Flexible Parametric Survival Analysis Using Stata
Beyond the Cox Model
Through real-world case studies, this book shows how to use Stata to estimate a class of flexible parametric survival models. It discusses the modeling of time-dependent and continuous covariates and looks at how relative survival can be used to measure mortality associated with a particular disease when the cause of death has not been recorded. The book describes simple quantification of differences between any two covariate patterns through calculation of time-dependent hazard ratios, hazard differences, and survival differences.
Table of Contents
A brief review of the Cox proportional hazards model
Beyond the Cox model
Why parametric models?
Why not standard parametric models?
A brief introduction to stpm
Basic relationships in survival analysis
The delta method
How our book is organized
Using stset and stsplit
What is the stset command?
Some key concepts
Syntax of the stset command
Variables created by the stset command
Examples of using stset
The stsplit command
Graphical introduction to the principal datasets
Rotterdam breast cancer data
England and Wales breast cancer data
Modeling rates with the Poisson distribution
Splitting the time scale
Collapsing the data to speed up computation
Splitting at unique failure times
Comparing a different number of intervals
Fine splitting of the time scale
Splines: Motivation and definition
FPs: Motivation and definition
Motivation and introduction
Proportional hazards models
Selecting a spline function
Royston–Parmar (RP) models
Developing and reporting a prognostic model
What does the baseline hazard function mean?
Quantitative outputs from the model
Goodness of fit
Out-of-sample prediction: Concept and applications
Visualization of survival times
What do we mean by a TD effect?
Proportional on which scale?
Poisson models with TD effects
RP models with TD effects
TD effects for continuous variables
Attained age as the time scale
Multiple time scales
Prognostic models with TD effects
What is relative survival?
Excess mortality and relative survival
Life-table estimation of relative survival
Poisson models for relative survival
RP models for relative survival
Some comments on model selection
Age as a continuous variable
Number needed to treat
Average and adjusted survival curves
Modeling distributions with RP models
Bayesian RP models
Crude probability of death from relative survival models
Patrick Royston is a senior medical statistician at the Medical Research Council, London, UK. He has published research papers on a variety of topics in leading statistics journals. His key interests include multivariable modeling and validation, survival analysis, design and analysis of clinical trials, and statistical computing and algorithms. He is an associate editor of the Stata Journal.
Paul Lambert is a reader in medical statistics at Leicester University, UK. His main interest is in the development and application of statistical methods in population-based cancer research and related fields. He has published widely in leading statistical and medical journals.