Author | Andersen, Per Kragh. author |
---|---|
Title | Statistical Models Based on Counting Processes [electronic resource] / by Per Kragh Andersen, รrnulf Borgan, Richard D. Gill, Niels Keiding |
Imprint | New York, NY : Springer US, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4348-9 |
Descript | XI, 784 p. online resource |
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 1971โ75 -- References -- Author Index