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El. knyga: Statistical Inference on Residual Life

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This is a monograph on the concept of residual life, which is an alternative summary measure of time-to-event data, or survival data. The mean residual life has been used for many years under the name of life expectancy, so it is a natural concept for summarizing survival or reliability data. It is also more interpretable than the popular hazard function, especially for communications between patients and physicians regarding the efficacy of a new drug in the medical field. This book reviews existing statistical methods to infer the residual life distribution. The review and comparison includes existing inference methods for mean and median, or quantile, residual life analysis through medical data examples. The concept of the residual life is also extended to competing risks analysis. The targeted audience includes biostatisticians, graduate students, and PhD (bio)statisticians. Knowledge in survival analysis at an introductory graduate level is advisable prior to reading this book.

Recenzijos

It is the very first book in its kind that is entirely devoted to the statistical methodologies aimed to analyze residual life and related quantities. would be a must-have item for researchers who are interested in learning statistical theory on the quantile residual life functions. would be a valuable asset to those who work on survival analysis. It would be beneficial to a wide group of audience who are interested in the analysis of quantile residual functions. (Sangwook Kang, Journal of Agricultural, Biological, and Environmental Statistics, Vol. 20, 2015)

This book on the statistical analysis of life expectancy focuses on history, research achievements, and recent developments in statistical inference on quantile residual lifetime. The intended audience includes graduate students and researchers both in academia and in industry who are interested in learning the theory and application of the residual life function. This book is strongly recommended to beginning researchers and statistician who are interested in learning the theory and application of the residual life function. (Samit Bhatheja, Doodys Book Reviews, May, 2014)

1 Introduction 1(18)
1.1 Almost Sure Convergence
1(1)
1.2 Strong Law of Large Numbers
2(1)
1.3 Brownian Motion and Brownian Bridge
3(4)
1.3.1 Brownian Motion
3(3)
1.3.2 Brownian Bridge
6(1)
1.4 Empirical and Quantile Processes
7(2)
1.4.1 Empirical Process
7(2)
1.4.2 Uniform Quantile Process
9(1)
1.5 Counting Process Martingale
9(8)
1.5.1 Definition of Counting Process
9(2)
1.5.2 Martingale
11(2)
1.5.3 Basic Counting Process Martingale
13(2)
1.5.4 Martingale Representation of the Kaplan-Meier Estimator
15(2)
1.6 Check Function
17(2)
2 Inference on Mean Residual Life-Overview 19(8)
2.1 Mean Residual Life Function
20(1)
2.2 One- and Two-sample Cases
21(2)
2.3 Regression on Mean Residual Life
23(4)
3 Quantile Residual Life 27(50)
3.1 Quantile Function
28(3)
3.1.1 Asymptotic Variance Formula
28(1)
3.1.2 Asymptotic Normality
29(2)
3.2 Quantile Residual Life Function
31(2)
3.3 Quantile Residual Life Process
33(3)
3.4 Parametric Inference
36(5)
3.4.1 One-Sample Case
36(4)
3.4.2 Independent Two-Sample Case
40(1)
3.5 Nonparametric Inference
41(14)
3.5.1 One-Sample Case
41(8)
3.5.2 Independent Two-Sample Case
49(6)
3.6 Regression on Quantile Residual Life
55(20)
3.6.1 Parametric Estimation of Regression Parameters
56(4)
3.6.2 "Setting the Clock Back to 0" Property
60(5)
3.6.3 Semiparametric Regression
65(10)
3.7 Further Reading and Future Direction
75(2)
4 Quantile Residual Life Under Competing Risks 77(42)
4.1 Competing Risks
78(5)
4.1.1 Cause-Specific Hazard and Cumulative Incidence Function
78(2)
4.1.2 Subdistribution Hazard Function
80(1)
4.1.3 Bivariate Point of View
81(2)
4.2 Quantile Residual Life Under Competing Risks
83(2)
4.3 Parametric Inference
85(13)
4.3.1 One-Sample Case
85(6)
4.3.2 Independent Two-Sample Case
91(1)
4.3.3 Parametric Regression
92(6)
4.4 Nonparametric Inference
98(19)
4.4.1 One-Sample Case
99(6)
4.4.2 Independent Two-Sample Case
105(5)
4.4.3 Semiparametric Regression
110(7)
4.5 Further Reading and Future Direction
117(2)
5 Other Methods for Inference on Quantiles 119(22)
5.1 Issues in Inference on Quantiles
119(1)
5.2 Empirical Likelihood Approach
120(17)
5.2.1 Empirical Likelihood Ratio for the Population Mean
121(3)
5.2.2 Kaplan-Meier Estimator; Nonparametric MLE
124(3)
5.2.3 Constrained EM Algorithm for Censored Data
127(6)
5.2.4 Estimating Equation for Quantile Residual Life
133(2)
5.2.5 Empirical Likelihood Inference on Quantile Residual Life Regression
135(2)
5.3 Bayesian Inference Under Heavy Censoring
137(2)
5.4 Further Reading and Future Direction
139(2)
6 Study Design Based on Quantile (Residual Life) 141(10)
6.1 Sample Size Calculation in the Absence of Competing Risks
142(4)
6.2 Sample Size Calculation Under Competing Risks
146(5)
Appendix: R Codes 151(30)
A.1 Example 3.3 in Sect. 3.5.1
151(3)
A.2 Example 3.4 in Sect. 3.5.2
154(4)
A.3 Example 3.11 in Sect. 3.6.3
158(8)
A.4 Example 4.3 in Sect. 4.3.1
166(5)
A.5 Example 4.4 in Sect. 4.4.2
171(7)
A.6 Example 5.2 in Sect. 5.2.3
178(3)
References 181(16)
About the Author 197(2)
Index 199
Dr. Jong-Hyeon Jeong is a full professor of Biostatistics at the University of Pittsburgh. Dr. Jeong's main research area has been survival analysis and clinical trials. In survival analysis, he has worked on frailty modeling, efficiency of survival probability estimates from the proportional hazards model, weighted log-rank test, competing risks, quantile residual life, and likelihood theory such as empirical likelihood and hierarchical likelihood. In clinical trials, he has been involved in several phase III clinical trials on breast cancer treatment as the primary statistician. He has been teaching statistical theory courses and survival analysis in the Department of Biostatistics at the University of Pittsburgh. Dr. Jeong holds his PhD degree in statistics from the University of Rochester and has been an elected member of the International Statistical Institute (ISI) since 2007.
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