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生物与健康生存分析自学手册(第三版)
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《生存分析自学手册》英文原版第三版是一本专注于生物与健康领域统计学的实用教材。该书由统计学家David G. Kleinbaum和Mitchel Klein合著,作为"Statistics for Biology and Health"系列的一部分,旨在帮助读者掌握生存分析这一关键的统计技术。生存分析在医学、生物学、社会科学等领域广泛应用,主要用于研究事件发生时间(如疾病发展、寿命预期或故障发生)的分布和影响因素。 本书适合自我学习者,特别是对生物医学研究感兴趣的人员,因为它提供了深入浅出的理论讲解和实践案例,涵盖了诸如 Cox回归、 Kaplan-Meier曲线、生存函数、截尾数据处理等核心概念。作者们强调了生存分析的实际应用,不仅介绍了理论模型,还通过使用常见的统计软件(如SAS、SPSS和STATA)来演示如何实施分析和解读结果。 第三版的出版进一步更新了内容,包括最新的研究方法和软件技巧,确保读者能够跟上快速发展的数据分析趋势。此外,本书附有详细的示例数据集和练习题,以便读者在实践中巩固所学知识。版权信息表明,本书享有Springer Science+Business Media公司的版权保护,适用于学术和教学目的。 《生存分析自学手册》英文原版第三版是一本全面且实用的指南,对于希望深入理解生存分析及其在实际问题中的应用的读者来说,无论是初学者还是经验丰富的专业人员,都是不可或缺的学习资料。通过阅读这本书,读者不仅能掌握生存分析的基本原理,还能提升数据处理和解释结果的能力,为科学研究和决策提供强有力的支持。
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1
Introduction
to Survival
Analysis
D.G. Kleinbaum and M. Klein, Survival Analysis: A Self-Learning Text, Third Edition,
Statistics for Biology and Health, DOI 10.1007/978-1-4419-6646-9_1,
#
Springer Science+Business Media, LLC 2012
1
Introduction This introduction to survival analysis gives a descriptive
overview of the data analytic approach called survival
analysis. This approach includes the type of problem
addressed by survival analysis, the outcome variable con-
sidered, the need to take into account “censored data,”
what a survival function and a hazard function represent,
basic data layouts for a survival analysis, the goals of sur-
vival analysis, and some examples of survival analysis.
Because this chapter is primarily descriptive in content, no
prerequisite mathematical, statistical, or epidemiologic
concepts are absolutely necessar y. A first course on the
principles of epidemiologic research would be helpful. It
would also be helpfu l if the reader has had some experi-
ence reading mathematical notation and formulae.
Abbreviated
Outline
The outline below gives the user a preview of the material
to be covered by the presentation. A detailed outline for
review purposes follows the presentation.
I. What is survival analysis? (pages 4–5)
II. Censored data (pages 5–8)
III. Terminology and notation (pages 9–15)
IV. Goals of survival analysis (page 16)
V. Basic data layout for computer (pages 16–23)
VI. Basic data layout for understanding analysis
(pages 23–28)
VII. Descriptive measures of survival experience
(pages 28–30)
VIII. Example: Extended remission data (pages 30–33)
IX. Multivariable example (pages 33–35)
X. Math models in survival analysis (pages 35–37)
XI. Censoring assumptions (pages 37–43)
2 1. Introduction to Survival Analysis
ᒧݩ
Objectives Upon completing the chapter, the learner should be able to:
1. Recognize or describe the type of problem addressed
by a survival analysis.
2. Define what is meant by censored data.
3. Define or recognize right-censored data .
4. Give three reasons why data may be cen sored.
5. Define, recognize, or interpret a survivor function.
6. Define, recognize, or interpret a hazard function.
7. Describe the relationship between a survivor function
and a hazard function.
8. State three goals of a survival analysis.
9. Identify or recognize the basic data layout for the
computer; in particular, put a given set of survival
data into this lay out.
10. Identify or recognize the basic data layout, or
components thereof, for understanding modeling
theory; in particular, put a given set of survival data
into this layout.
11. Interpret or compare examples of survivor curves or
hazard functions.
12. Given a problem situation, state the goal of a survival
analysis in terms of des cribing how explanatory
variables relate to survival time.
13. Compute or interpret average survival and/or average
hazard measures from a set of survival data.
14. Define or interpret the hazard ratio defined from
comparing two groups of survival data.
Objectives 3
Presentation
This presentation gives a general introduction
to survival analysis, a popular data analys is
approach for certain kinds of epidemiologic
and other data. Here we focus on the problem
addressed by survival analysis, the goals of a
survival analysis, key notation and terminol -
ogy, the basic data layout, and some examples.
I. What Is Survival
Analysis?
We begin by describing the type of analytic
problem addressed by survival analys is. Gener-
ally, survival analysis is a collection of statisti-
cal procedures for data analys is for which the
outcome variable of interest is time until an
event occurs.
By time, we mean years, months, weeks, or
days from the beginning of follow-up of an
individual until an event occurs; alternatively,
time can refer to the age of an individual when
an event occurs.
By event, we mean death, disease incidence,
relapse from remission, recovery (e.g., return to
work) or any designated experience of interest
that may happen to an individual.
Although more than one event may be consid-
ered in the same analysis, we will assume that
only one event is of designated interest. When
more than one event is considered (e.g., death
from any of several causes), the statistical prob-
lem can be characterized as either a recurrent
event or a competing risk problem, which are
discussed in Chaps. 8 and 9, respectively.
In a survival analysis, we usually refer to the
time variable as survival time, because it gives
the time that an individual has “survived” over
some follow-up period. We also typically refer
to the event as a failure, because the event of
interest usually is death, disease incidence, or
some other negative individual experience.
However, survival time may be “time to return
to work after an elective surgical procedure,” in
which case failure is a positive event.
the problem
FOCUS
goals
data layout
examples
terminology and
notation
Outcome variable: Time until an
event occurs
TIME
Start follow-up
Event
Event: death
disease
relapse
recovery
Assume 1 event
> 1 event
Recurrent event
or
Competing risk
Time ! survival time
Event ! failure
4 1. Introduction to Survival Analysis
ၞᤈየ
ݎ
Five examples of survival analysis problems
are briefly mentioned here. The first is a study
that follows leukemia patients in remission
over several weeks to see how long they stay
in remission. The second example follows a
disease-free cohort of individuals over several
years to see who develops heart disease. A third
example considers a 13-year follow-up of an
elderly population (60þ years) to see how long
subjects remain alive. A fourth example follows
newly released parolees for several weeks to
see whether they get rearrested. This type of
problem is called a recidivism study. The fifth
example traces how long patients survive after
receiving a he art transplant.
All of the above examples are survival analysis
problems because the outcome variable is time
until an event occurs. In the first example,
involving leukemia patients, the event of inter-
est (i.e., failure) is “going out of remission,”
and the outcome is “time in weeks until a
person goes out of remission.” In the second
example, the event is “developing heart dis-
ease,” and the outcome is “time in years until
a person develops heart disease.” In the third
example, the event is “death” and the outcome
is “time in years until death.” Example four,
a sociological rather than a medical study, con-
siders the event of recidi vism (i.e., getting rear-
rested), and the outcome is “time in weeks until
rearrest.” Finally, the fifth example considers
the event “death,” with the outcome being
“time until death (in months from receiving
a transplant).”
We will return to some of these examples later
in this presentation and in later presentations .
II. Censored Data
Most surviva l analyses must consider a key
analytical problem called censoring. In essence,
censoring occurs when we have some informa-
tion about individual survival time, but we don’t
know the survival time exactly.
EXAMPLE
1. Leukemia patients/time in remission
(weeks)
2. Disease-free cohort/time until heart
disease (years)
3. Elderly (60þ) population/time until
death (years)
4. Parolees (recidivism study)/time
until rearrest (weeks)
5. Heart transplants/time until death
(months)
Censoring: don’t know survival
time exactly
Presentation: II. Censored Data 5
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