# Competing Risks: A Practical Perspective

## Pintilie, M.

1ª Edición Agosto 2006

Inglés

Tapa dura

242 pags

497 gr

16 x 24 x 2 cm

### ISBN 9780470870686

### Editorial JOHN WILEY & SONS

Recíbelo en un plazo De 2 a 3 semanas

### Description

The need to understand, interpret and analyse competing risk data is key to many areas of science, particularly medical research. There is a real need for a book that presents an overview of methodology used in the interpretation and analysis of competing risks, with a focus on practical applications to medical problems, and incorporating modern techniques. This book fills that need by presenting the most up-to-date methodology, in a way that can be readily understood, and applied, by the practitioner.

### Reviews

"Competing Risks: A Practical Perspective is a second text in the field
that will help statisticians and researchers understand the complexity of the
competing-risks problem and to complete the required analysis. I am glad to
have it on my shelf. It meets the state goal of the Statistics in Practice series."*
(Technometrics, August 2008)*

"Will help statisticians and researchers understand the complexity of the
competing-risks problem and to complete the analysis. I am glad to have it on
my shelf." *(Technometrics, August 2008)*

"...a concise introduction to the field of competing risks in survival
analysis, especially useful for practitioners and researchers in the biostatistics
field." *(Zentralblatt MATH, 2007)*

### Table of Contents

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.

- 7.1 Introduction.
- 7.2 Sample size calculation when competing risks are not present.
- 7.3 Calculating power in the presence of competing risks.
- 7.3.1 General formulae.
- 7.3.2 Comparing cause-specific hazards.
- 7.3.3 Comparing hazards of the subdistributions.
- 7.3.4 Probability of event when the exponential distribution is not a valid assumption.
- 7.4 Examples.
- 7.4.1 Introduction.
- 7.4.2 Comparing the cause-specific hazard.
- 7.4.3 Comparing the hazard of the subdistribution.
- 7.5 Closing remarks.

8. Other issues in competing risks.

- 8.1 Conditional probability function.
- 8.1.1 Introduction.
- 8.1.2 Nonparametric estimation of the CP function.
- 8.1.3 Variance of the CP function estimator.
- 8.1.4 Testing a covariate.
- 8.1.5 Using R.
- 8.1.6 Using SAS.
- 8.2 Comparing two types of risk in the same population.
- 8.2.1 Theoretical background.
- 8.2.2 Using R.
- 8.2.3 Discussion.
- 8.3 Identifiability and testing independence.
- 8.4 Parametric modelling.
- 8.4.1 Introduction.
- 8.4.2 Modelling the marginal distribution.
- 8.4.3 Modelling the Weibull distribution.

9. Food for thought.

- Problem 1: Estimation of the probability of the event of interest.
- Problem 2: Testing a covariate.
- Problem 3: Comparing the event of interest between two groups when the competing risks are different for each group.
- Problem 4: Information needed for sample size calculations.
- Problem 5: The effect of the size of the incidence of competing risks on the coefficient obtained in the model.
- Problem 6: The KLY test and the non-proportionality of hazards.
- Problem 7: The KLY and Wilcoxon tests.
- A: Theoretical background.
- B: Analysing competing risks data using R and SAS.

References.

Index.

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