Background: Probability.- Background: General inference.- Background: Survival analysis.- Marginal survival.- Regression models and subject heterogeneity.- Inference: Estimating equations.- Inference: Functions of Brownian motion.- Inference: Likelihood.- Inference: Stochastic integrals.- Inference: Small samples.- Inference: Changepoint models.- Explained variation.- Explained randomness.- Survival given covariates.- Proofs of theorems, lemmas and corollaries.
Introduction.- Background: probability.- Background: inference.- Background: survival analysis.- Marginal survival.- Regression models and subject heterogeneity.- Estimating equations.- Inference: functions of the Brownian motion.- Inference: likelihood.- Inference: counting processes.- Inference: small samples.- Inference: changepoint models.- Explained variation.- Explained randomness.- Survival given covariates.- Proofs of theorems, lemmas and corollaries.
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models - proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter - which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.
There are some important, significant departures from much current thinking in the area of proportional hazards regression. Less weight is given to counting processes and martingale theory than is now common. More classical methods of inference are used and while solid theoretically, this is not a mathematical text.