Modelling Survival Data in Medical Research (Hardcover, 3)

Survival Analysis
Special Features of Survival Data
Some Examples
Survivor, Hazard and Cumulative Hazard Functions
Computer Software for Survival Analysis
Further Reading

Some Non-Parametric Procedures
Estimating the Survivor Function
Standard Error of the Estimated Survivor Function
Estimating the Hazard Function
Estimating the Median and Percentiles of Survival Times
Confidence Intervals for the Median and Percentiles
Comparison of Two Groups of Survival Data
Comparison of Three or More Groups of Survival Data
Stratified Tests
Log-Rank Test for Trend
Further Reading

The Cox Regression Model
Modelling the Hazard Function
The Linear Component of the Model
Fitting the Cox Regression Model
Confidence Intervals and Hypothesis Tests
Comparing Alternative Models
Strategy for Model Selection
Variable Selection Using the Lasso
Non-Linear Terms
Interpretation of Parameter Estimates
Estimating the Hazard and Survivor Functions
Risk Adjusted Survivor Function
Explained Variation in the Cox Regression Model
Proportional Hazards and the Log-Rank Test
Further Reading

Model Checking in the Cox Regression Model
Residuals for the Cox Regression Model
Assessment of Model Fit
Identification of Influential Observations
Testing the Assumption of Proportional Hazards
Recommendations
Further Reading

Parametric Proportional Hazards Models
Models for the Hazard Function
Assessing the Suitability of a Parametric Model
Fitting a Parametric Model to a Single Sample
Fitting Exponential and Weibull Models
A Model for the Comparison of Two Groups
The Weibull Proportional Hazards Model
Comparing Alternative Weibull Models
Explained Variation in the Weibull Model
The Gompertz Proportional Hazards Model
Model Choice
Further Reading

Accelerated Failure Time and Other Parametric Models
Probability Distributions for Survival Data
Exploratory Analyses
Accelerated Failure Model for Two Groups
The General Accelerated Failure Time Model
Parametric Accelerated Failure Time Models
Fitting and Comparing Accelerated Failure Time Models
The Proportional Odds Model
Some Other Distributions for Survival Data
Flexible Parametric Models
Modelling Cure Rates
Effect of Covariate Adjustment
Further Reading

Model Checking In Parametric Models
Residuals for Parametric Models
Residuals for Particular Parametric Models
Comparing Observed and Fitted Survivor Functions
Identification of Influential Observations
Testing Proportional Hazards in the Weibull Model
Further Reading

Time-Dependent Variables
Types of Time-Dependent Variables
A Model with Time-Dependent Variables
Model Comparison and Validation
Some Applications of Time-Dependent Variables
Three Examples
Counting Process Format
Further Reading

Interval-Censored Survival Data
Modelling Interval-Censored Survival Data
Modelling the Recurrence Probability in the Follow-Up Period
Modelling the Recurrence Probability at Different Times
Arbitrarily Interval-Censored Survival Data
Parametric Models for Interval-Censored Data
Discussion
Further Reading

Frailty Models
Introduction to Frailty
Modelling Individual Frailty
The Gamma Frailty Distribution
Fitting Parametric Frailty Models
Fitting Semi-Parametric Frailty Models
Comparing Models with Frailty
The Shared Frailty Model
Some Other Aspects of Frailty Modelling
Further Reading

Non-Proportional Hazards and Institutional Comparisons
Non-Proportional Hazards
Stratified Proportional Hazards Models
Restricted Mean Survival
Institutional Comparisons
Further Reading

Competing Risks
Introduction to Competing Risks
Summarising Competing Risks Data
Hazard and Cumulative Incidence Functions
Modelling Cause-Specific Hazards
Modelling Cause-Specific Incidence
Model Checking
Further Reading

Multiple Events and Event History Modelling
Introduction to Counting Processes
Modelling Recurrent Event Data
Multiple Events
Event History Analysis
Further Reading

Dependent Censoring
Identifying Dependent Censoring
Sensitivity to Dependent Censoring
Modelling with Dependent Censoring
Further Reading

Sample Size Requirements for a Survival Study
Distinguishing between Two Treatment Groups
Calculating the Required Number of Deaths
Calculating the Required Number of Patients
Further Reading

Appendix A: Maximum Likelihood Estimation
Inference about a Single Unknown Parameter
Inference about a Vector of Unknown Parameters

Appendix B: Additional Data Sets
Chronic Active Hepatitis
Recurrence of Bladder Cancer
Survival of Black Ducks
Bone Marrow Transplantation
Chronic Granulomatous Disease

Bibliography

Index of Examples

Index