Efnisyfirlit

• Cover Page
• Half-Title Page
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• Author Biography
• 1 Survival analysis
  • 1.1 Applications of survival analysis
  • 1.2 Special features of survival data
    • 1.2.1 Censoring
    • 1.2.2 Independent censoring
    • 1.2.3 Study time and patient time
  • 1.3 Some examples
  • 1.4 Survivor, hazard, and cumulative hazard functions
    • 1.4.1 The survivor function
    • 1.4.2 The hazard function
    • 1.4.3 The cumulative hazard function
  • 1.5 Computer software for survival analysis
  • 1.6 Further reading
• 2 Some non-parametric procedures
  • 2.1 Estimating the survivor function
    • 2.1.1 Life-table estimate of the survivor function
    • 2.1.2 Kaplan-Meier estimate of the survivor function
    • 2.1.3 Nelson-Aalen estimate of the survivor function
  • 2.2 Standard error of the estimated survivor function
    • 2.2.1 Standard error of the Kaplan-Meier estimate
    • 2.2.2 Standard error of other estimates
    • 2.2.3 Confidence intervals for values of the survivor function
  • 2.3 Estimating the hazard function
    • 2.3.1 Life-table estimate of the hazard function
    • 2.3.2 Kaplan-Meier type estimate
    • 2.3.3 Estimating the cumulative hazard function
  • 2.4 Estimating the median and percentiles of survival times
  • 2.5 Confidence intervals for the median and percentiles
  • 2.6 Comparison of two groups of survival data
    • 2.6.1 Hypothesis testing
    • 2.6.2 The log-rank test
    • 2.6.3 The Wilcoxon test
    • 2.6.4 The Peto-Peto test
    • 2.6.5 Comparison of the log-rank, Wilcoxon, and Peto-Peto tests
  • 2.7 Comparison of three or more groups of survival data
  • 2.8 Stratified tests
  • 2.9 Log-rank test for trend
  • 2.10 Further reading
• 3 The Cox regression model
  • 3.1 Modelling the hazard function
    • 3.1.1 A model for the comparison of two groups
    • 3.1.2 The general proportional hazards model
  • 3.2 The linear component of the model
    • 3.2.1 Including a variate
    • 3.2.2 Including a factor
    • 3.2.3 Including an interaction
    • 3.2.4 Including a mixed term
  • 3.3 Fitting the Cox regression model
    • 3.3.1 Likelihood function for the model
    • 3.3.2 Treatment of ties
    • 3.3.3 The Newton-Raphson procedure
  • 3.4 Confidence intervals and hypothesis tests
    • 3.4.1 Confidence intervals for hazard ratios
    • 3.4.2 Two examples
  • 3.5 Comparing alternative models
    • 3.5.1 The statistic -2⁢logL^
    • 3.5.2 Comparing nested models
  • 3.6 Strategy for model selection
    • 3.6.1 Variable selection procedures
  • 3.7 Variable selection using the lasso
    • 3.7.1 The lasso in Cox regression modelling
    • 3.7.2 Data preparation
  • 3.8 Non-linear terms
    • 3.8.1 Testing for non-linearity
    • 3.8.2 Modelling non-linearity
    • 3.8.3 Fractional polynomials
  • 3.9 Interpretation of parameter estimates
    • 3.9.1 Models with a variate
    • 3.9.2 Models with a factor
    • 3.9.3 Models with combinations of terms
  • 3.10 Estimating the hazard and survivor functions
    • 3.10.1 The special case of no covariates
    • 3.10.2 Some approximations to estimates of baseline functions
  • 3.11 Risk-adjusted survivor function
    • 3.11.1 Risk-adjusted survivor function for groups of individuals
  • 3.12 Concordance, predictive ability, and explained variation
    • 3.12.1 Measures of concordance
    • 3.12.2 Predictive ability
    • 3.12.3 Explained variation in the Cox regression model
    • 3.12.4 Measures of explained variation
    • 3.12.5 Model validation
  • 3.13 Time-dependent ROC curves
    • 3.13.1 Sensitivity and specificity
    • 3.13.2 Modelling the probability of disease
    • 3.13.3 ROC curves
    • 3.13.4 Time-dependent ROC curves
  • 3.14 Proportional hazards and the log-rank test
  • 3.15 Further reading
• 4 Model checking in the Cox regression model
  • 4.1 Residuals for the Cox regression model
    • 4.1.1 Cox-Snell residuals
    • 4.1.2 Modified Cox-Snell residuals
    • 4.1.3 Martingale residuals
    • 4.1.4 Deviance residuals
    • 4.1.5 Schoenfeld residuals
    • 4.1.6 Score residuals
  • 4.2 Assessment of model fit
    • 4.2.1 Plots based on the Cox-Snell residuals
    • 4.2.2 Plots based on the martingale and deviance residuals
    • 4.2.3 Checking the functional form of covariates
  • 4.3 Identification of influential observations
    • 4.3.1 Influence of observations on a parameter estimate
    • 4.3.2 Influence of observations on the set of parameter estimates
    • 4.3.3 Treatment of influential observations
  • 4.4 Testing the assumption of proportional hazards
    • 4.4.1 The log-cumulative hazard plot
    • 4.4.2 Use of Schoenfeld residuals
    • 4.4.3 Tests for non-proportional hazards
    • 4.4.4 Adding a time-dependent variable
  • 4.5 Recommendations
  • 4.6 Further reading
• 5 Parametric regression models
  • 5.1 Models for the hazard function
    • 5.1.1 The exponential distribution
    • 5.1.2 The Weibull distribution
    • 5.1.3 The log-logistic distribution
    • 5.1.4 The lognormal distribution
    • 5.1.5 The Gompertz distribution
    • 5.1.6 The gamma distribution
    • 5.1.7 The inverse Gaussian distribution
    • 5.1.8 Some other distributions
  • 5.2 Assessing the suitability of a parametric model
  • 5.3 Fitting a parametric model to a single sample
    • 5.3.1 Likelihood function for randomly censored data
  • 5.4 Fitting exponential and Weibull models
    • 5.4.1 Fitting the exponential distribution
    • 5.4.2 Fitting the Weibull distribution
    • 5.4.3 Standard error of a percentile of the Weibull distribution
  • 5.5 Comparison of two groups
    • 5.5.1 Exploratory analysis
    • 5.5.2 Fitting the model
  • 5.6 The Weibull proportional hazards model
    • 5.6.1 Fitting the model
    • 5.6.2 Standard error of a percentile in the Weibull model
    • 5.6.3 Log-linear form of the model
    • 5.6.4 Exploratory analysis
  • 5.7 Comparing alternative Weibull proportional hazards models
  • 5.8 The Gompertz proportional hazards model
  • 5.9 Model choice
  • 5.10 Accelerated failure model for two groups
    • 5.10.1 Comparison with the proportional hazards model
    • 5.10.2 The percentile-percentile plot
  • 5.11 The general accelerated failure time model
    • 5.11.1 Log-linear form of the accelerated failure time model
  • 5.12 Parametric accelerated failure time models
    • 5.12.1 The Weibull accelerated failure time model
    • 5.12.2 The log-logistic accelerated failure time model
    • 5.12.3 The lognormal accelerated failure time model
  • 5.13 Fitting and comparing accelerated failure time models
  • 5.14 Explained variation in parametric models
    • 5.14.1 Predictive ability of a parametric model
  • 5.15 The proportional odds model
    • 5.15.1 The log-logistic proportional odds model
  • 5.16 Modelling cure rates
  • 5.17 Effect of covariate adjustment
  • 5.18 Further reading
• 6 Flexible parametric models
  • 6.1 Piecewise exponential model
  • 6.2 Modelling using spline functions
    • 6.2.1 B-splines
    • 6.2.2 Restricted cubic splines
    • 6.2.3 Number and position of the knots
  • 6.3 Flexible models for the hazard function
  • 6.4 Flexible models for the log-cumulative hazard function
  • 6.5 Flexible proportional odds models
  • 6.6 Further reading
• 7 Model checking in parametric models
  • 7.1 Residuals for parametric models
    • 7.1.1 Standardised residuals
    • 7.1.2 Cox-Snell residuals
    • 7.1.3 Martingale residuals
    • 7.1.4 Deviance residuals
    • 7.1.5 Score residuals
  • 7.2 Residuals for particular parametric models
    • 7.2.1 Weibull distribution
    • 7.2.2 Log-logistic distribution
    • 7.2.3 Lognormal distribution
    • 7.2.4 Analysis of residuals
  • 7.3 Comparing observed and fitted survivor functions
  • 7.4 Identification of influential observations
    • 7.4.1 Influence of observations on a parameter estimate
    • 7.4.2 Influence of observations on the set of parameter estimates
  • 7.5 Testing proportional hazards in the Weibull model
  • 7.6 Further reading
• 8 Time-dependent variables
  • 8.1 Types of time-dependent variables
    • 8.1.1 Time-dependent coefficients
  • 8.2 Modelling with time-dependent variables
    • 8.2.1 Fitting models with time-dependent variables
  • 8.3 Coding of time-dependent variables
  • 8.4 Estimation of the survivor function
  • 8.5 Model comparison and validation
    • 8.5.1 Comparison of treatments
    • 8.5.2 Assessing model adequacy
  • 8.6 Some applications of time-dependent variables
    • 8.6.1 Some examples
  • 8.7 Joint modelling of longitudinal and survival data
    • 8.7.1 Longitudinal modelling
    • 8.7.2 A joint model
    • 8.7.3 Some extensions to the joint model
  • 8.8 Further reading
• 9 Interval-censored survival data
  • 9.1 Interval censoring
    • 9.1.1 Current status data
  • 9.2 Estimating the survivor function
    • 9.2.1 Derivation of the estimated survivor function
  • 9.3 Semi-parametric proportional hazards models
    • 9.3.1 Semi-parametric Turnbull model
    • 9.3.2 Piecewise exponential model for interval-censored data
  • 9.4 Parametric models
  • 9.5 Further reading
• 10 Frailty models
  • 10.1 Introduction to frailty
    • 10.1.1 Random effects
    • 10.1.2 Individual frailty
    • 10.1.3 Shared frailty
  • 10.2 Modelling individual frailty
    • 10.2.1 Frailty distributions
    • 10.2.2 Observable survivor and hazard functions
  • 10.3 The gamma frailty distribution
    • 10.3.1 Impact of frailty on an observable hazard function
    • 10.3.2 Impact of frailty on an observable hazard ratio
  • 10.4 Fitting parametric frailty models
    • 10.4.1 Gamma frailty
  • 10.5 Fitting semi-parametric frailty models
    • 10.5.1 Lognormal frailty effects
    • 10.5.2 Gamma frailty effects
  • 10.6 Comparing models with frailty
    • 10.6.1 Testing for the presence of frailty
  • 10.7 The shared frailty model
    • 10.7.1 Fitting the shared frailty model
    • 10.7.2 Comparing shared frailty models
  • 10.8 Some other aspects of frailty modelling
    • 10.8.1 Model checking
    • 10.8.2 Correlated frailty models
    • 10.8.3 Dependence measures
    • 10.8.4 Numerical problems in model fitting
  • 10.9 Further reading
• 11 Non-proportional hazards and institutional comparisons
  • 11.1 Non-proportional hazards
    • 11.1.1 Modelling the probability of an event at a given time
  • 11.2 Stratified proportional hazards models
    • 11.2.1 Non-proportional hazards between treatments
  • 11.3 Restricted mean survival
    • 11.3.1 Use of pseudo-values
  • 11.4 Institutional comparisons
    • 11.4.1 Interval estimate for the RAFR
    • 11.4.2 Use of the Poisson regression model
    • 11.4.3 Random institution effects
  • 11.5 Further reading
• 12 Competing risks
  • 12.1 Introduction to competing risks
  • 12.2 Summarising competing risks data
    • 12.2.1 Kaplan-Meier estimate of survivor function
  • 12.3 Hazard and cumulative incidence functions
    • 12.3.1 Cause-specific hazard function
    • 12.3.2 Cause-specific cumulative incidence function
    • 12.3.3 Some other functions of interest
  • 12.4 Modelling cause-specific hazards
    • 12.4.1 Likelihood functions for competing risks models
    • 12.4.2 Parametric models for cumulative incidence functions
  • 12.5 Modelling cause-specific incidence
    • 12.5.1 The Fine and Gray competing risks model
  • 12.6 Model checking
  • 12.7 Further reading
• 13 Multiple events and event history modelling
  • 13.1 Introduction to counting processes
    • 13.1.1 Modelling the intensity function
    • 13.1.2 Survival data as a counting process
    • 13.1.3 Survival data in the counting process format
    • 13.1.4 Robust estimation of the variance-covariance matrix
  • 13.2 Modelling recurrent event data
    • 13.2.1 The Anderson and Gill model
    • 13.2.2 The Prentice, Williams, and Peterson model
  • 13.3 Multiple events
    • 13.3.1 The Wei, Lin, and Weissfeld model
  • 13.4 Event history analysis
    • 13.4.1 Models for event history analysis
  • 13.5 Further reading
• 14 Dependent censoring
  • 14.1 Identifying dependent censoring
  • 14.2 Sensitivity to dependent censoring
    • 14.2.1 A sensitivity analysis
    • 14.2.2 Impact of dependent censoring
  • 14.3 Modelling with dependent censoring
    • 14.3.1 Cox regression model with dependent censoring
  • 14.4 Further reading
• 15 Sample size requirements for a survival study
  • 15.1 Distinguishing between two treatment groups
  • 15.2 Calculating the required number of deaths
    • 15.2.1 Derivation of the required number of deaths
  • 15.3 Calculating the required number of patients
    • 15.3.1 Derivation of the required number of patients
    • 15.3.2 An approximate procedure
  • 15.4 Further reading
• 16 Bayesian survival analysis
  • 16.1 Bayes’ theorem
  • 16.2 Bayesian inference
  • 16.3 Bayesian models for survival data
    • 16.3.1 Bayesian version of the simple exponential model
  • 16.4 Incorporating prior knowledge
    • 16.4.1 Non-informative prior information
    • 16.4.2 Vague prior information
    • 16.4.3 Substantial prior information
  • 16.5 Summarising posterior information
    • 16.5.1 Point estimates
    • 16.5.2 Interval estimates
    • 16.5.3 Bayesian hypothesis tests
  • 16.6 Evaluating a posterior distribution
    • 16.6.1 Rejection sampling
    • 16.6.2 Sampling from a posterior distribution using MCMC
  • 16.7 Predictive distributions
  • 16.8 Bayesian model comparison
    • 16.8.1 DIC statistic for comparing models
    • 16.8.2 WAIC statistic for comparing models
  • 16.9 Commentary
  • 16.10 Further reading
• 17 Survival analysis with R
  • 17.1 Introduction to R
  • 17.2 Data input and editing
    • 17.2.1 Reading and manipulating data from a file
    • 17.2.2 R packages
  • 17.3 Non-parametric procedures
  • 17.4 The Cox regression model
    • 17.4.1 Variable selection and the lasso
    • 17.4.2 Measures of predictive ability and explained variation
    • 17.4.3 Time-dependent ROC curves
  • 17.5 Model checking in the Cox regression model
    • 17.5.1 Analysis of residuals
    • 17.5.2 Identification of influential observations
    • 17.5.3 Testing the assumption of proportional hazards
  • 17.6 Parametric survival models
  • 17.7 Flexible parametric models
    • 17.7.1 Piecewise exponential model
    • 17.7.2 Models for the hazard function
    • 17.7.3 Models for the log-cumulative hazard function
  • 17.8 Model checking in parametric models
    • 17.8.1 Influential values
    • 17.8.2 Comparing observed and fitted survivor functions
  • 17.9 Time-dependent variables
    • 17.9.1 Time-varying coefficients
    • 17.9.2 Joint modelling of longitudinal and survival data
  • 17.10 Interval-censored data
    • 17.10.1 NPMLE of the survivor function
    • 17.10.2 Semi-parametric models for interval-censored data
    • 17.10.3 Parametric models for interval-censored data
  • 17.11 Frailty modelling
    • 17.11.1 Fitting parametric frailty models with individual frailty
    • 17.11.2 Fitting parametric frailty models with shared frailty
    • 17.11.3 Fitting semi-parametric models with individual lognormal frailty
    • 17.11.4 Fitting semi-parametric models with individual gamma frailty
    • 17.11.5 Fitting semi-parametric models with shared frailty
  • 17.12 Competing risks
    • 17.12.1 Estimating and modelling cause-specific hazard functions
    • 17.12.2 Estimating the cumulative incidence function
    • 17.12.3 The Fine and Gray model for cumulative incidence
  • 17.13 Multiple events and event history modelling
  • 17.14 Dependent censoring
  • 17.15 Bayesian survival analysis
    • 17.15.1 Bayesian parametric modelling
    • 17.15.2 Bayesian semi-parametric modelling
    • 17.15.3 Flexible models for the hazard function
  • 17.16 Further reading
• A Maximum likelihood estimation
  • A.1 Inference about a single unknown parameter
  • A.2 Inference about a vector of unknown parameters
• B Additional data sets
  • B.1 Chronic active hepatitis
  • B.2 Recurrence of bladder cancer
  • B.3 Survival of black ducks
  • B.4 Bone marrow transplantation
  • B.5 Chronic granulomatous disease
• Bibliography
• Index of examples
• Index

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