 1325.2 Competing Risks 1375.2.1 Cumulative Incidences 1395.2.2 Regression Models for Competing Risks 1425.3 Testing for Quasi-independence 1465.4 Dependent Truncation 1505.5 R Code for the Examples 1575.5.1 Code for Example 5.1.3 1575.5.2 Code for Example 5.2.4 1595.5.3 Code for Example 5.2.6 1605.5.4 Code for Example 5.3.1 1615.5.5 Code for Example 5.4.3 161References 162A Packages and Functions in R 165A.1 Computing the NPMLE and Standard Errors 166A.2 Assessing the Existence and Uniqueness of the NPMLE 167A.3 Semiparametric and Parametric Estimation 168A.4 Kernel Estimation 168A.5 Regression Analysis 169A.6 Competing Risks 169A.7 Simulating Data 170A.8 Testing Quasi-independence 170A.9 Dependent Truncation 170References 171Index 173

O autorze

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.