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• Preface
• Contents
• 1 Introduction
• 1.1 What Is Survival Analysis?
• 1.2 What You Need to Know to Use This Book
• 1.3 Survival Data and Censoring
• 1.4 Some Examples of Survival Data Sets
• 1.5 Additional Notes
• Exercises
• 2 Basic Principles of Survival Analysis
• 2.1 The Hazard and Survival Functions
• 2.2 Other Representations of a Survival Distribution
• 2.3 Mean and Median Survival Time
• 2.4 Parametric Survival Distributions
• 2.5 Computing the Survival Function from the Hazard Function
• 2.6 A Brief Introduction to Maximum Likelihood Estimation
• 2.7 Additional Notes
• Exercises
• 3 Nonparametric Survival Curve Estimation
• 3.1 Nonparametric Estimation of the Survival Function
• 3.2 Finding the Median Survival and a Confidence Interval for the Median
• 3.3 Median Follow-Up Time
• 3.4 Obtaining a Smoothed Hazard and Survival Function Estimate
• 3.5 Left Truncation
• 3.6 Additional Notes
• Exercises
• 4 Nonparametric Comparison of Survival Distributions
• 4.1 Comparing Two Groups of Survival Times
• 4.2 Stratified Tests
• 4.3 Additional Note
• Exercises
• 5 Regression Analysis Using the Proportional Hazards Model
• 5.1 Covariates and Nonparametric Survival Models
• 5.2 Comparing Two Survival Distributions Using a Partial Likelihood Function
• 5.3 Partial Likelihood Hypothesis Tests
• 5.3.1 The Wald Test
• 5.3.2 The Score Test
• 5.3.3 The Likelihood Ratio Test
• 5.4 The Partial Likelihood with Multiple Covariates
• 5.5 Estimating the Baseline Survival Function
• 5.6 Handling of Tied Survival Times
• 5.7 Left Truncation
• 5.8 Additional Notes
• Exercises
• 6 Model Selection and Interpretation
• 6.1 Covariate Adjustment
• 6.2 Categorical and Continuous Covariates
• 6.3 Hypothesis Testing for Nested Models
• 6.4 The Akaike Information Criterion for Comparing Non-nested Models
• 6.5 Including Smooth Estimates of Continuous Covariates in a Survival Model
• 6.6 Additional Note
• Exercises
• 7 Model Diagnostics
• 7.1 Assessing Goodness of Fit Using Residuals
• 7.1.1 Martingale and Deviance Residuals
• 7.1.2 Case Deletion Residuals
• 7.2 Checking the Proportion Hazards Assumption
• 7.2.1 Log Cumulative Hazard Plots
• 7.2.2 Schoenfeld Residuals
• 7.3 Additional Note
• Exercises
• 8 Time Dependent Covariates
• 8.1 Introduction
• 8.2 Predictable Time Dependent Variables
• 8.2.1 Using the Time Transfer Function
• 8.2.2 Time Dependent Variables That Increase Linearly with Time
• 8.3 Additional Note
• Exercises
• 9 Multiple Survival Outcomes and Competing Risks
• 9.1 Clustered Survival Times and Frailty Models
• 9.1.1 Marginal Survival Models
• 9.1.2 Frailty Survival Models
• 9.1.3 Accounting for Family-Based Clusters in the “ashkenazi” Data
• 9.1.4 Accounting for Within-Person Pairing of Eye Observations in the Diabetes Data
• 9.2 Cause-Specific Hazards
• 9.2.1 Kaplan-Meier Estimation with Competing Risks
• 9.2.2 Cause-Specific Hazards and Cumulative Incidence Functions
• 9.2.3 Cumulative Incidence Functions for ProstateCancer Data
• 9.2.4 Regression Methods for Cause-Specific Hazards
• 9.2.5 Comparing the Effects of Covariates on Different Causes of Death
• 9.3 Additional Notes
• Exercises
• 10 Parametric Models
• 10.1 Introduction
• 10.2 The Exponential Distribution
• 10.3 The Weibull Model
• 10.3.1 Assessing the Weibull Distribution as a Model for Survival Data in a Single Sample
• 10.3.2 Maximum Likelihood Estimation of Weibull Parameters for a Single Group of Survival Data
• 10.3.3 Profile Weibull Likelihood
• 10.3.4 Selecting a Weibull Distribution to Model Survival Data
• 10.3.5 Comparing Two Weibull Distributions Using the Accelerated Failure Time and Proportional Hazar
• 10.3.6 A Regression Approach to the Weibull Model
• 10.3.7 Using the Weibull Distribution to Model Survival Data with Multiple Covariates
• 10.3.8 Model Selection and Residual Analysis with Weibull Survival Data
• 10.4 Other Parametric Survival Distributions
• 10.5 Additional Note
• Exercises
• 11 Sample Size Determination for Survival Studies
• 11.1 Power and Sample Size for a Single Arm Study
• 11.2 Determining the Probability of Death in a Clinical Trial
• 11.3 Sample Size for Comparing Two Exponential Survival Distributions
• 11.4 Sample Size for Comparing Two Survival Distributions Using the Log-Rank Test
• 11.5 Determining the Probability of Death from a Non-parametric Survival Curve Estimate
• 11.6 Example: Calculating the Required Number of Patients for a Randomized Study of Advanced Gastric
• 11.7 Example: Calculating the Required Number of Patients for a Randomized Study of Patients with Me
• 11.8 Using Simulations to Estimate Power
• 11.9 Additional Notes
• Exercises
• 12 Additional Topics
• 12.1 Using Piecewise Constant Hazards to Model Survival Data
• 12.2 Interval Censoring
• 12.3 The Lasso Method for Selecting Predictive Biomarkers
• Exercises
• Erratum to
• A A Basic Guide to Using R for Survival Analysis
• A.1 The R System
• A.1.1 A First R Session
• A.1.2 Scatterplots and Fitting Linear Regression Models
• A.1.3 Accommodating Non-linear Relationships
• A.1.4 Data Frames and the Search Path for Variable Names
• A.1.5 Defining Variables Within a Data Frame
• A.1.6 Importing and Exporting Data Frames
• A.2 Working with Dates in R
• A.2.1 Dates and Leap Years
• A.2.2 Using the “as.date” Function
• A.3 Presenting Coefficient Estimates Using Forest Plots
• A.4 Extracting the Log Partial Likelihood and Coefficient Estimates from a coxph Object
• References
• Index
• R Package Index