Contents
1 Survival Data
1.1 Time-to-event data
1.2 Censoring
1.3 Why ordinary methods fail
1.4 Recording survival data
1.5 Survival data in software
1.6 Practice Problems
2 Survival, Hazard and Cumulative Hazard
2.1 The survival function
2.2 The hazard function
2.3 The cumulative hazard and the basic identity
2.4 Summaries: mean, median and residual life
2.5 Hazards in software
2.6 Practice Problems
3 Parametric Models
3.1 The likelihood with censored data
3.2 The exponential model
3.3 The Weibull and other families
3.4 Choosing a model
3.5 Parametric models in software
3.6 Practice Problems
4 The Kaplan–Meier Estimator
4.1 The product-limit estimator
4.2 Greenwood’s formula and confidence intervals
4.3 The median and reading the curve
4.4 Kaplan–Meier estimation in software
4.5 Practice Problems
5 The Nelson–Aalen Estimator and Life Tables
5.1 The Nelson–Aalen estimator
5.2 Using the cumulative hazard to choose a model
5.3 Life tables
5.4 Cumulative hazards and life tables in software
5.5 Practice Problems
6 Comparing Groups: the Log-rank Test
6.1 The test
6.2 Several groups, trends and strata
6.3 Weighted log-rank tests
6.4 The log-rank test in software
6.5 Practice Problems
7 The Cox Proportional Hazards Model
7.1 The model
7.2 The partial likelihood
7.3 Inference and interpretation
7.4 The baseline hazard and predicted survival
7.5 Cox regression in software
7.6 Practice Problems
8 Fitting Cox Models in Practice
8.1 Categorical covariates
8.2 Tied event times
8.3 Interactions and stratification
8.4 Model building
8.5 Adjusted survival curves
8.6 Model fitting in software
8.7 Practice Problems
9 Checking Proportional Hazards
9.1 Graphical checks
9.2 Schoenfeld residuals
9.3 What to do when hazards are not proportional
9.4 Checking the assumption in software
9.5 Practice Problems
10 Accelerated Failure Time Models
10.1 The model
10.2 The Weibull model: both AFT and proportional hazards
10.3 Log-normal and log-logistic models
10.4 Checking and choosing a model
10.5 AFT models in software
10.6 Practice Problems
11 Competing Risks, Frailty and Recurrent Events
11.1 Competing risks and the cumulative incidence function
11.2 Regression with competing risks
11.3 Frailty models
11.4 Recurrent events
11.5 Competing risks and multiple events in software
11.6 Practice Problems
12 Design, a Case Study and Review
12.1 How many events?
12.2 A case study: primary biliary cholangitis
12.3 Review: which method for which question
12.4 Design and the case study in software
12.5 Practice Problems
References
1.1 Time-to-event data
1.2 Censoring
1.3 Why ordinary methods fail
1.4 Recording survival data
1.5 Survival data in software
1.6 Practice Problems
2 Survival, Hazard and Cumulative Hazard
2.1 The survival function
2.2 The hazard function
2.3 The cumulative hazard and the basic identity
2.4 Summaries: mean, median and residual life
2.5 Hazards in software
2.6 Practice Problems
3 Parametric Models
3.1 The likelihood with censored data
3.2 The exponential model
3.3 The Weibull and other families
3.4 Choosing a model
3.5 Parametric models in software
3.6 Practice Problems
4 The Kaplan–Meier Estimator
4.1 The product-limit estimator
4.2 Greenwood’s formula and confidence intervals
4.3 The median and reading the curve
4.4 Kaplan–Meier estimation in software
4.5 Practice Problems
5 The Nelson–Aalen Estimator and Life Tables
5.1 The Nelson–Aalen estimator
5.2 Using the cumulative hazard to choose a model
5.3 Life tables
5.4 Cumulative hazards and life tables in software
5.5 Practice Problems
6 Comparing Groups: the Log-rank Test
6.1 The test
6.2 Several groups, trends and strata
6.3 Weighted log-rank tests
6.4 The log-rank test in software
6.5 Practice Problems
7 The Cox Proportional Hazards Model
7.1 The model
7.2 The partial likelihood
7.3 Inference and interpretation
7.4 The baseline hazard and predicted survival
7.5 Cox regression in software
7.6 Practice Problems
8 Fitting Cox Models in Practice
8.1 Categorical covariates
8.2 Tied event times
8.3 Interactions and stratification
8.4 Model building
8.5 Adjusted survival curves
8.6 Model fitting in software
8.7 Practice Problems
9 Checking Proportional Hazards
9.1 Graphical checks
9.2 Schoenfeld residuals
9.3 What to do when hazards are not proportional
9.4 Checking the assumption in software
9.5 Practice Problems
10 Accelerated Failure Time Models
10.1 The model
10.2 The Weibull model: both AFT and proportional hazards
10.3 Log-normal and log-logistic models
10.4 Checking and choosing a model
10.5 AFT models in software
10.6 Practice Problems
11 Competing Risks, Frailty and Recurrent Events
11.1 Competing risks and the cumulative incidence function
11.2 Regression with competing risks
11.3 Frailty models
11.4 Recurrent events
11.5 Competing risks and multiple events in software
11.6 Practice Problems
12 Design, a Case Study and Review
12.1 How many events?
12.2 A case study: primary biliary cholangitis
12.3 Review: which method for which question
12.4 Design and the case study in software
12.5 Practice Problems
References