Statistical models based on counting processes
Modern survival analysis and more general event history analysis may be handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, the subject of research for the past 15 years.
Read More ↓Title Statements
- Full title :Statistical models based on counting processes / Per Kragh Andersen [and others].
Summary
Modern survival analysis and more general event history analysis may be handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, the subject of research for the past 15 years.
Read More ↓Edition Statements
- Publication Date:©1993.
Publication Statements
- Publisher(s):Springer-Verlag
- Place of Publication:New York
- Language:eng
- Publication Date:©1993.
The Physical Object
- Description:xi, 767 pages : : illustrations ; : 24 cm
Edition Identifiers
- ISBN:0387978720, 9780387978727, 3540978720, 9783540978725, 0387945199, 9780387945194
- oclc:ocm25871722
- LC Classification:QA274.42
- Dewey Decimal:519.2/3
Table of 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 Proc…
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