生存分析 : 模型与应用

Preface

1 Introduction

1.1 What is survival analysis and how is it applied?

1.2 The history of survival analysis and its progress

1.3 General features of survival data structure

1.4 Censoring

1.4.1 Mechanisms of right censoring

1.4.2 Left censoring, interval censoring, and left truncation

1.5 Time scale and the origin of time

1.5.1 Observational studies

1.5.2 Biomedical studies

1.5.3 Health care utilization

1.6 Basic lifetime functions

1.6.1 Continuous lifetime functions

1.6.2 Discrete lifetime functions

1.6.3 Basic likelihood functions for right, left, and interval censoring

1.7 Organization of the book and data used for illustrations

1.8 Criteria for performing survival analysis

2 Descriptive approaches of survival analysis

2.1 The Kaplan-Meier （product-limit） and Nelson-Aalen estimators

2.1.1 Kaplan-Meier estimating procedures with or without censoring

2.1.2 Formulation of the Kaplan-Meier and Nelson-Aalen estimators

2.1.3 Variance and standard error of the survival function

2.1.4 Confidence intervals and confidence bands of the survival function

2.2 Life table methods

2.2.1 Life table indicators

2.2.2 Multistate life tables

2.2.3 Illustration: Life table estimates for older Americans

2.3 Group comparison of survival functions

2.3.1 Logrank test for survival curves of two groups

2.3.2 The Wilcoxon rank sum test on survival curves of two groups

2.3.3 Comparison of survival functions for more than two groups

2.3.4 Illustration: Comparison of survival curves between married and unmarried persons

2.4 Summar

3 Some popular survival distribution functions

3.1 Exponential survival distribution

3.2 The Weibull distribution and extreme value theory

3.2.1 Basic specifications of the Weibull distribution

3.2.2 The extreme value distribution

3.3 Gamma distribution

3.4 Lognormal distribution

3.5 Log-logistic distribution

3.6 Gompertz distribution and Gompertz-type hazard models

3.7 Hypergeometric distribution

3.8 Other distributions

3.9 Summary

4 Parametric regression models of survival analysis

4.1 General specifications and inferences of parametric regression models

4.1.1 Specifications of parametric regression models on the hazard function

4.1.2 Specifications of accelerated failure time regression models

4.1.3 Inferences of parametric regression models and likelihood functions

4.1.4 Procedures of maximization and hypothesis testing on ML estimates

4.2 Exponential regression models

4.2.1 Exponential regression model on the hazard function

4.2.2 Exponential accelerated failure time regression model

4.2.3 Illustration: Exponential regression model on marital status and survival among older Americans

4.3 Weibull regression models

4.3.1 Weibull hazard regression model

4.3.2 Weibull accelerated failure time regression model

4.3.3 Conversion of Weibull proportional hazard and AFI' parameters

4.3.4 Illustration: A Weibull regression model on marital status and survival among older Americans

4.4 Log-Iogistic regression models

4.4.1 Specifications of the log-logistic AFI' regression model

4.4.2 Retransformation of AFT parameters to untransformed log-logistic parameters

4.4.3 Illustration: The log-logistic regression model on mar:ital status and survival among the oldest old Americans

4.5 Other parametric regression models

4.5.1 The lognormal regression model

4.5.2 Gamma distributed regression models

4.6 Parametric regression models with interval censoring

4.6.1 Inference of parametric regression models with interval censoring

4.6.2 Illustration: A parametric survival model with independent interval censoring

4.7 Summary

5 The Cox proportional hazard regression model and advances

5.1 The Cox semi-parametric hazard model

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6 Counting processes and diagnostics of the Cox model

7 Competing risks models and repeated events

8 Structural hazard rate regression models

9 Special topics

Appendix A The delta method

《应用统计学丛书·生存分析：模型与应用 （英文版）》旨在系统地介绍生存分析的基本概念、理论设定和方法运用，重点在于通过SAS统计软件对实际数据进行分析，深入浅出地描述生存分析的各类模型。书中涉及的统计方法包括Kaplan-Meirer估算法、各类参数回归模型、Cox等比发生率模型、多向发生率模型和重复发生率模型、结构性风险率模型以及一些生存分析方面的专题研究方法。
《应用统计学丛书·生存分析：模型与应用 （英文版）》着重于各类生存分析模型的实际运用，而不拘泥于模型的纯理论推导，从而使对生存分析有兴趣的科研人员以及大学生、研究生从中受益。