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The Statistical Analysis of Multivariate Failure Time Data: A
Marginal Modeling Approach provides an innovative look at methods
for the analysis of correlated failure times. The focus is on the
use of marginal single and marginal double failure hazard rate
estimators for the extraction of regression information. For
example, in a context of randomized trial or cohort studies, the
results go beyond that obtained by analyzing each failure time
outcome in a univariate fashion. The book is addressed to
researchers, practitioners, and graduate students, and can be used
as a reference or as a graduate course text. Much of the literature
on the analysis of censored correlated failure time data uses
frailty or copula models to allow for residual dependencies among
failure times, given covariates. In contrast, this book provides a
detailed account of recently developed methods for the simultaneous
estimation of marginal single and dual outcome hazard rate
regression parameters, with emphasis on multiplicative (Cox)
models. Illustrations are provided of the utility of these methods
using Women's Health Initiative randomized controlled trial data of
menopausal hormones and of a low-fat dietary pattern intervention.
As byproducts, these methods provide flexible semiparametric
estimators of pairwise bivariate survivor functions at specified
covariate histories, as well as semiparametric estimators of cross
ratio and concordance functions given covariates. The presentation
also describes how these innovative methods may extend to handle
issues of dependent censorship, missing and mismeasured covariates,
and joint modeling of failure times and covariates, setting the
stage for additional theoretical and applied developments. This
book extends and continues the style of the classic Statistical
Analysis of Failure Time Data by Kalbfleisch and Prentice. Ross L.
Prentice is Professor of Biostatistics at the Fred Hutchinson
Cancer Research Center and University of Washington in Seattle,
Washington. He is the recipient of COPSS Presidents and Fisher
awards, the AACR Epidemiology/Prevention and Team Science awards,
and is a member of the National Academy of Medicine. Shanshan Zhao
is a Principal Investigator at the National Institute of
Environmental Health Sciences in Research Triangle Park, North
Carolina.
This book focuses on the calculus of variations, including
fundamental theories and applications. This textbook is intended
for graduate and higher-level college and university students,
introducing them to the basic concepts and calculation methods used
in the calculus of variations. It covers the preliminaries,
variational problems with fixed boundaries, sufficient conditions
of extrema of functionals, problems with undetermined boundaries,
variational problems of conditional extrema, variational problems
in parametric forms, variational principles, direct methods for
variational problems, variational principles in mechanics and their
applications, and variational problems of functionals with vector,
tensor and Hamiltonian operators. Many of the contributions are
based on the authors' research, addressing topics such as the
extension of the connotation of the Hilbert adjoint operator,
definitions of the other three kinds of adjoint operators, the
extremum function theorem of the complete functional, unified Euler
equations in variational methods, variational theories of
functionals with vectors, modulus of vectors, arbitrary order
tensors, Hamiltonian operators and Hamiltonian operator strings,
reconciling the Euler equations and the natural boundary
conditions, and the application range of variational methods. The
book is also a valuable reference resource for teachers as well as
science and technology professionals.
This book focuses on the calculus of variations, including
fundamental theories and applications. This textbook is intended
for graduate and higher-level college and university students,
introducing them to the basic concepts and calculation methods used
in the calculus of variations. It covers the preliminaries,
variational problems with fixed boundaries, sufficient conditions
of extrema of functionals, problems with undetermined boundaries,
variational problems of conditional extrema, variational problems
in parametric forms, variational principles, direct methods for
variational problems, variational principles in mechanics and their
applications, and variational problems of functionals with vector,
tensor and Hamiltonian operators. Many of the contributions are
based on the authors' research, addressing topics such as the
extension of the connotation of the Hilbert adjoint operator,
definitions of the other three kinds of adjoint operators, the
extremum function theorem of the complete functional, unified Euler
equations in variational methods, variational theories of
functionals with vectors, modulus of vectors, arbitrary order
tensors, Hamiltonian operators and Hamiltonian operator strings,
reconciling the Euler equations and the natural boundary
conditions, and the application range of variational methods. The
book is also a valuable reference resource for teachers as well as
science and technology professionals.
The Statistical Analysis of Multivariate Failure Time Data: A
Marginal Modeling Approach provides an innovative look at methods
for the analysis of correlated failure times. The focus is on the
use of marginal single and marginal double failure hazard rate
estimators for the extraction of regression information. For
example, in a context of randomized trial or cohort studies, the
results go beyond that obtained by analyzing each failure time
outcome in a univariate fashion. The book is addressed to
researchers, practitioners, and graduate students, and can be used
as a reference or as a graduate course text. Much of the literature
on the analysis of censored correlated failure time data uses
frailty or copula models to allow for residual dependencies among
failure times, given covariates. In contrast, this book provides a
detailed account of recently developed methods for the simultaneous
estimation of marginal single and dual outcome hazard rate
regression parameters, with emphasis on multiplicative (Cox)
models. Illustrations are provided of the utility of these methods
using Women's Health Initiative randomized controlled trial data of
menopausal hormones and of a low-fat dietary pattern intervention.
As byproducts, these methods provide flexible semiparametric
estimators of pairwise bivariate survivor functions at specified
covariate histories, as well as semiparametric estimators of cross
ratio and concordance functions given covariates. The presentation
also describes how these innovative methods may extend to handle
issues of dependent censorship, missing and mismeasured covariates,
and joint modeling of failure times and covariates, setting the
stage for additional theoretical and applied developments. This
book extends and continues the style of the classic Statistical
Analysis of Failure Time Data by Kalbfleisch and Prentice. Ross L.
Prentice is Professor of Biostatistics at the Fred Hutchinson
Cancer Research Center and University of Washington in Seattle,
Washington. He is the recipient of COPSS Presidents and Fisher
awards, the AACR Epidemiology/Prevention and Team Science awards,
and is a member of the National Academy of Medicine. Shanshan Zhao
is a Principal Investigator at the National Institute of
Environmental Health Sciences in Research Triangle Park, North
Carolina.
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