
| Preface. Acknowledgements. 1. Introduction. 1.1 Historical notes. 1.2 Defining competing risks. 1.3 Use of the Kaplan–Meier method in the presence of competing risks. 1.4 Testing in the competing risk framework. 1.5 Sample size calculation. 1.6 Examples. 1.6.1 Tamoxifen trial. 1.6.2 Hypoxia study. 1.6.3 Follicular cell lymphoma study. 1.6.4 Bone marrow transplant study. 1.6.5 Hodgkin’s disease study. 2. Survival – basic concepts. 2.1 Introduction. 2.2 Definitions and background formulae. 2.2.1 Introduction. 2.2.2 Basic mathematical formulae. 2.2.3 Common parametric distributions. 2.2.4 Censoring and assumptions. 2.3 Estimation and hypothesis testing. 2.3.1 Estimating the hazard and survivor functions. 2.3.2 Nonparametric testing: log-rank and Wilcoxon tests. 2.3.3 Proportional hazards model. 2.4 Software for survival analysis. 2.5 Closing remarks. 3. Competing risks – definitions. 3.1 Recognizing competing risks. 3.1.1 Practical approaches. 3.1.2 Common endpoints in medical research. 3.2 Two mathematical definitions. 3.2.1 Competing risks as bivariate random variable. 3.2.2 Competing risks as latent failure times. 3.3 Fundamental concepts. 3.3.1 Competing risks as bivariate random variable. 3.3.2 Competing risks as latent failure times. 3.3.3 Discussion of the two approaches. 3.4 Closing remarks. 4. Descriptive methods for competing risks data. 4.1 Product-limit estimator and competing risks. 4.2 Cumulative incidence function. 4.2.1 Heuristic estimation of the CIF. 4.2.2 Nonparametric maximum likelihood estimation of the CIF. 4.2.3 Calculating the CIF estimator. 4.2.4 Variance and confidence interval for the CIF estimator. 4.3 Software and examples. 4.3.1 Using R. 4.3.2 Using SAS. 4.4 Closing remarks. 5. Testing a covariate. 5.1 Introduction. 5.2 Testing a covariate. 5.2.1 Gray’s method. 5.2.2 Pepe and Mori’s method. 5.3 Software and examples. 5.3.1 Using R. 5.3.2 Using SAS. 5.4 Closing remarks. 6. Modelling in the presence of competing risks. 6.1 Introduction. 6.2 Modelling the hazard of the cumulative incidence function. 6.2.1 Theoretical details. 6.2.2 Model-based estimation of the CIF. 6.2.3 Using R. 6.3 Cox model and competing risks. 6.4 Checking the model assumptions. 6.4.1 Proportionality of the cause-specific hazards. 6.4.2 Proportionality of the hazards of the CIF. 6.4.3 Linearity assumption. 6.5 Closing remarks. 7. Calculating the power in the presence of competing risks. 8. Other issues in competing risks. 9. Food for thought. A: Theoretical background. B: Analysing competing risks data using R and SAS. References. Index. |
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