Survival Models and Data Analysis

Regina C. Elandt-Johnson, Norman L. Johnson

• Publisher: Wiley-Interscience
• Year: 2014
• Print ISBN: 9780471349921, 9780471031741
• eBook ISBN: 9781119011033
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Survival analysis deals with the distribution of life times, essentially the times from an initiating event such as birth or the start of a job to some terminal event such as death or pension. This book, originally published in 1980, surveys and analyzes methods that use survival measurements and concepts, and helps readers apply the appropriate method for a given situation. Four broad sections cover introductions to data, univariate survival function, multiple-failure data, and advanced topics.

Part 1

SURVIVAL MEASUREMENTS AND CONCEPTS

CHAPTER 1

Survival Data

1.1 SCOPE OF THE BOOK

The title of this book indicates that we discuss the treatment of “mortality data.” The direct meaning of this term is data that arise from recording times of death of individuals in a specified group. There will usually be additional data from observations of characters (other than survival or death) on the individuals in the group. These may be made at or near the moment of death (e.g., cause of death, length of illness, physical characteristics near the moment of death) or at earlier times (e.g., sex, age, family history, physical characteristics at earlier epochs). Certain of these variables—most commonly age (time elapsed since birth) and/or time elapsed since other important events (e.g., commencement of illness, date of operation)—are regarded as being of primary interest. It is often desired to assess the relationship between mortality and these primary variables, allowing, as far as possible for some of the other characteristics. The latter, in this context, are called concomitant variables. (Note that, for a given set of data, the distinction between primary and concomitant variables depends on the relationships to be studied.)

Individuals in the group may be humans, animals, fishes, insects, and so on. The group itself may be defined in various ways—by geographical location (e.g., population of a town or state, patients in a hospital or in a set of hospitals), by previous history (e.g., medical treatment, type of sickness, employment).

Occasionally we consider situations in which the replacement of “mortality” by the more general term “failure” is appropriate. In such contexts, the individuals are not necessarily (although they may be) living organisms. They may, for example, be mass-produced articles, such as electric lamps, with failure meaning inability to function in a specified role.

We are not primarily concerned with reversible changes of status, such as sickness causing temporary inability to work or repairable failure of electrical or mechanical systems. However there are occasional references to these matters, and Chapter 14 is devoted to discussing the distribution of age of onset of a disease.

Also, we are not concerned with statistics of birth, except as defining entry into a specific group of individuals and contributing to the assessment of mortality at juvenile ages. In particular, we do not study the measurement of fertility or the general province of demography.

Primarily, we are concerned with the study of failure data, and the relation of failure to a few important variables, such as age or time elapsed since some event (other than birth or manufacture). Other variables (concomitant variables) are introduced because of a possible relationship with failure but are not studied for their own sake.

1.2 SOURCES OF DATA

From the foregoing description, it can be seen that the methods discussed are applicable to a wide variety of situations. The sources of data are correspondingly varied. We first describe sources of mortality data, later turning to the topic of failure data in general.

A major subdivision of mortality data is between data relating to populations under more or less uncontrolled conditions (such as statistics of human deaths in a state or nation) and those observed under controlled conditions of a more or less experimental nature (as in a clinical trial).

Usually, the amount of data collected in the former situation is considerably greater than in the latter, though this need not be so. On the other hand, we almost always have more detailed information on each individual exposed to risk in the latter situation. In fact, in the uncontrolled situation we rarely have an exact enumeration of all the individuals who might be observed to fail (those exposed to risk). (A more precise discussion and definition of exposed to risk can be found in Chapter 2.)

When the date of death is recorded in a specific area over a specific period of time, estimates of the number exposed to ri...

Table of contents

• Cover
• Half Title page
• Title page
• Copyright page
• Preface
• Part 1: Survival Measurements and Concepts
• Part 2: Mortality Experiences and Life Tables
• Part 3: Multiple Types of Failure
• Part 4: Some More Advanced Topics
• Author Index
• Subject Index