Zhou Empirical Likelihood Method in Survival Analysis

Erscheinungsjahr 2015
ISBN: 978-1-4665-5493-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 220 Seiten

Reihe: Chapman & Hall/CRC Biostatistics Series

Add the Empirical Likelihood to Your Nonparametric Toolbox

Empirical Likelihood Method in Survival Analysis explains how to use the empirical likelihood method for right censored survival data. The author uses R for calculating empirical likelihood and includes many worked out examples with the associated R code. The datasets and code are available for download on his website and CRAN.

The book focuses on all the standard survival analysis topics treated with empirical likelihood, including hazard functions, cumulative distribution functions, analysis of the Cox model, and computation of empirical likelihood for censored data. It also covers semi-parametric accelerated failure time models, the optimality of confidence regions derived from empirical likelihood or plug-in empirical likelihood ratio tests, and several empirical likelihood confidence band results.

While survival analysis is a classic area of statistical study, the empirical likelihood methodology has only recently been developed. Until now, just one book was available on empirical likelihood and most statistical software did not include empirical likelihood procedures. Addressing this shortfall, this book provides the functions to calculate the empirical likelihood ratio in survival analysis as well as functions related to the empirical likelihood analysis of the Cox regression model and other hazard regression models.

Autoren/Hrsg.

Zhou, Mai

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Epidemiologie, Medizinische Statistik
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Introduction

Survival Analysis

Empirical Likelihood

Empirical Likelihood for Right Censored Data
Confidence Intervals Based on the EL Test

Datasets

Historical Notes

Empirical Likelihood for Linear Functionals of Hazard

Empirical Likelihood, Poisson Version

Feasibility of the Constraints (2.5)

Maximizing the Hazard Empirical Likelihood

Some Technical Details

Predictable Weight Functions

Two Sample Tests

Hazard Estimating Equations
Empirical Likelihood, Binomial Version

Poisson or Binomial?

Some Notes on Counting Process Martingales

Discussion, Remarks, and Historical Notes

Empirical Likelihood for Linear Functionals of the Cumulative Distribution Function

One Sample Means
Proof of Theorem 23

Illustration

Two Independent Samples

Equality of k Medians

Functionals of the CDF and Functionals of Hazard

Predictable Mean Function

Discussion, Historical Notes, and Remarks

Empirical Likelihood Analysis of the Cox Model

Introduction

Empirical Likelihood Analysis of the Cox Model

Confidence Band for the Baseline Cumulative Hazard

An Alternative Empirical Likelihood Approach

Yang and Prentice Extension of the Cox Model

Historical Notes

Some Known Results about the Cox Model

Empirical Likelihood Analysis of Accelerated Failure Time Models

AFT Models

AFT Regression Models

The Buckley–James Estimator

An Alternative EL Analysis for the Buckley–James Estimator

Rank Estimator for the AFT Regression Model

AFT Correlation Models

EL Analysis of AFT Correlation Models

Discussion and Historical Remarks

Computation of Empirical Likelihood Ratio with Censored Data

Empirical Likelihood for Uncensored Data

EL after Jackknife

One or Two Sample Hazard Features

Empirical Likelihood Testing Concerning Mean Functions

EL Testing within the Cox Models and Yang and Prentice Models

Testing for AFT Models

Empirical Likelihood for Overdetermined Estimating Equations
Testing Part of the Parameter Vector

Intermediate Parameters

Lorenz Curve and Trimmed Mean

Confidence Intervals

Historical Note and Generalizations

Optimality of Empirical Likelihood and Plug-in Empirical Likelihood
Pseudo Empirical Likelihood Ratio Test

Tests Based on Empirical Likelihood

Optimal Confidence Region

Illustrations

Adjustment of the Pseudo Empirical Likelihood Test

Weighted Empirical Likelihood

Discussion and Historical Notes

Miscellaneous
Smoothing

Exponential Tilted Likelihood
Confidence Bands

Discussion and Historical Notes

Bibliography

Index

Exercises appear at the end of each chapter.

Über Autor(innen)

Mai Zhou is a professor in the Department of Statistics at the University of Kentucky. His research interests include large sample theory and survival analysis. He earned a PhD from Columbia University.