Empirical likelihood method in survival analysis

Table of Contents

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.

Features

Demonstrates the power of the empirical likelihood method in various applications
Discusses how to infer a recent extension of the Cox model using the method
Shows how to optimize confidence regions that are different in shape and orientation
Incorporates historical notes and exercises in each chapter
Provides the R packages (emplik and ELYP) for download on CRAN and the author’s website

Summary

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.

https://www.crcpress.com/Empirical-Likelihood-Method-in-Survival-Analysis/Zhou/p/book/9781466554924