1 Introduction

2 Using stset and stsplit

• 2.1 What is the stset command?
• 2.2 Some key concepts
• 2.3 Syntax of the stset command
• 2.4 Variables created by the stset command
• 2.5 Examples of using stset
  • 2.5.1 Standard survival data
  • 2.5.2 Using the scale( ) option
  • 2.5.3 Date of diagnosis and date of exit
  • 2.5.4 Date of diagnosis and date of exit with the scale( ) option
  • 2.5.5 Restricting the follow-up time
  • 2.5.6 Left-truncation
  • 2.5.7 Age as the time scale
• 2.6 The stsplit command
  • 2.6.1 Time-dependent effects
  • 2.6.2 Time-varying covariates
• 2.7 Conclusion

3 Graphical introduction to the principal datasets

4 Poisson models

• 4.1 Introduction
• 4.2 Modeling rates with the Poisson distribution
• 4.3 Splitting the time scale
  • 4.3.1 The piecewise exponential model
  • 4.3.2 Time as just another covariate
• 4.4 Collapsing the data to speed up computation
• 4.5 Splitting at unique failure times
  • 4.5.1 Technical note: Why the Cox and Poisson approaches are equivalent
• 4.6 Comparing a different number of intervals
• 4.7 Fine splitting of the time scale
• 4.8 Splines: Motivation and definition
  • 4.8.1 Calculating splines
  • 4.8.2 Restricted cubic splines
  • 4.8.3 Splines: Application to the Rotterdam data
  • 4.8.4 Varying the number of knots
  • 4.8.5 Varying the location of the knots
  • 4.8.6 Estimating the survival function
• 4.9 FPs: Motivation and definition
  • 4.9.1 Application to Rotterdam data
  • 4.9.2 Higher order FP models
  • 4.9.3 FP function selection procedure
• 4.10 Discussion

5 Royston–Parmar models

• 5.1 Motivation and introduction
  • 5.1.1 The exponential distribution
  • 5.1.2 The Weibull distribution
  • 5.1.3 Generalizing the Weibull
  • 5.1.4 Estimating the hazard function
• 5.2 Proportional hazards models
  • 5.2.1 Generalizing the Weibull
  • 5.2.2 Example
  • 5.2.3 Comparing parameters of PH(1) and Weibull models
• 5.3 Selecting a spline function
  • 5.3.1 Knot positions
    Example
  • 5.3.2 How many knots?
• 5.4 PO models
  • 5.4.1 Introduction
  • 5.4.2 The loglogistic model
  • 5.4.3 Generalizing the loglogistic model
  • 5.4.4 Comparing parameters of PO(1) and loglogistic models
    Example
• 5.5 Probit models
  • 5.5.1 Motivation
  • 5.5.2 Generalizing the probit model
  • 5.5.3 Comparing parameters of probit(1) and lognormal models
  • 5.5.4 Comments on probit and POs models
• 5.6 Royston–Parmar (RP) models
  • 5.6.1 Models with θ not equal to 0 or 1
  • 5.6.2 Example
  • 5.6.3 Likelihood function and parameter estimation
  • 5.6.4 Comparing regression coefficients
  • 5.6.5 Model selection
  • 5.6.6 Sensitivity to number of knots
  • 5.6.7 Sensitivity to location of knots
• 5.7 Concluding remarks

6 Prognostic models

• 6.1 Introduction
• 6.2 Developing and reporting a prognostic model
• 6.3 What does the baseline hazard function mean?
  • 6.3.1 Example
• 6.4 Model selection
  • 6.4.1 Choice of scale and baseline complexity
    Example
  • 6.4.2 Selection of variables and functional forms
    Example
• 6.5 Quantitative outputs from the model
  • 6.5.1 Survival probabilities for individuals
  • 6.5.2 Survival probabilities across the risk spectrum
  • 6.5.3 Survival probabilities at given covariate values
  • 6.5.4 Survival probabilities in groups
  • 6.5.5 Plotting adjusted survival curves
  • 6.5.6 Plotting differences between survival curves
  • 6.5.7 Centiles of the survival distribution
• 6.6 Goodness of fit
  • 6.6.1 Example
• 6.7 Discrimination and explained variation
  • 6.7.1 Example
  • 6.7.2 Harrell’s C index of concordance
• 6.8 Out-of-sample prediction: Concept and applications
  • 6.8.1 Extrapolation of survival functions: Basic technique
  • 6.8.2 Extrapolation of survival functions: Further investigations
  • 6.8.3 Validation of prognostic models: Basics
  • 6.8.4 Validation of prognostic models: Further comments
• 6.9 Visualization of survival times
  • 6.9.1 Example
• 6.10 Discussion

7 Time-dependent effects

• 7.1 Introduction
• 7.2 Definitions
• 7.3 What do we mean by a TD effect?
• 7.4 Proportional on which scale?
• 7.5 Poisson models with TD effects
  • 7.5.1 Piecewise models
  • 7.5.2 Using restricted cubic splines
• 7.6 RP models with TD effects
  • 7.6.1 Piecewise HRs
  • 7.6.2 Continuous TD effects
  • 7.6.3 More than one TD effect
  • 7.6.4 Stratification is the same as including TD effects
• 7.7 TD effects for continuous variables
• 7.8 Attained age as the time scale
  • 7.8.1 The orchiectomy data
  • 7.8.2 Proportional hazards model
  • 7.8.3 TD model
• 7.9 Multiple time scales
• 7.10 Prognostic models with TD effects
  • 7.10.1 Example
• 7.11 Discussion

8 Relative survival

• 8.1 Introduction
• 8.2 What is relative survival?
• 8.3 Excess mortality and relative survival
  • 8.3.1 Excess mortality
  • 8.3.2 Relative survival is a ratio
• 8.4 Motivating example
• 8.5 Life-table estimation of relative survival
  • 8.5.1 Using strs
• 8.6 Poisson models for relative survival
  • 8.6.1 Piecewise models
  • 8.6.2 Restricted cubic splines
• 8.7 RP models for relative survival
  • 8.7.1 Likelihood for relative survival models
  • 8.7.2 Proportional cumulative excess hazards
  • 8.7.3 RP models on other scales
  • 8.7.4 Application to England and Wales breast cancer data
  • 8.7.5 Relative survival models on other scales
  • 8.7.6 Time-dependent effects
• 8.8 Some comments on model selection
• 8.9 Age as a continuous variable
• 8.10 Concluding remarks

9 Further topics

• 9.1 Introduction
• 9.2 Number needed to treat
  • 9.2.1 Example
• 9.3 Average and adjusted survival curves
  • 9.3.1 Renal data
• 9.4 Modeling distributions with RP models
  • 9.4.1 Example 1: Rotterdam breast cancer data
  • 9.4.2 Example 2: CD4 lymphocyte data
  • 9.4.3 Example 3: Prostate cancer data
• 9.5 Multiple events
  • 9.5.1 Introduction
  • 9.5.2 The AG model
  • 9.5.3 The WLW model
  • 9.5.4 The PWP model
  • 9.5.5 Multiple events in RP models
  • 9.5.6 Summary
• 9.6 Bayesian RP models
  • 9.6.1 Introduction
  • 9.6.2 The “zeros trick” in WinBUGS
  • 9.6.3 Fitting a RP model
  • 9.6.4 Summary
• 9.7 Competing risks
  • 9.7.1 Summary
• 9.8 Period analysis
  • 9.8.1 Introduction
  • 9.8.2 What is period analysis?
  • 9.8.3 Application to England and Wales breast cancer data
• 9.9 Crude probability of death from relative survival models
  • 9.9.1 Introduction
  • 9.9.2 Application to England and Wales breast cancer data
  • 9.9.3 Conclusion
• 9.10 Final remarks
  

References

Author index

Subject index