Statistical Models Based on Counting Processes / by Per K. Andersen, Ornulf Borgan, Richard D. Gill, Niels Keiding.

Format:

Book

Author/Creator:

Andersen, Per K., author.

Borgan, Ørnulf, Author.

Gill, R. D., Author.

Keiding, Niels, Author.

Series:

Springer Series in Statistics, 2197-568X

Language:

English

Subjects (All):

Statistics.

Statistical Theory and Methods.

Local Subjects:

Statistical Theory and Methods.

Physical Description:

1 online resource (XI, 784 pages)

Edition:

1st ed. 1993.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1993.

Language Note:

English

Summary:

Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a- half decades. The exposition of the theory is integrated with careful presentation of many practical examples, almost exclusively from the authors' own experience, with detailed numerical and graphical illustrations. Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in concrete detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliabilty engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject. "This book is a masterful account of the counting process approach...is certain to be the standard reference for the area, and should be on the bookshelf of anyone interested in event-history analysis." International Statistical Institute Short Book Reviews "...this impressive reference, which contains a a wealth of powerful mathematics, practical examples, and analytic insights, as well as a complete integration of historical developments and recent advances in event history analysis." Journal of the American Statistical Association.

Contents:

I. Introduction

I.1 General Introduction to the Book

I.2 Brief Survey of the Development of the Subject

I.3 Presentation of Practical Examples

II. The Mathematical Background

II.1 An Informal Introduction to the Basic Concepts

II.2 Preliminaries: Processes, Filtrations, and Stopping Times

II.3 Martingale Theory

II.4 Counting Processes

II.5 Limit Theory

II.6 Product-Integration and Markov Processes

II.7 Likelihoods and Partial Likelihoods for Counting Processes

II.8 The Functional Delta-Method

II.9 Bibliographic Remarks

III. Model Specification and Censoring

III.1 Examples of Counting Process models for Complete Life History Data. The Multiplicative Intensity Model

III.2 Right-Censoring

III. 3 Left-Truncation

III.4 General Censorship, Filtering, and Truncation

III.5 Partial Model Specification. Time-Dependent Covariates

III.6 Bibliographic Remarks

IV. Nonparametric Estimation

IV. 1 The Nelson-Aalen estimator

IV.2 Smoothing the Nelson-Aalen Estimator

IV.3 The Kaplan-Meier Estimator

IV.4 The Product-Limit Estimator for the Transition Matrix of a Nonhomogeneous Markov Process

IV.5 Bibliographic Remarks

V. Nonparametric Hypothesis Testing

V.1 One-Sample Tests

V.2 k-Sample Tests

V.3 Other Linear Nonparametric Tests

V.4 Using the Complete Test Statistic Process

V.5 Bibliographic Remarks

VI. Parametric Models

VI.1 Maximum Likelihood Estimation

VI.2 M-Estimators

VI.3 Model Checking

VI.4 Bibliographic Remarks

VII. Regression Models

VII.1 Introduction. Regression Model Formulation

VII.2 Semiparametric Multiplicative Hazard Models

VII.3 Goodness-of-Fit Methods for the Semiparametric Multiplicative Hazard Model

VII.4 Nonparametric Additive Hazard Models

VII.5 Other Non- and Semi-parametric Regression Models

VIL6 Parametric Regression Models

VII.7 Bibliographic Remarks

VIII. Asymptotic Efficiency

VIII.1 Contiguity and Local Asymptotic Normality

VIII.2 Local Asymptotic Normality in Counting Process Models

VIII.3 Infinite-dimensional Parameter Spaces: the General Theory

VIII.4 Semiparametric Counting Process Models

VIII.5 Bibliographic Remarks

IX. Frailty Models

IX.1 Introduction

IX.2 Model Construction

IX. 3 Likelihoods and Intensities

IX.4 Parametric and Nonparametric Maximum Likelihood Estimation with the EM-Algorithm

IX.5 Bibliographic Remarks

X. Multivariate Time Scales

X.1 Examples of Several Time Scales

X.2 Sequential Analysis of Censored Survival Data with Staggered Entry

X.3 Nonparametric Estimation of the Multivariate Survival Function

X.4 Bibliographic Remarks

Appendix The Melanoma Survival Data and Standard Mortality Tables for the Danish Population 1971–75

References

Author Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9781461243489

1461243483