Survival Analysis: Proportional and Non-Proportional Hazards Regression (Springer the Data Sciences)

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