Models for Multi-State Survival Data (Chapman & Hall/CRC Texts in Statistical Science)

Science & Math

ANDERSEN, PER KRAGH

Ravn, Henrik

Mathematics

Chapman and Hall/CRC

Statistical Models Based on Counting Processes (Springer Series in Statistics)

Modern survival analysis and more general event history analysis may be effectively handled within the mathematical framework of counting processes. This book presents this theory, which has been the subject of intense research activity over the past 15 years. The exposition of the theory is integrated with careful presentation of many practical examples, drawn almost exclusively from the authors'own experience, with detailed numerical and graphical illustrations. Although Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, almost all the methods are given in concrete detail for use in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliability 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.

Borgan, Ornulf

Gill, Richard D.

Keiding, Niels

Springer, Verlag

Models For Multi-state Survival Data

Boca Raton, FL : CRC Press

Regression with Linear Predictors (Statistics for Biology and Health)

This is a book about regression analysis, that is, the situation in statistics where the distribution of a response (or outcome) variable is related to - planatory variables (or covariates). This is an extremely common situation in the application of statistical methods in many ?elds, andlinear regression,- gistic regression, and Cox proportional hazards regression are frequently used for quantitative, binary, and survival time outcome variables, respectively. Several books on these topics have appeared and for that reason one may well ask why we embark on writing still another book on regression. We have two main reasons for doing this: 1. First, we want to highlightsimilaritiesamonglinear,logistic,proportional hazards,andotherregressionmodelsthatincludealinearpredictor. These modelsareoftentreatedentirelyseparatelyintextsinspiteofthefactthat alloperationsonthemodelsdealingwiththelinearpredictorareprecisely the same, including handling of categorical and quantitative covariates, testing for linearity and studying interactions. 2. Second, we want to emphasize that, for any type of outcome variable, multiple regression models are composed of simple building blocks that areaddedtogetherinthelinearpredictor:thatis,t-tests,one-wayanalyses of variance and simple linear regressions for quantitative outcomes, 2×2, 2×(k+1) tables and simple logistic regressions for binary outcomes, and 2-and (k+1)-sample logrank testsand simple Cox regressionsfor survival data. Thishastwoconsequences. Allthesesimpleandwellknownmethods can be considered as special cases of the regression models. On the other hand, the e?ect of a single explanatory variable in a multiple regression model can be interpreted in a way similar to that obtained in the simple analysis, however, now valid only for the other explanatory variables in the model “held ?xed”.

Skovgaard, Lene Theil

Biological Sciences

Springer

This text provides, in a non-technical language, a unified treatment of regression models for different outcome types, such as linear regression, logistic regression, and Cox regression. This is done by focusing on the many common aspects of these models, in particular the linear predictor, which combines the effects of all explanatory variables into a function which is linear in the unknown parameters. Specification and interpretation of various choices of parametrization of the effects of the covariates (categorical as well as quantitative) and interaction among these are elaborated upon. The merits and drawbacks of different link functions relating the linear predictor to the outcome are discussed with an emphasis on interpretational issues, and the fact that different research questions arise from adding or deleting covariates from the model is emphasized in both theory and practice. Regression models with a linear predictor are commonly used in fields such as clinical medicine, epidemiology, and public health, and the book, including its many worked examples, builds on the authors' more than thirty years of experience as teachers, researchers and consultants at a biostatistical department. The book is well-suited for readers without a solid mathematical background and is accompanied by Web pages documenting in R, SAS, and STATA, the analyses presented throughout the text.

Statistical Models Based on Counting Processes (Principles of Pediatric Neurosurgery)

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