Censoring and Stochastic Integrals


Book Description

We study the basic nonparametric statistical methods of survival analysis using the tools of counting processes, martingale theory, and stochastic integration, introduced by O. O. Aalen. Covered are: the two-sample tests of Gehan and of Efron, the two sample log rank test of Mantel and others; and the Kaplan Meier estimator. Asymptotic normality under a wide range of censoring mechanisms is obtained using the martingale central limit theorem.




Statistical Inference from Stochastic Processes


Book Description

Comprises the proceedings of the AMS-IMS-SIAM Summer Research Conference on Statistical Inference from Stochastic Processes, held at Cornell University in August 1987. This book provides students and researchers with a familiarity with the foundations of inference from stochastic processes and intends to provide a knowledge of the developments.




Analysis of Censored Data


Book Description




Empirical Processes with Applications to Statistics


Book Description

Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables; applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods; and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition. Audience: researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.




Statistical Methods for Cancer Studies


Book Description

This book focuses on public health and epidemiologic aspects of cancer, and explores the sources of information concerning the frequency of occurrence of human cancer. It describes statistical methods useful in studying problems arising in the field of cancer and its concurrent development.




Probabilistic Causality in Longitudinal Studies


Book Description

In many applied fields of statistics the concept of causality is central to a scientific investigation. The author's aim in this book is to extend the classical theories of probabilistic causality to longitudinal settings and to propose that interesting causal questions can be related to causal effects which can change in time. The proposed prediction method in this study provides a framework to study the dynamics and the magnitudes of causal effects in a series of dependent events. Its usefulness is demonstrated by the analysis of two examples both drawn from biomedicine, one on bone marrow transplants and one on mental hospitalization. Consequently, statistical researchers and other scientists concerned with identifying causal relationships will find this an interesting and new approach to this problem.




Recent Advances in Reliability Theory


Book Description

This book presents thirty-one extensive and carefully edited chapters providing an up-to-date survey of new models and methods for reliability analysis and applications in science, engineering, and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.




Advances in Statistical Methods for the Health Sciences


Book Description

Statistical methods have become an increasingly important and integral part of research in the health sciences. Many sophisticated methodologies have been developed for specific applications and problems. This self-contained comprehensive volume covers a wide range of topics pertaining to new statistical methods in the health sciences, including epidemiology, pharmacovigilance, quality of life, survival analysis, and genomics. The book will serve the health science community as well as practitioners, researchers, and graduate students in applied probability, statistics, and biostatistics.




Nonparametric Tests for Censored Data


Book Description

This book concerns testing hypotheses in non-parametric models. Generalizations of many non-parametric tests to the case of censored and truncated data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.