Survival analysis proportional and non-proportional hazards regression / John O'Quigley.

Format:

Book

Author/Creator:

O'Quigley, John, author.

Language:

English

Subjects (All):

Hazardous substances--Risk assessment.

Hazardous substances.

Regression analysis.

Physical Description:

1 online resource (476 pages)

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

This book provides an extensive coverage of the methodology of survival analysis, ranging from introductory level material to deeper more advanced topics. The framework is that of proportional and non-proportional hazards models; a structure that is broad enough to enable the recovery of a large number of established results as well as to open the way to many new developments. The emphasis is on concepts and guiding principles, logical and graphical. Formal proofs of theorems, propositions and lemmas are gathered together at the end of each chapter separate from the main presentation. The intended audience includes academic statisticians, biostatisticians, epidemiologists and also researchers in these fields whose focus may be more on the applications than on the theory. The text could provide the basis for a two semester course on survival analysis and, with this goal in mind, each chapter includes a section with a range of exercises as a teaching aid for instructors.

Contents:

Intro

Preface

Contents

Summary of main notation

1 Introduction

1.1 Chapter summary

1.2 Context and motivation

1.3 Some examples

1.4 Main objectives

1.5 Neglected and underdeveloped topics

1.6 Model-based prediction

1.7 Data sets

1.8 Use as a graduate text

1.9 Classwork and homework

2 Survival analysis methodology

2.1 Chapter summary

2.2 Context and motivation

2.3 Basic tools

2.4 Some potential models

2.5 Censoring

2.6 Competing risks

2.7 Classwork and homework

3 Survival without covariates

3.1 Chapter summary

3.2 Context and motivation

3.3 Parametric models for survival functions

3.4 Empirical estimate (no censoring)

3.5 Kaplan-Meier (empirical estimate with censoring)

3.6 Nelson-Aalen estimate of survival

3.7 Model verification using empirical estimate

3.8 Classwork and homework

3.9 Outline of proofs

4 Proportional hazards models

4.1 Chapter summary

4.2 Context and motivation

4.3 General or non-proportional hazards model

4.4 Proportional hazards model

4.5 Cox regression model

4.6 Modeling multivariate problems

4.7 Classwork and homework

5 Proportional hazards models in epidemiology

5.1 Chapter summary

5.2 Context and motivation

5.3 Odds ratio, relative risk, and 2times2 tables

5.4 Logistic regression and proportional hazards

5.5 Survival in specific groups

5.6 Genetic epidemiology

5.7 Classwork and homework

6 Non-proportional hazards models

6.1 Chapter summary

6.2 Context and motivation

6.3 Partially proportional hazards models

6.4 Partitioning of the time axis

6.5 Time-dependent covariates

6.6 Linear and alternative model formulations

6.7 Classwork and homework

7 Model-based estimating equations

7.1 Chapter summary

7.2 Context and motivation.

7.3 Likelihood solution for parametric models

7.4 Semi-parametric estimating equations

7.5 Estimating equations using moments

7.6 Incorrectly specified models

7.7 Estimating equations in small samples

7.8 Classwork and homework

7.9 Outline of proofs

8 Survival given covariate information

8.1 Chapter summary

8.2 Context and motivation

8.3 Probability that Ti is greater than Tj

8.4 Conditional survival given ZinH

8.5 Other relative risk forms

8.6 Informative censoring

8.7 Classwork and homework

8.8 Outline of proofs

9 Regression effect process

9.1 Chapter summary

9.2 Context and motivation

9.3 Elements of the regression effect process

9.4 Univariate regression effect process

9.5 Regression effect processes for several covariates

9.6 Iterated logarithm for effective sample size

9.7 Classwork and homework

9.8 Outline of proofs

10 Model construction guided by regression effect process

10.1 Chapter summary

10.2 Context and motivation

10.3 Classical graphical methods

10.4 Confidence bands for regression effect process

10.5 Structured tests for time dependency

10.6 Predictive ability of a regression model

10.7 The R2 estimate of Ω2

10.8 Using R2 and fit to build models

10.9 Some simulated situations

10.10 Illustrations from clinical studies

10.11 Classwork and homework

10.12 Outline of proofs

11 Hypothesis tests based on regression effect process

11.1 Chapter summary

11.2 Context and motivation

11.3 Some commonly employed tests

11.4 Tests based on the regression effect process

11.5 Choosing the best test statistic

11.6 Relative efficiency of competing tests

11.7 Supremum tests over cutpoints

11.8 Some simulated comparisons

11.9 Illustrations

11.10 Some further thoughts

11.11 Classwork and homework.

11.12 Outline of proofs

A Probability

A.1 Essential tools for survival problems

A.2 Integration and measure

A.3 Random variables and probability measure

A.4 Convergence for random variables

A.5 Topology and distance measures

A.6 Distributions and densities

A.7 Multivariate and copula models

A.8 Expectation

A.9 Order statistics and their expectations

A.10 Approximations

B Stochastic processes

B.1 Broad overview

B.2 Brownian motion

B.3 Counting processes and martingales

B.4 Inference for martingales and stochastic integrals

C Limit theorems

C.1 Empirical processes and central limit theorems

C.2 Limit theorems for sums of random variables

C.3 Functional central limit theorem

C.4 Brownian motion as limit process

C.5 Empirical distribution function

D Inferential tools

D.1 Theory of estimating equations

D.2 Efficiency in estimation and in tests

D.3 Inference using resampling techniques

D.4 Conditional, marginal, and partial likelihood

E Simulating data under the non-proportional hazards model

E.1 Method 1-Change-point models

E.2 Method 2-Non-proportional hazards models

Further exercises and proofs

Bibliography

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

3-030-33439-2

OCLC:

1248899908