生存分析

章节摘录

版权页：   插图：   Another popular graphical method for checking the proportional hazards assumption in the Cox model is using the Arjas(1988)plots.Specifically,the Arjas plots are designed to make direct comparisons between observed and estimated event frequencies without adding a time-dependent variable.Therefore,this method is not based on the estimation of alternative models and only involves parameter estimates already derived from the partial likelihood procedure. According to Arjas(1988),the application of the stratified Cox model is subject to two types of defects:(1)an influential covariate may be deleted from the model(this defect has been discussed in Section 5.5 of this book)and(2)the stratified Cox model is based on the assumption of a common baseline hazard for all individuals,so that the individuals are stratified according to the baseline hazard.These two defects can seriously influence the efficiency of the Cox model,thus making it difficult to perform a graphical check correctly on the validity of the proportionality hypothesis.Accordingly,he proposes to test the pro-portionality assumption directly from the proportional hazard model including all(M+1)covariates. Practically,deriving the Arjas plots can be performed by taking the following steps.First,divide n individuals into K strata of the(M+1)th covariate according to the research interest of a particular study or previous findings.If the(M+1)th covariate is a continuous variable,classify the sample respondents into a few categories according to an existing theory or results from a previous empirical analysis.Second,calculate the estimated cumulative hazard rate at each observed survival time for each stratum using the parameter estimates obtained from the Cox model.Third,compute the cumulative number of actual events at each survival time for each stratum.Fourth,plot the estimated cumulative hazard rate at each actual survival time along the y axis against the corresponding observed cumulative number of events on the x axis for each stratum.Eventually,discrepancies between the estimated cumulative hazard rate and the empirical data can display whether the estimated hazard rates of those stata are scattered randomly or systematically too high or too low.

内容概要

　　刘宪，1991年5月获密歇根大学社会学博士学位，现任美国国防医科大学（Uniformed Services
University of the Health
Sciences）精神病学系高级研究员、副教授及美国沃尔特里德国家军事医学中心（Walter Reed Army Medical
Center）研究员、高级统计师。在国际顶级刊物发表学术论文数十篇。截至2012年3月，所发表学术论文在国际各类刊物被引用1000多次。刘宪博士的主要研究领域为生存分析与死亡率交叉研究、纵向资料分析、创伤事件与精神疾病。

书籍目录

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
……
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

编辑推荐

《生存分析:模型与应用(英文)》是由刘宪著，高等教育出版社出版的。《生存分析:模型与应用(英文)》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。

作者简介

生存分析：模型与应用（英文版），ISBN：9787040348262，作者：刘宪 著

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